ASTM - STP 234 - Symposium On Particle Size Measurement

SYMPOSIUM ON
P A R T I C L E SIZE M E A S U R E M E N T
Presented at the
S I X T Y - F I R S T ANNUAL MEETING
AMERICAN SOCIETY FOR TESTING MATERIALS

Boston, Mass., June 26 and 27, 1958
@
Reg. U.S. Pat. Off.
.~IS T M Special Technical Publication No. 234
Price $6.25; to Members $5.oo
Published by the
1916 Race St., Philadelphia 3, Pa.
9 BY A M E R I C A N SOCIETY FOR TESTING MATERIALS 1959
Library of Congress Catalog Card Number: 69-14900
Printed in Baltimore~ Md
August, 1959
FOREWORD
The papers and discussions in this 1958 Symposium on Particle Size

Measurement were presented at the Sixty-second Annual Meeting of the
American Society for Testing Materials held in Boston, Mass., on June 26
and 27, 1958.
This Symposium was sponsored by Subcommittee 11 on Subsieve Testing,
of ASTM Committee E-1 on Methods of Testing. It was organized by
Lincoln T. Work, Consulting Engineer, chairman of Subcommittee 11, who
also served as chairman for the third and final session of the Symposium.
The first session was presided over by A. E. Reed, Vice President, The
W. S. Tyler Co., Cleveland, Ohio, and the chairman of the second session
was A. E. Jacobsen, Research Chemist, National Lead Co., Titanium Divi-
sion, South Amboy, N. J.
In order to make this publication more complete, two additional papers
on particle size measurement, published by the ASTM, have been included
although they were not presented as part of the Symposium. The paper on
"Light Scattering Instrumentation for Particle Size Distribution Measure-
ment" by C. T. O'Konski, M. D. Bitron and W. I. Higuchi has been
reprinted from the Symposium on Instrumentation, ASTM Special Tech-
nical Publication No. 250. The paper on "Methods of Particle Size Analy-
sis" by R. P. Loveland is reprinted from the Symposium on Light Micro-
scopy, first published in 1952.
NoTE.--The Society is not responsible, as a body, for the statements
and opinions advanced in this publication.
CONTENTS
PAGE
I n t r o d u c t i o n - - L i n c o l n T. Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
T h e Mechanics of Fine Sieving--K. T. W h i t b y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Application of Electroformed Precision Micromesh Sieves to the Determination of
Particle Size D i s t r i b u t i o n - - H . W. Daeschner, E. E. Seibert, and E. D. Peters . . . . 26
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
M e a s u r e m e n t of Physical Properties of Cracking C a t a l y s t s - - A Review of the
Work of A P I Committee on Analytical Research--L. M i t t e l m a n . . . . . . . . . . . . . 51
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Methods of Particle Size A n a l y s i s - - R . P. Loveland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Recent Developments in the H y d r o m e t e r M e t h o d as Applied to Soils--E. E. B a u e r . . . 89
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Sedimentation Procedures for Determining Particle Size D i s t r i b u t i o n - - W . F. Sullivan
and A. E. Jacobsen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Centrifuge Sedimentation Size Analysis of Samples of Airborne D u s t s Collected in
M e m b r a n e F i t t e r s - - K . T. W h i t b y , A. B. Algren, and J. C. Annis . . . . . . . . . . . . 117
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A Liquid Sedimentation M e t h o d for Particle Size D i s t r i b u t i o n s - -
L. M. Cartwright and R. Q. Gregg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Determination of Particle Size Distribution by Examining Gravitational and Cen-
trifugal Sedimentation According to tile Pipet M e t h o d and With D i v e r s - -
S. Berg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
A Photoelectric Sedimentation M e t h o d for Particle Size Determination in the Sub-
sieve R a n g e - - H . R. Harner and J. R. Musgrave . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Light Scattering I n s t r u m e n t a t i o n for Particle Size Distribution M e a s u r e m e n t - -
C. T. O'Konski, M. D. Bitron, and W. I. Higuchi . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Turbidimetric Particle Size Distribution Theory: Application to Refractory Metal
and Oxide Powders--A. I. Michaels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Electronic Size Analysis of Subsieve Particles by Flowing T h r o u g h a Small Liquid
R e s i s t o r - - R . H. Berg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
T h e Determination of Particle Size by Adsorption M e t h o d s - - R . J. Fries . . . . . . . . . . 259
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
A Study of the Blaine Fineness Tester and a Determination of Surface Area from Air
Permeability D a t a - - S . S. Ober and K. J. Frederick . . . . . . . . . . . . . . . . . . . . . . . . 279
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
A Discussion of the A S T M R e c o m m e n d e d Practice For Reporting Particle Size Char-
acteristics of Pigments (D 1366)--J. H. Calbeck . . . . . . . . . . . . . . . . . . . . . . . . . . 288
T h e Stanford Research I n s t i t u t e Particle B a n k - - R . D. Cadle and W. T h u m a n . . . . . . 296
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
List of A S T M Standards for Particle Size M e a s u r e m e n t . . . . . . . . . . . . . . . . . . . . . . . . 302
STP23 4-EB/Aug. 1959
S Y M P O S I U M ON P A R T I C L E SIZE M E A S U R E M E N T
INTRODUCTION
BY LINCOLN T. WORK1
I n 1941, the American Society for himself frustrated with regard to the
Testing Materials published a sympo- choice of method and to the details in
sium on particle size measurement. I t using a method. The A S T M has devel-
comprised a series of papers presented oped a substantial amount of literature
at the Washington Spring Meeting of in its standards which m a y be helpful on
that year. The booklet has been in much that score. A list of these standards is
demand even to this date, having been included.
reprinted only a short while ago. A simi- Two aspects of the situation in particle
lar symposium was presented in Boston size measurement call for special note.
during 1958; the papers of that meeting One of these pertains to sieves. There is
are the basis for the present publication. an A S T M specification defining sieve
The field has broadened since 1941 both cloth and its tolerances (E 11 - 58 T). 4
with respect to methods available and This is tentative because certain objec-
as to the needs to meet new applications. tion was raised concerning wire diameters
I t has not been possible to cover this and tolerances when it was offered through
field in all its aspects; but the coverage the American Standards Association
is representative of the current trends. to the International Standards Organiza-
To make it more complete, papers by tion (ISO) for development of an inter-
Loveland 2 and O'KonskP et at have national standard. The series of apertures
been included. These are current publi- in this specification varies by a root of
cations of A S T M having their origin two, in accordance with es[ablished prac-
elsewhere than this symposium. The dis- tice in fields where sieves are employed.
cussions of the papers has been included The ISO is also considering a root-of-ten
to insure the full value of the treatment series. I t does not appear that this series
given. has more merit than the established one.
Since the monograph is largely devoted By far the large majority of testing
to research papers, the reader m a y find sieves throughout the world are based on
1 Consulting engineer, New York, N. Y.; chair- the root-of-two series, and it would be
man of the symposium committee. costly to change by any sudden step.
R. P. Loveland, "Methods of Particle Size Reasons for change are not adequately
Analysis," Symposium on Light Microscopy, Am.
Soe. Testing Mats., p. 94 (1952). (Issued as sep- convincing. Hence, though this is a ten-
arate publication A S T M S T P No. 143.) tative specification, it is currently the
C. T. O'Konski, M. D. Bitron, and W. I. best effort based on sound experience
tIiguehi, "Light Scattering Instrumentation for
Particle Size Distribution Measurements, "Sym- and should soon become standard. I n
posium on Instrumentation in Atmospheric Anal-
ysis, Am. Soc. Testing Mats., p. 2 (1959). (Issued 4 1958 Book of ASTM Standards, Parts 3, 4,
as separate publication A S T M S T P Mo. 250.) 5, 7, 8, 9, 10.
Copyright* 1959 by ASTM International www.astm.org

2 SYMPOSIUM ON PARTICLE SIZE MEASUREMENT
connection with sieves, it might be particle. The Coulter counter reported

pointed out that there is room for sieves here is indicative of a strong trend to-
of smaller aperture than specified in ward devices of this type still awaiting
E 1 1 - 58 T. Electrolytically deposited development.
sheet with controlled apertures is noted This symposium is the work of several
in this symposium. Wire cloth manufac- people who know this field. Acknowledg-
turers are now able to make apertures of ment is made to the authors and to those
25.2 ~ and hope to reach sizes of 18 ~. who contributed to the discussion. Their
This is promising, but it may present names appear in the script. Acknowledge-
problems in sieving technique in these ment is made to the members of the
finer sizes, not to mention those of fragil- editorial committee of ASTM Committee
ity of the screen plate or cloth. Such di- E-1 on Methods of Testing, Subcommit-
rect separations are to be desired, and tee 11 on Sub-Sieve Testing, who were
the achievements toward that end are selected to preside at sessions and to re-
commendable and useful. A second as- view the papers. They are: R. L. Blaine,
pect for attention is the use of electronic L. E. Gregg, A. E. Jacobsen, R. P.
means for rapid registry and sorting of Loveland, A. E. Reed, and L. T. Work,
measurements of some criterion on each chairman.
STP23 4-E
T H E M E C H A N I C S OF F I N E S I E V I N G
BY KENNETH T. WHITBY1
SYNOPSIS
It has been found for the nonsteady state conditions existing during test
sieving on such machines as the standard Rotap sifter that the mechanism of
sieving can be divided into two distinctly different regions with a transition
region between.
Region 1 exists where there are many particles much less than the mesh size
still on the sieve. An equation relating major sieving variables such as mesh
size, particle size distribution, sieve loading, etc., was developed from experi-
ments using four typical materials.
As particles much less than the mesh size are removed the mechanism
changes and region 2 sieving begins. In region 2 all particles much less than the
mesh size have been eliminated from the residue, and the particles remaining
that can pass the sieve are very near mesh size. The cumulative percentage
passing the sieve has been found to follow the log-normal law in region 2. From
this fact an equation relating the major sieving variables in region 2 has been
derived analytically and proven experimentally.
Using the laws developed for regions 1 and 2, the effects of material, sieve
load, sieve motion, relative humidity and sieve material were investigated to
a limited extent. These laws were also extended analytically to steady state
sieving.
It is believed that the proposed sieving laws represent the best fit over the
broadest range of conditions of any sieving laws that have been proposed to
date.
I n spite of the importance of sieving countered in most industrial processes.

as a means of size analysis and as an Here particulate material is fed contin-
industrial separation process, there have uously at a constant rate into a sieving
been few attempts to elucidate the laws machine and the amount and quality of
that govern the sieving process. This the material passing and residue is
study represents an a t t e m p t to derive studied.
and prove the physical laws which govern The second approach is to study the
the sieving of fine particulates through nonsteady conditions which result when
conventional sieves with conventional a given quantity of the particulate is
equipment. placed on a screen and sieved in a device
I n making a study of sieving, there are such as the Tyler Rotap sieve shaker.
two possible approaches. The first corre- Here the amount and quality of the pass-
sponds to the steady state condition ening material and residue must be studied
as functions of time.
1 Assistant Professor of Mechanical Engineer-
ing, University of Minnesota, Minneapolis, The nonsteady state approach was
Minn. chosen for this study because the equip-

merit is far simpler and the continuously determine the correct form of the prob-
changing conditions on the sieve provide ability.
an infinite graduation of conditions that Preliminary experiments using U. S.
would be very difficult to duplicate in a standard sieves and a standard Tyler
steady state experiment. Rotap sieve shaker showed that the
The principal piece of data available percentage passings v e r s u s sieving time
in the nonsteady state experiment is the curve could be divided into two regions
amount passing the sieve as a function with a transition between. Region 1
of time. Based on probability considera- exists at the beginning of sieving when
9O
/
8O
7O /
f
6O ~ f
~o
o~0~ 5O /
t
q,
4O /s"
/
g~
og
3O
/
a_a-
2O
/
10
/
5
100 I
flegiOn 2 . ~ . . . . ~
/
5O
0-o
/
g o~
~v
5
i I I i I ii I I I I I I III I i i i I i ii
2 10 I00 I000
Time, sec
FIG. 1 . - - T y p i c a l Per Cent Passing - Ti me Curve.
tions, Fagerholt (1)5 derived a mathe- there are many particles much less than
matical formula for the weight passing-- the mesh size still on the sieve. Region 2
time curve. However the derivation was exists when the residue on the sieve con-
found to fit the data over only a narrow sists entirely of near-mesh or larger
range of conditions. In planning this particles.
study it was believed that Fagerholt was I t was further discovered that the
correct insofar as he recognized the im- rate at which material passed the sieve
portance of probability, but that more in region 1 was very nearly constant and
experimental work was necessary to obeyed the following simple relationship:
Per cent passing = a# ......... (1)
2 The boldface numbers in parentheses refer
to the list of references appended to this paper. where:
WtIITBY ON MECHANICS OF FINE SIEVING 5
t = sieving time, only two dimensions, a will be a function

b = a constant very nearly equal to 1, of five dimensionless groups, or:
and
a = a sieving rate constant.
a = f SAo ' d ' A ' d ' . .... (2)
This preliminary work also revealed
that region 2 could be plotted with high For the usual sieve, A o / A is a constant.
accuracy as a straight line on log prob- A / S 2 and T / d are sa large as to make it
ability paper as shown in Fig. 1. improbable that t~@(would have any
The following discussion summarizes appreciable effec(sl;~:Detailed studies
the findings of the detailed studies (2) described by the author (2) indicated that
that were made to discover the mecha- T / d was significant under certain condi-
nism underlying these observations and tions however.
to derive the relationships between the Thus Eq 2 reduces to:
important sieve, material and operational
variables.
REGrON 1 Experimental:
Theory: I n order to discover the functional
Since b in Eq 1 was found to be nearly relationship between the variables in
equal to 1, the functional relationship Eq 3, a series of carefully designed ex-
between a and such sieving variables as periments and analysis of variance was
material, mesh size, etc., a is the sub- used to separate the effect of each varia-
ject of interest. Considerable data can ble.
be learned from a dimensional analysis Sieving was done on a standard Rotap
relating a to the sieving variable. sifter with 8-in. full height U.S. standard
If the units of a are considered, it is sieves. A single sieve without cleaners
seen that, for the usual sieving machine was clamped so that there was ~ - i n .
such as the Rotap, a has the dimensions play between the lugs and the cover
of the fraction passing the sieve per unit plate.
time. However, if the sieving is per- After the material was weighed out
formed by striking the sieve by hand, it was carefully poured onto the center
then a would have the units of the frac- of the sieve. Any material passing the
tion passing per blow. Thus a does not sieve was emptied from the pan and
depend on time and only the dimensions poured back onto the top of the pile
of length and mass need be considered. The sieve was then carefully placed in
Further consideration suggests the fol- the shaker with a minimum of jarring.
lowing variables as possibly being im- The material passing was then deter-
portant: mined for a geometric progression of time
intervals until sufficient points to deter-
W = total load on sieve . . . . . . . . M, mine a straight line were obtained.
p = particle density . . . . . . . . . . M / L 3,
Most of the particle sizes and mesh
S = mesh opening . . . . . . . . . . . L,
sizes were measured as accurately as
A0 = sieve open area . . . . . . . . . . L 2,
A = sieve area . . . . . . . . . . . . . . . L 2, possible by microprojection, but some
d = particle size . . . . . . . . . . . . . L, and size analyses on the finer materials were
T = bed depth on sieve . . . . . . . L. measured by centrifuge sedimentation
(3). Relative humidity was measured and
Since there are seven variables and controlled for all but the initial work.
Detailed descriptions of apparatus and quartz is irregular with smooth surfaces,

procedures may be found in reference (1). and the hard wheat middlings are ir-
The four typical materials selected are regular with rough surfaces.
Fro. 2.--Photomicrographs of Particle Types Used in This Study.

A, glass beads; B, St. Peter sand; C, flint; and D, wheat middlings.
shown in Fig. 2. Glass beads are spherical Typical data for flour are shown in Fig.
with smooth surfaces, St. Peter sand is 3. Values of a from such plots were
spherical with rough surfaces, crushed tested in an equation of the form:
WHITBY ON MECHANICS OF F I N E SIEVING 7
oSAo S . . . . . . . . . . . (4) sieve opening, the differences were not

a = C1 - - -
W d significant. Therefore, the nominal sieve
openings were used in all subsequent
From this series of experiments it was
calculations.
concluded that:
1. a is not linear in S/d; a was found
Study of the data suggested that Eq
to increase more rapidly than S, suggest-
4 should be revised to the following form:
ing that S / d should be raised to a power.
2. There was no significant humidity -~-A~ S )~
~, = c~ ~ ........ (s)
effect for inorganic materials within the
range from 15 to 60 per cent. There
where ks dm is a linear function of the
100
a 1160 Beeds-200 g
8 o Original No.I
9 47 percent 120/170
6 31 percent 80/120
22 percent 60/80 /
,o
L)
'I I I I I I I I I I
1
0.8
0.6
I O'4
200o~
I 016
S
' 0/8 '
1; ' I , ' I1• 0

Time, t,sec
FIG. 4.--Dimenslonless Region 1 P a r a m e t e r s
FIO. 3 . 1 T y p i c a l Region 1 D a t a Used to De- for Glass Beads.
termine a, 200 g of H a r d W h e a t Flour on a Stand-
ard R o t a p Sifter; Relative H u m i d i t y = 57 per Note similarity of curve for the No. 1 beads
cent. to the particle size distribution in Fig. 5.
were indications that relative humidities geometric mass mean of the particle size
below 15 per cent could result in electro- distribution, and n is some function of
static effects, but these were not studied the size distribution.
further due to the difficulties of obtaining Equation 5 was tested by putting it
these low humidities. in the form:
The hard wheat and cake flour did
aW = Cl (6)
show humidity effects. These are dis- AopS .........
cussed later.
3. There is a significant load effect. aW
If the group A ~ p S is plotted against
This is discussed later.
4. Though there were small differences S
between the nominal and the measured k~ dm on log-log paper, C1 is the intercept
8 SYMPOSIUI~{ ON PARTICLE SIZE MEASUREMENT
99.8 W h e n such plots were m a d e for the

d a t a of series 1, it was observed t h a t the
99 LAtoIg4OgW,4-B: 2.224-1.927 =0,407 resulting lines h a d a v a r i e t y of shapes.
c~ However it was noted t h a t those m a t e -
'g 95
rials having a narrow size distribution
90
had steeper slope ( t h a t is, higher n value).
=a S0 A few runs on very narrow size distribu-
i-
70 tion resulted in a rapid increase in slope.
~, 60 Also it was observed t h a t for the original
50
40 No. 1 beads (Fig. 4) t h a t the shape of
30 the line was similar to the particle size
2O distribution when p l o t t e d on log-prob-
10 I ability p a p e r (Fig. 5). E x a m i n a t i o n of
I the d a t a for the other materials con-
5
, ,i B , , , IA ,
firmed this observation.
1.7 1.8 1,9 2.0 2,1 2.2 2.3 2.4
Log of Particle Size F o r the shape of the curve on a plot of
aW S
FIG. &--Graphical Determination of crgp of versus ~ on log-log p a p e r to be
the Particle Size Distribution at a Particular Par- AopS ~ ,,~
ticle Size. similar to t h a t of the cumulative size
Size distribution by sieving on No. 1 glass beads. distribution on a log p r o b a b i l i t y plot
means t h a t :
S n = f (log , g p ) . . . . . . . . . . . (7)
of the line at - - - - 1 and n is the slope
h
- - - .(8)
of the line. log o'gp
o
:F&roduc,&O ~
A 0 O0
4
n o 0//" n-- -0.4364-0.406 .1
LOg ocJp
o./
oe e-/~ a 9
0 ~ ~0~Q
09 0
l & O ~ li
AEI 1O@ ~A I I P I I
0
0 2 4 6 8 10 12 14 16 18
[
Log a-gp
FIO. &--Regression of n on 1/log (rgp for the Different Materials.
WHITBY ON M E C H A N I C S O F F I N E SIEVING 9
where ~gp is the geometric standard by combining narrow size range fractions
deviation at a particular particle size on which had been carefully sized by micro-
the size distribution curve and h is a scope.
constant. The final equation then be- Log ~gp was obtained graphically from
TABLE L--HIGH-LOAD SIEVING CONSTANTS.
Material Weight Relative CI Particle Shape

Humidity Factor, ks
FLINT
Medium ............................. 500 0.51

V e r y fine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 0.62
V e r y fine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 0.80
V e r y fine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000 0.38
1/4 m e d i u m ; 1/4 coarse . . . . . . . . . . . . . . . . . 500 0.80
1/~ v e r y fine; 1/~ m e d i u m ; 1/~ coarse; 1/~
v e r y coarse . . . . . . . . . . . . . . . . . . . . . . . . 500 3.00 1
ST, PETER SAND
Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 2.45 1

Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000 0.65 1
Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2000 0.18 1
45/60 ............................... 500 1.07 1
~4 60/80; 1~445/60 . . . . . . . . . . . . . . . . . . . 500 1.57 1
60/80; 1~i 45/60; ~i 35/45 . . . . . . . . . . 500 2.07 1
Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 2.48 1.14
45/60 ............................... 500 2.60 1.14
1/4 6 0 / 8 0 ; ) i 4 5 / 6 0 . . . . . . . . . . . . . . . . . . . 500 2.45 1.14
~ 60/80; ~ 45/60; ~t 35/45 . . . . . . . . . . 500 2.60 1.14
BEADS
Original No. 1 . . . . . . . . . . . . . . . . . . . . . . . . 500 2.64

Original No. 1 . . . . . . . . . . . . . . . . . . . . . . . . 1000 1.95
Original No. 1 . . . . . . . . . . . . . . . . . . . . . . . . 2000 1.40
47 p e r c e n t 120/170; 31 p e r c e n t 8 0 / 1 2 0 ;
22 p e r c e n t 6 0 / 8 0 . . . . . . . . . . . . . . . . . . . 450 1.64 1
1160 b e a d s . . . . . . . . . . . . . . . . . . . . . . . . . . 200 5.4 1
H a r d w h e a t i%ur . . . . . . . . . . . . . . . . . . . . . 200 16 0.67 1
H a r d w h e a t flour . . . . . . . . . . . . . . . . . . . . . 200 34 1.44 1
H a r d w h e a t flour . . . . . . . . . . . . . . . . . . . . . 200 57 2.05 1
Original semolina . . . . . . . . . . . . . . . . . . . . . 200 Avg 1.22 1
60/80 hard wheat middlings ........... 200 38 0.60 1
H a r d w h e a t flour . . . . . . . . . . . . . . . . . . . . . . 200 34 1.84 1.21
Hard wheat middlings 60/80 ............ 200 38 1.83 1.21
Original s e m o l i n a . . . . . . . . . . . . . . . . . . . . . . 200 Avg 1.77 1.21
comes: plots similar to Fig. 5 and n from plots

simitar to Fig. 4.
To determine the value of the constant
AopS log ~ g p . . . .
h in Eq 9, and also to test the hypothesis
Equation 10 was tested by additional h
that n - log crgp' the regression of n on
determinations of a on distributions hav-
ing a range of log crgp. Since it was neces- 1
log ~gp was obtained. Results are plotted
sary to obtain very accurate size analyses,
tile various distributions were obtained in Fig. 6. A statistical correlation coeffi-
10 SYMPOSIUM: ON I)ARTICLE SIZE MEASUREMENT
cient of 0.932 was obtained which is Characteristics of Region 1 (High Load)

surprisingly good considering the diffi- Sieving:
culties inherent in the graphical deter- The rate at which material passes
mination of n and log agp. This includes through the sieve can be obtained explic-
data on four quite different materials
- - in~rgp
having a wide range of size distributions, itly from Eq 11. The group k, dm
sieved through sieves from 30 to 270 is a probability. It is interesting to note
mesh. that the weight rate passing the sieve is
G
\
x Original Semolina x ,~
0.1
i I I I i i i i I t i = i i ~ | I i i I . . . . .
100 IOOO too Io0o

S i e v e Load, W, g Volume of Material on Sieve, /, cu c m
FIG. 7.--Region 1 Sieving Constant as a Function of Sieve Load,
The intercept in the regression equa- equal to this probability times a group
tion C1 p N S ~ which is the weight of a layer
of particles about 1 mesh opening thick
1
n = --0.4364 + 0.406 l o Tagp
-" (10) on the top of the sieve, since C1 is of the
order of magnitude of 1. This indicates
was found to be just significantly differ- that the particle interaction which in-
ent from 0.1/h is approximately equal fluences the sieving rate extends only
to the conversion factor between log to about 1 mesh opening above the sieve.
the base 10 and log to the base e. Mesh Size and Particle Size:
The other two constants in Eq 9 are
tabulated in Table I along with the The relationship between the two
particle size composition and sieve toad chief sieving variables, mesh opening,
and particle size is apparent from Eq 11.
for each run.
If in Eq 9, A0 is replaced by N S 3 For a given cgp and ratio of mesh opening
where N is the total number of mesh to mean size, the sieving rate will be
inversely proportional to the mean par-
openings in the sieve, and h/log agp is
ticle size. For narrow distributions, the
replaced by 1/ln agp, then we obtain:
rate will increase very rapidly with in-
( S ~'/'~ S
aW = C,oNS~ \ k - - ~ l .... (12) creasing k, d~"
WHITBY ON MECHANICS OF FINE SIEVING 11
Effect of Material and Load: where Vc is a critical volume and C1, the
From Table I it will be noted that C1 constant corresponding to the intersec-
increases geometrically with load. Equa- tion of the toad curves in Fig. 7 for the
tion 3 indicates that a should be a func- materials of the same shape. Vc appears
tion of the dimensionless ratio T/d, which to be constant within a factor of about 2
is a function of load. This suggests that for these experiments.
the load effect could be accounted for I t may also be noted that the ratio
by a dimensionless load function to a V , / V could be replaced by a ratio of bed
power. This hypothesis may be tested thickness T,/T. For the sieves used, a
by plotting C1 against load as in Fig. 7 value of V~ = 250 cu cm corresponds to a
since for given conditions of particle size critical bed depth of about 1.4 cm de-
etc., C1 would have to contain the load pending on the bulk density.
function. The vertical displacement of the lines
From Fig. 7 it will be noted that the on the C1 versus V plot may be taken as
glass beads and flint form a pair of ap- an index of the relative sieving rates of
proximately straight lines and the the four materials. The rounded particles,
semolina and St. Peter sand another beads and St. Peter sand will have a
pair. high load sieving rate roughly four times
If these four materials are studied that of the irregular materials. But the
(Fig. 2) it is discovered that the beads rough-surfaced materials St. Peter sand
have in common with the St. Peter sand and semolina drop off in sieving rate,
a rounded shape and the flint and semo- with increasing load at a much higher
lina have in common a very irregular rate than do the smooth surfaced mate-
shape, but the flint and beads have rials.
smooth glassy surfaces while the St. Peter
Effect of Sieve Material:
sand and semolina both have very rough
surfaces. Only one specimen each of a silk and
These two effects can be summarized nylon bolting cloth was tested besides
in an equation of the form the U. S. Standard sieves. In no case was
the silk or nylon found to be significantly
C = s h a p e ( l o a d ) -Burr . . . . . . ~h . . . . . . (12)
different from the wire after the effects of
If it is assumed that Fig. 7 represents mesh opening and open area were ac-
a fundamental separation of the shape counted for. However, it will be shown
and surface effects, the Eqs 11 and 12 later that there are highly significant
may be combined to yield a new equation effects in region 2 sieving.
that accounts for the effects of sieve load
Effect of Sieve Motion:
and particle shape.
Only a few experiments using a Gen-
Let eral Mill Equipment gyratory sifter were
R, = a surface roughness factor, made. I t was found that blinding was so
~, = a shape factor, and rapid for most of the materials that a
20
V ~ _ ,
satisfactory straight line could not be
p obtained for the rather long starting and
Then stopping time.
Ca = ~,VRs . . . . . . . . . . . (13) The limited data indicated that C1
and for the pure gyratory sifter was about
one half the value for the Rotap sifter.
ff,V = Cle ~- - Rs NS" S Since it was found that the mechanism
\L~.,/ of sieving for region 2 was the same for
12 S Y M P O S I U M ON P A R T I C L E Size ~V~lgASUREMENT
both the standard Rotap sifter and the about 15 sec but that in Fig. 8 (a) over
gyratory sifter there is no reason to 16 min were required even though load,
doubt that Eq 11 applies to the gyratory sieve, and particle size distribution were
sifter. Equation 11 offers a convenient the same.
method for evaluating sieve motion
since the effects of particle size distribu- REGION 2
tion and sieve mesh opening can be ac- The discovery that region 2 sieving
counted for. followed a log normal law proved to be
70 ._=m -~
e
80
70
I[III 60 ~ o
5 0 o - =',
60 ~ , ~ 4 0 ~e
30 3~
40 ~ o~ O
20 m ~
30 . =
zo ~ -O
~8 J 80 .a ~,
10 a_~ 6 0 ~'--
- - 40~r
5
2 2 0 ~ .2
9O O-
70
5O
30 .~
20 ~--
o D
~CO 50
1ogo~O_l ,o,
6 ~- 3O ~
4
2O
0
0.063 0.125025 0.5 1 2 4 8 16 32
Time, L min
5O
40 (a) T i m e - w e i g h t c u r v e s and size d i s t r i b u t i o n s
of c a k e flour, 25 g. S t a n d a r d R o t a p sifter.
~o ~- (b) T i m e - w e i g h t c u r v e s a n d size d i s t r i b u t i o n
20 of p a r t i c l e s p a s s i n g . 1160 g l a s s b e a d s , 25 g l o a d .
10 S t a n d a r d R o t a p sifter, 2 7 0 W .
0.060130.250.5 1 2 4 8 16 32 92
Time,f, min
F I e . 8 . - - P e r c e n t a g e P a s s i n g a n d P a r t i c l e Size C u r v e s f o r T w o M a t e r i a l s of E x t r e m e C h a r a c t e r -
istics.
G l a s s b e a d s r e p r e s e n t a n e a s y m a t e r i a l a n d c a k e flour a difficult m a t e r i a l to sieve o n a fine
sieve.
Particle Size of Particles Passing During the key to the understanding of the
Region 1: mechanism in this region.
Figure 8 illustrates very well that Figure 9 illustrates some typical
during region 1 only particles much less curves. For the hard wheat flour and the
than the mesh size pass through the sieve. 220 flint, both regions 1 and 2 exist, but
The duration of region 1 will depend on for the beads and the --170 flint, the
the material being sieved and on a which size range is so narrow that only region
can be calculated from Eq 11. Figures 8 2 exists. Note that for the --170 flint a
(a) and (b) represent extremes. Note in nearly straight line exists from 10 sec to
Fig. 8 (b) that region 2 was entered in 90 min, during which interval the per
W I I I T B u ON MECHANICS O]? F I N E SIEVING 13
cent passing has gone from 5 to 70 per the total passing through will be the
cent. This is a striking illustration of the sum of these random passages of indi-
applicability of the log-normal plot. vidual particles.
If each particle makes only a small
The Log-Normal Distribution:
contribution to the amount passing,
A brief discussion of the log-normal Cramer (4) has shown that the sum of
law is given below. Further information such contributions is
can be obtained from Cramer (4), Kottler
~ dN
(5-7) and Herdan (8).
Figure 8 shows that in region 2 all
particles much less than the mesh size
O~+ O~ + 03 + . . . . G =
Under the general regularity condi-

f; g(N) " " ( 1 6 )
have passed through the sieve. Of those tions of the central limit theorem it
Typical Weight-rime Data

Standard ROrAP Sifter
25 g on 200 W
99
3 61assBeadsl160 Passing170 W _~ ~ ~ -
95
90
70
g_
c 50
3
3o
lO
5
10 30 100 300 1000 3000
Time, sec (Log Scale)
FIG. 9.--Typical Per Cent Passing - T i m e Curves for Different Materials.
that remain, attention may be focused dN

on those that are capable of passing the follows that the quantity g ~ is nor-
sieve but are so near-mesh size that the mally distributed. In this case, since
probability of passage is small. At a given g ( N ) = N , it follows that log t is nor-
instant of time in region 2, there will be mally distributed and t has the frequency
a definite number of particles that can function.
pass the sieve. I t may be assumed that
the number that can pass in a given time N0 [ (logt-
f ( N ) - cgt t X , / G exp ~r .j. . (17)
interval will be proportional to the num-
ber on the sieve at that instant:
or
d2V = kNdt . . . . . . . . . . . . (15)
dN IVo
where N equals the number on the sieve. d (log t) - log c g t x / ~
A single particle on the sieve will have
a certain probability that it will pass exp I . (log t -- log i)~1
j (18)
through in any given time interval, and
14 S~m, OSltr~ ON P A R T I C L E S I Z E 1ViEASUREMENT
Equations 17 and 18 are expressions ary importance and that chance is the
of the so-called log-normM distribution. determining factor for near-mesh size
In the above derivation two important particles.
assumptions were made. The first, given
by Eq 15 says that the number passing Experimental:
the sieve is proportional to the number Sieving was done with single sieves on
that can pass the sieve at any instant. a standard Tyler Rotap sieve shaker
dN and on the General Mill Equipment
The ratio d (log t~--~may be looked upon gyratory sifter. Time-weight through
as the probability of change and will be curves were determined by sieving in
a constant for region 2. Furthermore this TABLE II.
ratio can be related to the log geometric
standard deviation agp, of the log prob- Per Cent Zr
Time, sec Passing Z Z -- Z'
ability plot of the time-weight curve and
to the log geometric standard deviation, 25 g 8 0 / 1 2 0 F L I ~ T ON 9XX SILK STAND&RD
]~OTA~ SIFTER.
~rgp, of the particle size distribution
originally placed on the sieve. 7.5 ...... 3.96 --1.754 --1.7401 0.014
15 . . . . . . . . 6.20 --1.534 I-1.542-0.009
The number of particles passing 30 . . . . . . . . 8.96 --1.344/-1.346-0.002
through the sieve is given by Eq 18. The 60 . . . . . . . . 12.64 --1.144/-1.147-0.003
number on the sieve having a particle 120 . . . . . . . . 17.12 --0.950 --0.951 --0.001
240 ........ 22.52 --0.755 --0.753 0.002
size near the mesh opening size can be 480 ........ 28.72 -- 0. 5 6 2 -- 0. 557 0. 005
given by:
rz'log t = 0.99906
No
N = f(d) = 25 g - - 1 7 0 W 1160 BEADS ON 2 7 0 W ST&NDARD
log a g p % / 2 ~ ROTAP SIFTEt
I. (log d - - log d ) 2 1 7.5 ..... 50.36

exp 2 log- ( - a g ~ j (19) 15 . . . . . . . 56.20
30 . . . . . . . 58.52
where d is the particle size and (rgp is the 60 . . . . . . . 63.76 0.352 0.00O
220 . . . . . . . 66.88 0.437 0.431 0.006
geometric standard deviation at the sieve 240 ....... 69.04 0.507 0.51C --0.003
mesh size. 480 ....... 71.84 0. 5 7 8 O. 582 - - 0 . 0 1 1
If agp and crgt are expressed in terms 960 ....... 75.12 0. 678 o. 644 0. 034
1920 . . . . . . . 77.32 0.750 0.74f 0. 0 0 4
of the same normal deviate, then the 5520 ....... 80.60 0 . 863 0 . 867 0. 004
exponentials in Eqs 18 and 19 are equal.
rz-log t = 0.99933
Therefore:
dN log (rgp
geometric progression times. By careful
P2 - .. (20) handling losses were kept below 0.05 per
N d (log t) log agt
cent for coarse materials and below 0.2
This important relationship relates the per cent for fine.
probability of change to (rgp of the par- In order to study the blinding of the
ticle size distribution and to the (rgt of sieves, a particular cleaning procedure
the time--per cent passing curve. was adopted. After the residue was
The second important assumption poured off the sieve was jarred on the rim
made in deriving Eq 20 is that the pas- several times with the palm of the hand
sage of particles through the sieve are while inverted. The material stuck in the
independent random events. The con- sieve was brushed out and called the
firmation of Eq 20 by experiment means blind. While arbitrary, this procedure
that the relationship of particle size to nevertheless gave useful information on
the size of the mesh opening is of second- some of the factors affecting blinding.
WItITBu ON MECHANICS 0]~ FINE SIEVING 15
Loads were kept below 25 g to mini- log-normal law. The very high correla-
mize the effects of blinding on the time- tion coefficients obtained illustrate the
weight curves. excellent fit of this law to the data.
1
Regression of a'on Log Cgp
25 g on Standard ROTAP Sifter
Beads St. Peter Sand

1
a'=-0.0145+0 01097
1
u'=0.00019 +0.00791 L--'~g
~g p
0.2
o/to
0.1
0
Flint Hard Wheat Flour
] 1
u' u,c0.0525 +0.01451 t=-0.0568 + 0.0555 - -
Log o-gp
0.4 o
0.3
~
0.2
0/4
/o
0.1
0 ! I I I I I ,
0 10 20 0 10 20
1
Log o-gp
FIG. 10.--Regression of a' on I/log agp for the Four Types of Material.
Fit of the Log-Normal Law to Region 2 of Relation of Particle Size Distribution to

the Time-Weight Curve: Time-Weight Curve in Region 2:
Table I I illustrates the correlation of To test Eq 20, log ~gp and log ~gt were
two of the more than 350 runs with the determined for a range of sieves and size
16 SYI~eosiu~ ON PARTICLE SIZE MEASURE~IENT
TABLE III,--COEFFICIENTS FOR THE cept should be zero. T h o u g h this was

1
REGRESSION OF s ON - - true for the glass beads and St. P e t e r
log crgp "
sand, the intercepts for the flint a n d

Correla- h a r d w h e a t were significantly different
Material Intercept
o
slop =-Pg
I tion
Coeffi- from zero.
cient
P r o b a b l y this was caused b y some bias
Glass beads . . . . . 0.00019 / 0.00791 0.972 on the microprojection size measure-
St. Peter sand... --0.0143 / 0.01097~ 0. 946 ments of the two irregular materials.
Flint . . . . . . . . . . . 0.0525 /0.01451 0. 902 F r o m Table I I I it can be seen t h a t P~
Hard wheat . . . . . . i--0.0568 } 0-0335 0. 990
is quite different for the four materials.
Hard Wheat Middlings /

50 g on 100 W / /
Standard ROTAP S i f t e r / 99
x"
"/20/'/70 Pe --O.180 95
90
80
/~20P2--0.0/82 7o ~
60 -~
n
= 40
30 o
zo g.
10
PerCentP a s s i n g - - o l ' - ~ . / ~ -100

80 ~
8
, -~
40
"~,
ft.
zo ,3c
9 , .1 , , t , 10
0.063 0.125 O.25 O.5 1 2 4 8
Time, t, min (Loq Scale)
FIO. ll.--Effect of Particle Size Range on Per Cent ;Passing - Time Curves.
distributions on each of the four mate- P~ no doubt depends on the distribution

I of mesh opening sizes as well as the ori-
rials. T h e linear regression of a t = log o'gt e n t a t i o n of the particles. A glass bead,
1 for instance, will depend for its passage
on _v~gc~gp is shown in Fig. 10 and T a b l e on finding a mesh opening of a p p r o p r i a t e
I I I . E q u a t i o n 20 indicates t h a t the inter- size, b u t a quartz particle can pass a
smaller opening if oriented in a certain theory and these experiments indicate

way. Thus it will have a higher probabil- that the transition time is directly pro-
ity of passage than the glass bead. In portional to load.
addition a somewhat plastic material 2. Unless a significant amount of
such as the hard wheat middlings can blinding is encountered, ~' and 7' are un-
deform if subject to sufficient force. affected by load. The slight differences
An interesting experiment that was in per cent passing and hence in 7' in
performed to further evaluate the effect Fig. 12 can be attributed to sampling
of particle size on P~, is illustrated in errors.
Fig. 11. Various size fractions of hard
wheat middlings were mixed together Effect of Speed on Region 2:
and sieved on a 100W sieve. Note that Both the Rotap and the gyratory sifter
in region 1 the small differences in mean were powered by variable speed drives.
particle size have very little effect so that Most of the variable speed runs were
Effect of Load on Region 2

95
1/2 120/170, 112 80/120 St. Peter Sond
90 g OhiO0 W-Standard ROTAP Sifter
80
70
6O
50
4O
30 200 g~,/
2O
10
5 I I i & i i ii i I b t , , , ,i i , 1 1 r , l ~*
10 . 100 1000
Time, t. see
FIG. 1 2 . - - E f f e c t of L o a d o n P e r C e n t P a s s i n g - T i m e C u r v e .
the sieving rate is the same for all three made with the gyratory sifter because
size distributions. Thus in region 1 the its circular motion could be subjected to
near-mesh size particles do not control the following mathematical analysis:
the sieving rate. If a particle of mass m rests on a plane
The high P2 value for the 120/170 which is being rotated about an axis at a
fraction shows that the log-normal law radius r, there will be three forces acting
still describes the basic mechanism even on the particle: a gravitational force mg,
for particles somewhat less than the mesh a centrifugal force mr~o, and a frictional
size. force frog. Equating and solving yields
Eq 21:
Effect of Load on Region 2:
Loads of 25, 50, and 200 g were sieved r . . . . . . . . . . . . (21) =
and the region 2 sieving constants deter-

mined. Figure 12 illustrates typical re- In this study the coefficient of friction,
sults. The effect of load may be sum- f, was determined from angle of repose
marized as follows: measurements as follows:
1. Increasing the load delays transi- With the sieve horizontal, a 3-in. di-
tion from region 1 to region 2. Region 1 ameter pile of particulate material about
88 deep was placed on the sieve. The motion relative to the sieve begins. I t
angle made by the sieve with the hori- was postulated that cool might represent
zontal was then increased as the sieve the sieve speed at which particles just
was tapped gently until either the mate- begin to pass the sieve and that o~c,might
rial slid down the sieve in a body or be related to the optimum sieving speed.
sheared within itself leaving a layer on To test this theory a series of experi-
the sieve. If the angle where internal ments was conducted in which the calcu-
shear takes place is designated by 0~ and lated values of o~,~and ~0cewere compared
to curves of the various region 2 sieving
Effect of Speed on Time-Weight parameters measured over a range of
Curve Perometers-Gyralory Sifter
10 g 80/120 St, Peter Sand on I00 W
gyratory sifter sieve speeds.
Figure 13 illustrates typical results.
From Fig. 13 and the data from similar
CO
experiments reported by the author (2),
the following may be concluded.
o_ 0 t- 1. od, Z, and the per cent blind usually
show a maximum at or near co,, though
+oz I I for flint and hard wheat middlings a '
-0.2
showed a minimum at o~,,. The per cent
I ~ I00 sec passing the sieve represented by Z
reaches a maximum at or very near c0c~.
-0.6
Thus if the per cent passing the sieve for
-0.8
a given sieving time is used as the cri-
-1,0
terion, o~cecould be used to predict the
-I.2
~ optimum sieving speed.
2. The blind also reaches a maximum
O.16
at coc~. To minimize blinding a speed 15
0.14
to 20 per cent above ~o~,would appear to
. 0.12
be optimum.
0.10
3. A limited number of runs on the
0.08
Rotap sifter indicates that its motion is
0.06
I I I I I I
considerably better than the gyratory
0"04120 140 160 180 200 220 2-0 sifter for all speeds. The sieving rate is
rpm higher and the blinding effect is one
FIG. 13.--Effect of Sieving Speed on Per- third as great.
Cent-Passing--Time Curve Parameters. 4. The sieving rate drops off abruptly
at or below wc~.
where the particles slide on the sieve by
0, then the two coefficients of friction Effect of Sieve Material in Region 2:
are defined by: To determine the effect of sieve mate-
rial, a silk and a nylon bolting cloth were
fi- = tan o~ (22)
f, tan 0~J". . . . . . . . . .
h
compared to the U. S. standard 100W
on both the standard Rotap and gyra-
Inserted in Eq 21 these two coefficients tory sifter. Results for the Rotap sifter
of friction define two critical angular are tabulated in Table IV. I m p o r t a n t
velocities; c%~ is that velocity at which conclusions are as follows:
motion just begins within the particle 1. a ~ values are two to four times as
layer and ~o~, is the velocity at which high for the silk and nylon cloth as for
T A B L E IV.--25 g--80/120 F R A C T I O N S ON S T A N D A R D R O T A P S I F T E R - - R E L A T I V E H U M I D I T Y = 34 P E R C E N T .
Beads St. Peter Sand Flint Hard Wheat Middlings

Parameter
W N S W N o
149 143 158

log r . . . . . . . . . . . . . . . . . . . 0.016 0. 056 0.03~ 310 N S
r , per cent . . . . . . . . . . . . . . . . 33.6 29.1 30.0
Per cen~ passing sieve, 480
see . . . . . . . . . . . . . . . . . . . . 47.0 98.9 98.2 55.9 76.6 78.0 28.7 53.2 55.2 N
OLp . . . . . . . . . . . . . . . . . . . . . . . 0.15 0.67 0.182 0.50 0.48 0.31 [ 0.71 0.69 0.20 I 0.47 0.45
~Ps
2.75
11621o
... 2.29 .. 2.35 -'' O
~j
4.47 2.64 2.22 2.25

~w
Microscope size at per cent
passing, tz . . . . . . . . . . . . . . 143 19G 187 167 181 182 188 200 200 157 181 183
W = U. S. standard 100W
N = 8xx nylon
S = 9xx silk
20 SYMPOSIUM ON PARTICLE SIZE M E A S U R E M E N T
the wire mesh. This is probably due to the choice of a suitable end point for a
the mesh elasticity of the former, d val- case such as this is difficult.
ues are highest for the flint passing Prediction of Sieving Error.--From the
through the silk and nylon cloth and theory describing region 2, an equation
lowest for the beads through the wire for predicting sieving error may be de-
mesh. rived. From Eq 18 we can obtain:
2. Indications are that the larger open-
ings of the silk and nylon cloth determine dN No e_i/2z~, dZ (23)
dt -- t~r d (log t) . . . . . .
the region 2 parameters but that for the
wire mesh the average mesh opening is
more important. Now dZ - a' and since
d (log t)
APPLICATIONS , P2
O~ m
log
m
~gp' Eq 23 becomes
There are a number of applications for
the results of this study. I t is believed
dN No e_l/~z~ P ~ .. (24)
that the method of analysis suggested
dt tx,/~ log crgp""
here and the reduction of sieving results
to the sieving constants of Eqs 11 and 20 Since the ag of a log-normal distribution
offers a rational system for comparing is the same by weight as by number and
the results of sieving studies. since the size of the particles passing the
sieve in region 2 is nearly constant Eq 24
Test Sieving: may be transformed to a weight basis:
T i m e - - Weight Passing Curve.--One of
de(W) lOOP2
the problems in test sieving is to estab- - e-l/2z~ .... (25)
lish a proper end point. From this study dt log ~rgptV/~

it is obvious that sieving should be con- Since d is small, Eq 25 when integrated
tinued until region 2 is reached. A good becomes:
procedure might be to plot the time-
100P2 /2
weight curve on log probability paper AC(W)I-2 log ergp r log h'" .(26)
and then select as an end point a time
at the beginning of region 2. e- i/2Zm2
Even if it is assumed that sieving is Where qS(Zm) - ~ and

carried into region 2, it must be remem- AC(W)I_~ = per cent by weight passing
bered that an original truncation of the the sieve in the time interval h to t2.
distribution, resulting in a high log crgp
will result by Eq 20 in a high d . For Log agp can be obtained from the par-
materials with a high P2 value where ticle size distribution, P2 is a constant
only a few per cent pass the sieve, dou- for a given material and sieving method,
bling the sieving time may result in a 30 and 4~(Zm) may be obtained from a
per cent increase in the particles passing table of normal areas and ordinates for
even though the sieving is in region 2. the expected per cent passing the sieve.
The data of Table I I serve as an extreme For example, if 25 g of flint for which
illustration of this fact. Though the en- P2 = 0.014 and log ~gp = 0.114 are
tire curve is in region 2, increasing the sieved on an 80W sieve on a standard
sieving time from 1 to 2 min would result Rotap sifter the fraction passing the sieve
in 35 per cent increase in the particles from 3 to 5 rain would be 0.71 per cent
passing. Since the size of the particles if 18 per cent is expected to pass the
passing the sieve in region 2 is constant, sieve. The 0.71 per cent passing from 3
WHITBu ON MECHANICS OF FINE SIEVING 21
to 5 rain is actually not a sieving error dC(W, x) aW

- .(30)
but results from the normal operation of Bdx A
the laws of sieving in region 2. AC(W),
and for region 2
therefore, represents a fundamental un-
certainity in the determination of par- dC(W, x) W~oP~
- - r .... (31)
ticle size by sieving. Bdx - Ax log agp
Steady State Sieving: where d C ( W x ) is the weight per unit
Though the laws for regions 1 and 2 time passing the sieve at x. Equations
sieving were developed from nonsteady 30 and 31 now express the sieving rate
state experiments, they are readily ex- as a function of x. From the above a
tended to steady state sieving. number of conclusions concerning the
In steady state sieving, the particles mechanism of steady state sieving may
which cannot pass the sieve must be be drawn:
disposed of by having them travel from 1. The region of sieving is a function
one part of the sieve to another, which of x. Region 1 sieving will exist where the
means that a graduation of region exists material is being fed onto the sieve and
this will transform to region 2 sieving as
F eed = Wo the overs move away from the feed point.
2. The rate at which region 1 trans-
forms into region 2 can be calculated
from the analogy between the time-
weight curve of unsteady state sieving
and the distance-weight curve of steady
state sieving providing that ~30 is known
FIG. 14.--Idealized Steady State Sieve with as a function of x.
Linear Travel of Material. 3. All of the characteristics of non-
steady state sieving previously discussed
from one part of the sieve to another. apply as well to the steady state case.
For example, let us consider the case of Further information on the effect of
a rectangular vibratory sieve arranged as load, sieve dimensions, etc., for region 1
in Fig. 14 so that the velocity of travel may be obtained if Eq 14 is substituted
from xl to x2 is constant and equal to into Eq 30 and if we assume that for
X30, and the distance traveled is ~O0t. most industrial sieving a constant per-
For nonsteady state sieving, the rate centage of the feed passes the sieve. Then
of passage through the sieve on a weight
dC(W, x) w~- G
basis is:
dx [W0 - C(W, x)]- G B6... (32)
de(W, t) W
dt - f(t) -~ . . . . . . . . (27) Ao~( S~ 1/lnagp
where ~ = C1~ ~ - \ k - ~ ]
For region 1 sieving
and Wc = pVc is a critical load on the
f(t) ---- a . . . . . . . . . . . . . . (28)
sieve. Integration of Eq 32 from x = 0
and for region 2 to x yields
P2 Wo (~-R~) - [Wo - C (W, x ) l l - G
f(t) log ,gpt $(Z) . . . . . . . . . (29)
1 - R~
Therefore for region 1 = Wc-R~pBpX.. (33)

Equation 33 relates the various sieving considered constant and equal to W1 and
variables to the distance traveled on the Z1. Since W / A = WI~oB, Eq 31 be-
sieve. For any given value of C ( W , x ) comes
that it is desired to pass the sieve, and WiP2 x
for given values of W0, B and ~, the C(W, x) = - - q,(Z1) log --
log agp xl
sieve length can be calculated. Since Eq
33 is complex it is worthwhile to discuss + C(W, x)1..(36)
two limiting cases. It is immediately noted that even a
Where only a small amount passes small increase in the amount that is de-
the sieve: sired to pass the sieve during region 2
[Wo- C(W,x)] ~-R~ ~-- wo - (1 - R~)C(W,x) will require a large increase in sieve
length. For this reason it is usually im-
Therefore: practical to carry steady state sieving
-" very far into region 2.
+ (1 - R~)c(w, x) Though no equations describing the
LxW~/ transition region have been developed,
= (1 - R~)pBCX..(34) there are some worthwhile conclusions
that can be derived from the knowledge
for the case where everything passes
of regions 1 and 2 theory.
through the sieve C ( W , x ) = W o , and
From what the author has seen of com-
therefore:
mercial sieving, it is likely that separa-
( W o y ~d tion is usually ended somewhere in the
W0 \ ~ / = (1 + R,)pB~X... (35)
transition region. Because of the large
change in the size of the largest particles
Thus for R, = --2 (St. Peter sand and passing the sieve in the transition region,
wheat middlings) the sieve length re- it is desirable to end the sieving process
quired increases rapidly for loads above either in region 1 or region 2 rather than
We. For loads below Wc and for low in the transition region.
C ( W , x ) it will be noted that the left Equations 30 and 31 suggest how this
hand member in Eq 34 could become might be accomplished without an in-
negative. Since this is impossible phys- crease in sieve area. Equation 30 shows
ically, it means that the effect of load as that for region 1 a certain sieve area is
/ V\-R~
represented b Y ( v / in Eq 14 does not required to pass a certain amount of
material under given conditions. For re-
hold for very low loads. This plus the gion 2 we see from Eq 31 that the situa-
. /Wo\ -~ tion is quite different since the amount
fact that ~ ) increases very rapidly
passing depends only on time and not
for loads above W~ indicates that high on sieve area. Thus in region 2 the veloc-
loading of sieves is very undesirable. ity of travel over the sieve should be as
This is particularly true for rough par- slow as possible whereas in region 1 the
ticles such as St. Peter sand or the mid- velocity is fixed by the required sieve
dlings. area. It thus appears that if steady state
Next let us consider region 2. The sieving is to be carried into region 2 in
relationship among the variables may be order to get complete separation, the re-
obtained by integrating Eq 31 from x~ gion 1 and region 2 sieving should be
to x, letting W1 equal the load at x~ and performed on different sieves so that the
assuming that the variation in W and Z velocity of travel can be reduced during
is small enough so that they may be the later portion of the transition region.
There is also another reason why such a sound theoretical foundation for future
a split sieve arrangement would be de- research on sieving.
sirable. I t has been shown that in region
Acknowledgments:
1, very few near-mesh size particles pass
the sieve. Therefore a larger mesh size The author wishes to acknowledge the
could be used for region l, with a con- direction and inspiration of his advisor
Mr. Newman A. Hall, Professor of Me-
sequent increase in sieving rate, than can
chanical Engineering during this inves-
be used for region 2.
tigation and the assistance of Mr. R. C.
The above extensions of the nonsteady Jordan, Head of the Department of
state sieving results to the steady state Mechanical Engineering for making
problem, indicate what can be accom- available the necessary facilities and to
plished as further data become available. the Quaker Oats Co. for financial sup-
I t is hoped that the basic theories devel- port for the author's laboratory during
oped from this investigation will provide this study.
REFERENCES
(1) G. Fagerholt, "Particle Size Distribution of (5) F. Kottler, "The Goodness of Fit and the
Products Ground in Tube Mill," G.E.C. Distribution of Particle Sizes," Journal,
Gads Forlag, Copenhagen (1945). Franklin Inst., Philadelphia, Pa., Vol. 251,
(2) K. T. Whitby, "The Mechanics of Fine pp. 499, 617 (1951).
Sieving," Thesis, University of Minnesota,
Minneapolis, Minn. (1954). (6) F. Kottler, "The Logarithmico-Normal Dis-
(3) K. T. Whitby, "A Rapid General Purpose tribution of Particle Sizes: Homogeneity
Centrifuge Sedimentation Method for and Heterogeneity," Journal of Physical
Measurement of Size Distribution of Small Chemistry, Vol. 56, pp. 442-448 (1952).
Particles, Part I--Apparatus and Method; (7) F. Kottler, "The Distribution of Particle
Part II--Procedures and Applications," Sizes," Journal, Franklin Inst., Phila-
Journal HP & AC 27, pp. 121-128 (i955). delphia, Pa., Vol. 250, pp. 339-356 (1950).
(4) H. Cramer, "Mathematical Methods of Sta-
tistics," Journal, Am. Soc. Heating Air Con- (8) G. Herdan, "Small Particle Statistics,"
ditioning, Princeton University Press, Prince- Elsevier Publishing Co., New York, N. Y.
ton, N. J. (1946). (1953).
APPENDIX
L I S T OF SYMBOLS
A sieve area, sq cm,
A0 = sieve open area, sq cm,
fraction passing sieve per second in region 1,
B = sieve width, cm,
b = slope of region 1 time-weight curve on log-log plot,
C1 = region 1 sieving constant at S/ks elm = 1, per sec,
Cle region 1 sieving constant at critical sieve loading,

C(w) = cumulative per cent by weight passing sieve,
C(w,t) = cumulative weight passing sieve at time t,
C(w,x) = cumulative weight passing sieve per unit time at distance x from feed point, g per
sec~
d = particle size, cm or t%
& = geometric mass mean particle size,
= geometric n u m b e r m e a n particle size,

f = coefficient of friction of particles on sieve,
h = defined f r o m E q 9, h ~ 0.406,
k = c o n s t a n t of p r o p o r t i o n a l i t y ,
ks = particle s h a p e factor,
~ mass,
n = e x p o n e n t in region 1 r a t e of sieving c o n s t a n t , or o t h e r q u a n t i t y as n o t e d ,
N = n u m b e r of particles or o t h e r q u a n t i t y as noted,
No = n u m b e r of particles initially on sieve t h a t can pass t h e sieve,
log ~gp
P2 - region 2 sieving p r o b a b i l i t y ,
log ~gt
R = radius of rotation, ft,
R~ = region 1 particle r o u g h n e s s factor,
r = Ao/A,
S = sieve m e s h size, cm or #,
W
T - = s i e v e b e d thickness, cm,
A
t = time, sec or min,
V = v o l u m e of m a t e r i a l on sieve, cu cm,
Vc = critical volume,
~0 = s t e a d y s t a t e velocity of t r a v e l of m a t e r i a l on sieve,
W = sieve load, g,
We = critical sieve load,
W0 = s t e a d y s t a t e sieve feed rate, g p e r sec,
x = distance, cm,
Z = n u m b e r of s t a n d a r d d e v i a t i o n s a b o v e or below t h e m e a n of a n o r m a l d i s t r i b u t i o n
log t - log
Z = "
log ~ agt
C(W) = 100 r
oz r = normal probability integral
Z,~ = m e a n v a l u e of Z o v e r a g i v e n t i m e interval,
d = t r u e slope of s t r a i g h t line p o r t i o n of a l o g - p r o b a b i l i t y p l o t of t h e sieving curve,
~,t = Z o r d i n a t e a t t = 1 (see aP),
ogp = geometric s t a n d a r d d e v i a t i o n of a p a r t i c l e size d i s t r i b u t i o n a t a p a r t i c u l a r size;
d e t e r m i n e d b y d r a w i n g a t a n g e n t to t h e size d i s t r i b u t i o n curve on a log-prob-
ability plot,
~rgt = geometric s t a n d a r d d e v i a t i o n of t h e s t r a i g h t line p o r t i o n of a w e i g h t - t i m e c u r v e
on log-probability p a p e r , s t = 1/log ~gt,
0 = as noted, a n d
w = a n g u l a r velocity, r a d i a n s or r p m .
DISCUSSION
MR. ALAN R. LI014ENSJ--In our lab- ticularly true when flaky or fibrous par-
oratories we have spent most of our time ticles are being evaluated.
for more than thirty years studying and The author has indeed given us an
devising methods of measuring particle effective method of minimizing this
size. We believe that no one or even two difficulty.
methods are accurate for all particulates. MR. CHARLES M. HUNT.2--What par-
We have done much with sieving. ticle size range was covered in your
Based upon this experience, may I be study?
permitted to commend the author upon MR. K. T. WHITBY (author).--The
his excellent analysis of the science of particle size range covered here was from
sieving, particularly fine sieving. perhaps 300 or 400 ~ down to approxi-
Although I believe sieve analyses are mately 1 ~.
largely faulty, there is presently no other The particle size distributions of neces-
reliable method of measuring particles sity had to cover a range of mean par-
larger than 50 ~. ticle size and breadth of distribution.
In the fine sieves there are offered to Many of the distributions were as nar-
us sieves designated as Nos. 200, 300, row as we could make them by the means
325, and 400. The fabrics of these sieves of classification available. All of these
are extremely delicate and become dis- different distributions of sizes and spread
torted by brushing, shaking or bumping. were necessary to determine the sieving
If particles flocculate, as they fre- parameters.
quently do in dry sieving, the results I might add one comment with refer-
may be inaccurate. This is due to the ence to what Mr. Lukens said. The pur-
inter-particle attraction. In wet sieving, pose of this study was purely to find out
precisely the right choice of and propor- how the sieving process behaves. There
tion of dispersing agent must also be was no effort made to improve sieving
used. techniques. We were simply studying the
But most of all is the uncertainty standard methods in order to find out
caused by particle shape, this being par- what makes them tick.
1President, Lukens Laboratories, Inc., New- Chemist, National Bureau of Standards,
ton, Mass. Washington, D. C.
[See also Discussion of Daeschner, SeibeIt, and Peters paper, page 48.1
25
S T P 2 3 4 - E B / A u g . 1959
A P P L I C A T I O N OF E L E C T R O F O R M E D P R E C I S I O N M I C R O M E S H
SIEVES TO T H E D E T E R M I N A T I O N OF
P A R T I C L E SIZE D I S T R I B U T I O N
BY H. W. DAESCHNER, 1 E. E. SEIBERT, 1 AND E. D. PETERS~
SYNOPSIS
Woven-wire sieves present a variety of problems to the petroleum refiner

who tries to use them for the determination of particle size distribution of
cracking catalysts. Not only are the sieves limited in the lower range to 44 #,
but they are inherently not sufficiently reliable for the measurements of these
catalysts. The strongly entrenched popularity of the sieving procedure, due to
its simplicity, prompted an investigation of a new product made by electro-
forming nickel in meshes of precise square openings ranging from 15 to 105 ~.
A satisfactory sieve has been developed and details of procedures for use
established. These micromesh sieves are recommended as a primary standard
for testing size distribution of cracking catalysts because of their highly precise
openings, which can be reliably measured with a microscope, and because they
are available in the range of interest.
One of the most important processes in for measuring the particle size distribu-
a modern refinery is catalytic cracking tion of materials in the range of 1 to 100
which converts heavy oils chiefly to more in diameter. The results of any given
desirable lighter products, such as gaso- method depend upon some parameter of
line. I t is carried out generally by bring- the particle in question and upon the con-
ing the oil into contact with silica-alu- ditions under which the particles are
mina catalysts in the form of pellets or measured. Therefore, only partial agree-
fine microspheroidal particles in a circu- ment between methods can be expected.
lating fluidized bed. This catalyst goes I t is practically impossible to define the
through cycles of reaction, then regenera- diameter of most particles because of
tion to burn off a small amount of carbon their more or less nonspherical shape,
formed during the reaction. An impor- therefore some compromise on what is to
tant problem in the fluidized system is be measured must be made. The long-
the particle size of the catalyst; this is a standing esteem of the sieving procedure
controlling factor in the fluidization has been due solely to the ease and ra-
which affects the yields of the reaction as pidity of the method. Wire sieves have
well as the regeneration rate. been entirely satisfactory for material
Many methods (1,2)2 have been devised not finer than about 100 ~; however be-
low that size their permissible variation
I Shell Development Co., Emeryville, Calif. is too great for precise classification.
s The boldface numbers in parentheses refer
to the list of references appended to this paper. The strongly entrenched popularity of
26
Copyright* 1959 by ASTM Intemational www.astm.org
DAESCHNER ET AL ON PARTICLE SIZE DISTRIBUTION 27
the sieving procedure prompted a search niques they have developed a new process
for screens or meshes made to closer tol- for producing fine mesh precision screens.
erances than the standard woven-wire
cloth sieves (ASTM Specification E 11 - MICROMESII SIEVE CONSTRUCTION
39) .3 Of several meshes investigated, the The production of the Buckbee Meats
ones made by Buckbee Mears Co. of St. micromesh sieves involves six basic op-
Fro. 1.--Typical Precision Micromesh Sieves. Nominal Size (X55).
Paul, Minn., appeared especially attrac- erations. (a) A flawless negative is made
tive. Through the utilization of basic by crossline ruling on a wax-coated glass
photoengraving and electroplating tech- plate with a ruling engine capable of pre-
cisely ruling up to 8000 lines per in. (b)
Specification for Sieves for Testing Pur- The rulings are etched and filled to com-
poses (Wire Cloth Sieves, Round-Hole and
Square-Hole Screens or Sieves) (E 11 - 39), 1955
plete a negative which is printed photo-
Book of ASTM Standards, Parts 3, 4, 5, 6, 7. graphically onto a nickel-clad copper
plate coated with a photosensitive en- cycle the micromesh is bonded to the sup-
amel. (c) After development, this copper porting grid electrolyfically, the thick-
plate, or matrix, is submerged in a puri- ness of the micromesh increased and the
fied nickel plating bath where the mesh hole size reduced uniformly to the desired
is electrodeposited to a thickness of about size.
3 #. After stripping the mesh from the Frequent inspection of the hole size
matrix, the matrix may be used again with a specially adapted electric densi-
for another plating cycle. (d) The next tometer assures adequate control of the
step is the preparation of the supporting process. The bonded mesh is given a
Fro. 2.--Cross-Sectionof Micromesh Mounted on Supporting Grid. 45 ~ mesh size (;4100).
grid. A grid pattern of 14 lines per in. is physical check for hole size with a tool-
printed simultaneously and in perfect maker's microscope, after which it is
register on both sides of photosensitized trimmed to size and soldered in a 3-in.
copper foil about 0.015 in. thick. (e) brass frame. A final densitometer check
After development, the foil is etched sion the finished sieve supplies the hole
multaneously from both sides and the re- size measurement which is engraved on
sulting grid cleaned of the protective en- the certification plate attached to the
amel. (f) The fragile micromesh is drawn frame.
tightly over the supporting grid which is Figure 1 shows examples of typical
mounted on an inert curved holder and meshes produced by this process. The
immersed in the accurately controlled 20-v mesh shows a few openings blinded
nickel plating tank. In this final plating by particles. The supporting grid is not
shown in these photomicrographs; how- wavelike with slight spurs or bulges pro-
ever, Fig. 2 which is a cross-section of a jecting into a few of the openings,
45-~ mesh shows the unique profile of the thereby decreasing the effective size by
supporting grid. Preparation of the sec- as much as 3 ~. This experience with the
tion has distorted the fine mesh from a first set of sieves led to recommending a
flat plane. specification of 35 4- 5 per cent open
Early in the investigation it was found area; that is, the width of metal between
from experimental meshes that certain holes should be 66 per cent of the width
structural conditions needed to be met in of an opening.
order to produce a sieve having maxi- The sets of micromesh sieves used in
mum strength and maximum per cent this investigation were formed from mas-
open area and at the same time retaining ter rulings of 500 lines per in. for the 20
uniformity of hole size. In the first sieves and 30 ~ sizes, 250 lines per in. for 45 and
made it was apparent that the metal por- 60 ~ sizes, 250 and 200 lines for 75 ~,
tion of the meshes was heavier or thicker and 200 and 120 lines for 90 ~. It is hoped
in some screens than in others. This was that increased popularity of micromesh
as expected since the manufacturer used sieves will promote the making of addi-
only their available master series of rul- tional master rulings so that each of a
ings to fabricate this set of sieves. Obvi- series of sieves may be formed from a
ously, a given master ruling cannot be different ruling and as a consequence
used to produce a mesh of a different have approximately the same percentage
number of openings per unit area. There- open area.
fore, in order to obtain a mesh with a
CALIBRATION
smaller hole size than the nearest avail-
able master it is necessary to continue Although the manufacturing company
the plating process until the required certifies its micromesh sieves to 4-2 ~ of
opening is obtained by electrodepositing the nominal value at the present time,
metal on the lines, thus increasing the it is possible and probable that two sets
width and thickness of the metal with a could differ by 4 v with the consequence
corresponding decrease in per cent open that fractions for particle size distribu-
area. The desirable feature of heavier tion analysis might disagree by as much
plating is the increase in strength of the as 15 per cent. Therefore, an effort was
mesh. However, with a decrease in per made to measure the effective size of the
cent open area there is the necessity to sieve by microscopic measurements with
increase the screening time. Microscopic a filar micrometer.
examination showed that the additional The micromesh may be calibrated with
build-up of metal to form smaller open- the apparatus described in the appendix
ings than those for which the master was to ASTM Specification E 1 1 - 39, 3 pro-
intended produced a somewhat conical vided the total magnification is 500;4 or
aspect of the openings to screening par- more. Most microscopes will accommo-
ticles. I t was believed, and later shown, date the 3-in. sieve on the existing stage
that the slight conical entrance to the without modification. Therefore, a micro-
holes in sieves having increased thickness scope fitted with a 20 or 43N objective
caused by extended plating would pro- and a filar micrometer eyepiece of 10 or
mote the tendency to blind. In addition 12.5 powers is more convenient and may
to forming smaller openings, prolonged be more accurate than measurements
electrodeposition causes the sides of the made on a projected image. Bottom il-
perfectly square openings to become lumination with essentially parallel rays
30 S~Posltr~ ON P A R T I C L E S I Z E M E A S U R E M E N T
and top vertical illumination is neces- ard deviation of the ability of one opera-
sary to be able to focus on the narrowest tor to make repeat measurements on 24
point of the open area which is generally selected openings at different times was
midway between the top and bottom estimated to be 0.7 tt for a 90-t~ sieve, 1.3
planes of the mesh. Measurement is made /z for a 74-/z sieve and 0.6 for a 30-# sieve.
by aligning the cross hair of the microm- When two operators measured the effec-
eter with the edges of the largest of sev- tive size of six different sieves from 30
eral openings and measuring across the measurements per sieve, the standard de-
openings to similar edges on the opposite viation of the difference between opera-
side by turning the micrometer in only tor averages was 0.56/~. Horizontal and
one direction to avoid backlash in the vertical measurements were made on 20
leadscrew. Only those openings with
straight sides (no spurs or bulges project- TABLE II.--EFFECT OF REFERRING
A SIZE DISTRIBUTION OF THE NOM-
ing into the opening from the center por- INAL VALUE COMPARED TO THE CALI-
tion of the side) are measured. The num- BRATED VALUE OF TWO SETS OF
SIEVES.
TABLE I.--CALIBRATED VALUES OF Difference Be-

MICROMESH SIEVES S E T N O . 1). Micromesh Micromesh tween Sets Re-
Set No. 2 Set No. 3 ]erred to, weigh
per cent
Vertical Measure- Horizontal Measure-
ment, g ment, g
Nominal]
Nominal )r Refer-
Value, # Mean Mean race Size 9~, ~ .-~
~z
Average Standard Average Standard Nomi- Meas-
Value Devia- Value Devia- nal ured
tion tion Value Value
90. .. 85.8 1.7 86.6 2.1

75... 74.O 1.5 73.9 1.4
60... 57.9 1.8 59.2 1.4 .~0........ 88.7 14.7 92.3 12.5 2.2 0.9
45... 42.7 1.0 43.5 1.3 .75.
....... 76.8 13.5 74.0 17.3 3.8 0.8
30... 31.6 1.2 31.6 0.8 .30........ 60.7 22.1 61.4 17.8 4.3 0.8
20.. 19.0 0.8 19.7 1.2 .t5.
....... 46.7 18.3 48.3 19.2 0.9 1.0
.30........ 31.3 15.5 32.0 19.1 3.6 1.0
.20........ 22.G 9.1 22.5 6.0 3.0 0.4
<20. 6.8 8.1 1.3 1.0
ber of openings actually measured and
the number under size for each setting
are noted. About twenty settings, or a random openings of each sieve by one
sufficient number to account for 100 operator as shown in Table I.
openings, are made at random over the In view of the repeatability standard
sieve surface. At least two thirds of these deviation, 0.6 to 1.3 tz, the differences in
largest uniform openings are actually opening size between horizontal and ver-
measured, either singly or in groups of tical measurements is not significant;
two or more. therefore, an average value of the two
The effective size of the mesh is ob- measurements may be assigned to the
tained from the average of the openings sieve. In some cases this measured size
which fall within the maximum size is significantly different from the nominal
range of about 2 ~. After considerable value; therefore the measured rather
experience has been gained, measurement than the nominal values were used in all
of the average effective opening should subsequent tests. I t should be noted that
be reliable to -4-0.5/~. the ratio of the variance due to openings
A number of exercises in the statistics to that of operator repeatability is not
of measurement were made. The stand- significant.
Table I I illustrates the measured size tween sets for the same determination
of two sets of sieves compared to the after the amounts retained by each sieve
nominal value and the consequence of have been plotted as accumulated per
referring the particle size distribution of a cent finer than the calibrated size and the
distribution corresponding to the refer-
TABLE I I I . - - T Y P I C A L M E A S U R E M E N T S ence size-range interpolated from the
OF S T A N D A R D W O V E N - W I R E SIEVES. constructed curves.
Mean Calibration with glass spheres (3) was
Nominal Average Standard not attempted because a sample with
Size, # Range, Value, # Dr
accurately known distribution in the per-
tinent size range was not available. To
74 . . . . . 69.9 to 115.9 87.1 12.4 prepare such a sample was considered
43 . . . . . . 40.6 to 57.3 1467 I 51
unwarranted since measurement with a
FIG. 3.--Typical Woven-Wire Sieves (X 55).
catalyst sample to the nominal value secondary standard involves errors which
rather than to the calibrated size. Most are avoided by measurement with a
sieves of both sets fall within the manu- microscope. Unlike the three-dimensional
facturer's certification of 4-2 # from the configuration of the woven-wire sieve
nominal value. When a standardized openings, the micromesh openings are
method of specification has been two-dimensional, that is, in a single
achieved, it is expected that the certified plane. Sieving a sample of glass beads
value of a sieve will be much closer to having a broad distribution on the micro-
the effective or calibrated value. In the mesh sieves resulted in considerable
present case, Table II, the difference be- blinding. I t was observed that glass
tween amounts of catalyst retained by spheres had a tendency to blind the
the corresponding sieves of both sets, ex- woven-wire and micromesh sieves very
pressed as per cent of the whole sample, is much more than catalyst particles and
shown in the sixth column. The last col- the blinding was more severe with woven-
umn shows the differences obtained be- wire than with micromesh sieves.
32 SYMPOSIU~r ON P A R T I C L E SIZE M E A S U R E M E N T
Total Range and Range of Effective scope in a manner similar to that used
Openings for Micromesh Sieves for the micromesh sieves. The values are
Permissible Variation in Average
~] Opening of Woven Wire Sieves shown in Table I I I . A typical area of the
Permissible Range for 5 per cent of 74-~ sieve is illustrated in Fig. 3(a) to
[7 Woven Wire Sieve Openings [1 show the large range in size of the open-
120 (Range for Maximum Opening
not Shown] ings. Figure 3(b) shows a sample of a
110 15-v woven-wire mesh made in Germany 4
for precision sieving. Here again there
100
are many openings greater than the nom-
90 inal value. These figures may be a biased
g estimate because it is difficult to select a
~: 8o random distribution of holes. The range
indicated is within the specifications,
however. The woven-wire sieves used
for this observation and those for subse-
quent experiments were essentially new
but not tested and certified by the Na-
40
tional Bureau of Standards.
Permissible ranges of mesh openings
50 for pertinent woven-wire sieves accord-
ing to ASTM Specification E l l - 39 are
2O L [ f I I I I
37 44 .55 62 74 88 105 compared in Fig. 4 with those measured
Nominal Sieve Opening, lx for micromesh sieves. The measured
FIG. 4 . - - P e r m i s s i b l e R a n g e for M i c r o m e s h ranges for the 74 and 43-~ woven-wire
Sieves C o m p a r e d to t h a t for W o v e n - W i r e Sieves.
sieves shown in Table I I I fall within the
lZeeent a c t i o n b y A S T M C o m m i t t e e E-1 h a s maximum permissible opening size.
been t a k e n to r e d u c e t h e permissible r a n g e s for
w o v e n - w i r e sieves. To illustrate the retention efficiency
TABLE IV.--RETENTION EFFICIENCY OF MICROMESH COMPARED

TO WOVEN-WIRE SIEVES.
S y n t h e t i c C a t a l y s t G.
Micromesh Sieves Woven-Wire Sieves
Fraction Originally Retained Sieve Fraction Originall3

Per Cent of Per Cent of Retained on 53-g
Sieve Size, ~ Total Retained on 43-/~ Size, Total
Size, per cent Size, per cent
R e t a i n e d on:
86. 11.1 88 9.5
74 9.8 "0.'0 74 9.4 "0.'0
58.5. 24.0 5.8 61 10.6 2.2
43 27.8 91.6 53 13.2 58.9
32. 15.9 2.6 43 27.9 37.6
19 8.9 O.0 P a s s i n g 43 29.4 1.3
P a s s i n g 19 2.5
COMPARISON W I T H W O V E N - W I R E SIEVES of the micromesh sieves compared to

that of the woven-wire sieves, fractions
To illustrate the irregularity of open-
ings in wire sieves, two standard woven- 4 Steinhaus, GmbH, Mtilheim-Speldorf
wire sieves were measured with a micro- (Ruhr), G e r m a n y .
DAESCItNER ET AL ON PARTICLE SIZE DISTRIBUTION 33
were isolated with a set of each type, SIEVING PROCEDURE

and, after cleaning the sieves, one of the After a thorough study of the variables
fractions was p u t through the entire set evident in a sieving method, the follow-
again. Typical results are shown in Ta- ing procedure, capable of producing the
ble IV. most accurate and repeatable results, was
I t is believed t h a t the redistribution developed.
shown in Table I V for the micromesh is
not unusual for particles where the shape Sample Size:
factor is unknown. T h e p r o b a b i l i t y t h a t Withdraw from the bulk sample, after
a particle will be retained b y or pass proper mixing, about 2.0 to 2.5 ml, repre-
through an opening in a given time de- senting about 1.0 to 1.5 g of sample. Take
pends upon the uniformity of the shape care not to disturb the mixed bulk sample to
of the particle. an extent which would cause segregation
A further screening experiment was according to particle size.
performed to illustrate the wide range of
Humidification:
mesh sizes in two of the woven-wire
Spread the sample taken in a thin layer on
a flat dish and allow to stand in the room at-
TABLE V.--REDISTRIBUTION OF
FRACTIONS FROM WIRE SIEVES mosphere for about 15 to 30 min or for a
BY MICROMESH SIEVES. time consistent with the rate at which the
moisture content of the catalyst equilibrates
74 to 88-~ Wire 61 to 74-# Wire
Retained on Micro- Range, per cent Range, per cent with that of the atmosphere.
mesh Sieve Size, # of fraction of fraction
Sieving:
86 ............... 86.8 28.0
74 ............... 12.9 38.5
Weigh each sieve and the pan, previously
58.5 . . . . . . . . . . . . . 0.3 33.5 cleaned and dried, to the nearest milligram
43 ............... 0.0 0.0 on an analytical balance. Assemble the sieves
in proper order and add the entire sample
from the humidifying dish to a top sieve. In-
screens and to s u b s t a n t i a t e the measure- stall the cover and place the stack of sieves
m e n t d a t a shown in T a b l e I I I for the on the shaker.
74-~ screen. T h e "on 74" and "on 61" Make certain that the stack is electrically
fractions from the woven-wire screening grounded and shake the sieves for 20 or 30
min, depending upon the nature of the cat-
of the catalyst, shown in Table IV, were
alyst and shaking motion.
separately screened through the micro- Remove the stack and as rapidly as pos-
mesh sieves and the results in Table V sible weigh each sieve and pan to the nearest
were obtained. milligram, taking care not to disturb the
If the uniformity of wire openings had contents of any sieve.
been as perfect as the micromesh open- Replace the stack on the shaker, attach
ings, there should have been retained the grounding wire, and shake for 5 addi-
about 90 per cent of the 74-~ size for the tional minutes.
74 to 88-~ wire range and something Reweigh, and if the weight of sample on
greater than 90 per cent on the 58.5-# any sieve has changed by more than 3 lug
from the previous weight, repeat the 5-rain
size for the 61 to 74-v woven-wire range.
shaking and weighing procedure until the
T h e three nearly equal fractions obtained weight change is less than this amount.
from the " t h r o u g h 74-/~ and on 61-/z" Calculate the fraction on each sieve and
woven-wire screen illustrate the large through the finest sieve by dividing the net
range in size of openings for this screen weight of each fraction by the sum of the net
as measured and shown in Table I I I . weights on all the sieves plus that in the pan.
34 SYMPOSIUI~ ON PARTICLE SIZE M E A S U R E M E N T
Reporting Results: bulk quantity becomes a problem be-

Convert the various fractions to cumu- cause of the tendency for the more or
less spherical particles to classify during
lative per cent finer than the calibrated size
of the mesh and plot on arithmetic-probabil-the sampling procedure. This is most pro-
ity paper, using the calibrated size values nounced with spherical particles which
for each sieve. Draw a smooth curve through form the bulk of synthetic silica-alumina
the points and read from the curve the values
cracking catalysts. The larger the sample
for the desired sizes. Report results in "per
that can be used the greater is the proba-
cent finer than size." bility that it will be representative. I t is
DISCUSSION OF PROCEDURE almost impossible to secure a representa-
VARIABLES tive sample of less than 0.2 g even though
this amount represents considerably over
Most of the variables associated with
10,000 particles per 3-in. sieves which ac-
the use of woven-wire sieves are present
cording to Carpenter and Deitz (7) is the
in the use of micromesh sieves. Variables
absolute minimum for a heterogeneous
in the sieving procedure may be of two
material on 8-in. sieves. Static charges
types: (1) those associated with the ap-
and stray air currents may deplete the
paratus, and (2) those pertaining to the
sample of fine material during the sam-
particle.
pling procedure and the larger spherical
Silica-alumina catalyst particles pre-
particles have a tendency to roll to one
sent a few unusual problems because of
side or work to the top surface when the
their structure. Silica gel and cracking
mass is slightly disturbed. If the con-
catalysts derived therefrom consist of a
tainer is of convenient size and not over
loosely cemented aggregate of some 1015
two thirds full, mixing may be accom-
particles averaging approximately 40 fit
plished by rapid tumbling, rolling, or
in diameter, bonded into large, roughly
shaking by hand otherwise a twin shell
spherical particles with diameters from
blender is satisfactory. After mixing,
less than 1 ~ to over 100 ~ (4). Such a
the container must not be vibrated or
structure has a surface area of about 600
struck before a sample has been with-
sq m per g and a pore volume of about
drawn since segregation of particles
0.8 cu cm per g. The extremely large and
would result.
active surface combined with the pore
volume causes the catalyst to adsorb Sample Size:
moisture rapidly from the atmosphere.
Determinations of the pore volume I t is generally considered that the ideal
(5,6) show that a catalyst sample has the quantity of sample is one that covers
same pore volume, per unit weight, ir- each sieve one particle deep. For an
respective of particle size. Since the min- average catalyst sample, much less than
eral density is identical for all sizes, it 1 g covers each 3-in. sieve one particle
follows that the particle density (that deep. Carpenter and Deitz (7) recom-
of the mineral skeleton combined with mend that each sieve fraction contain at
the pores) is also the same for all sizes. least 10,000 particles or a number not
I t is necessary to consider both the po- in excess of four to six particles deep on
rosity and hygroscopicity of the catalyst any one sieve, otherwise, excessive blind-
in preparing the sample for sieving. ing of the woven-wire meshes occurs. For
a sieve with 25 per cent open area, the
Mixing and Sampling: latter corresponds roughly to 24 particles
To take a relatively small but repre- per opening if cubic packing is assumed.
sentative sample of catalyst from a large Since it is difficult to determine the
D A E S C H N E R E T AL ON P A R T I C L E SIZE D I S T R I B U T I O N 35
weight of sample corresponding to a ing is to decrease the rate of particles

layer on a sieve six particles deep, a more passing through the sieve with smaller
easily calculated and more meaningful es- openings in relation to the rate through
timate is the number of particles per the larger openings. In the event that
sieve opening. Table VI illustrates the additional master rulings are made, this
relation between the number of normally condition can be corrected.
distributed particles in a 1-g sample of It has been the practice to sieve 25 to
TABLE VI.--RELATION BETWEEN CATALYST PARTICLES PER GRAM

OF SAMPLE AND THE NUMBER OF OPENINGS PER SIEVE.
Normally Distributed Particles 3-in. Micromesh
Size Range, #
Average Sample, PerCent
Diameter, weight Number of Particles Size, ~ Meshes per Sieve
per cent Particles
1__2_
> 105 . . . . . . . . . . . . . . . . 120 5 4,4 X 10* 0.2 110 5 X 104
88 t o 105 . . . . . . . . . . . . . 96.5 10 17 0.9 90 16
74 t o 88 . . . . . . . . . . . . . . 81 10 29 1.5 75 16
62 to 74 . . . . . . . . . . . . . . 68 15 73 3.9 60 25
53 to 62 . . . . . . . . . . . . . . . 57.5 20 161 8.6
44 to 53 . . . . . . . . . . . . . . . 48,5 15 201 10.8
37 to 44 . . . . . . . . . . . . . . . 40.5 12 277 14.8
26 to 37 . . . . . . . . . . . . . . . 31.5 8 392 21.0
18 to 26 . . . . . . . . . . . . . . . 22 5 714 38.2 20 120
TABLE VII.--EFFECT O F S A M P L E S I Z E ON RESULTS AND PRECISION

OF PARTICLE SIZE DISTRIBUTION,
Synthetic Catalyst A Synthetic Catalyst C
Sample size, g . . . . . . . . . . . . . 3 3 1 1 3 3 1 1
Shaking time, rain . . . . . . . . . 35 35 25 20 45 35 30 25
Size Range,/* Retained in Size Range, per cent
>90 .................. 29.8 29.4 29,3 30.9 0.5 0.3 0.0 0.6
75 t o 90 . . . . . . . . . . . . . . . 15.9 17.0 17.0 15.7 0.9 0.8 0.9 1.2
60 to 75 . . . . . . . . . . . . . . . 24.3 23.7 24.3 24.2 3.2 3.5 4.2 3.9
45 to 60 . . . . . . . . . . . . . . 16.5 16.2 15.9 15.3 7.9 8.1 8.4 8,6
30 to 45 . . . . . . . . . . . . . . 11.1 11.6 11.4 11.9 25.6 26.2 26.2 25.4
20 to 30 . . . . . . . . . . . . . . 1.9 1.9 1.8 1.6 24.9 25,0 26.1 26,1
<20 ................. 0.5 0.4 0.2 0.4 37.0 36.1 34.2 34.2
catalyst having a particle density of 1.25 30 g of catalyst on 8-in. woven-wire

g per ml and the number of openings in sieves. In proportion to the sieving area,
an experimental set of micromesh sieves. a 3-in. sieve would require over 3 g of
In an ideal set of sieves, the number of sample. Tests have shown that a 3-g
meshes per sieve should increase as nom- sample of some catalysts blinds the 45-/~
inal size of openings decreases, in pro- size of the micromesh sieve by about 50
portion to the number of particles in a per cent, the maximum for any one mesh.
sample with normal distribution. The It is considered that this amount seri-
consequence of using adjacent micromesh ously reduces the efficiency, but 25 per
sieves formed from the same master rul- cent can probably be tolerated. Therefore
it follows that a sample not greater than here to each other should first be heated
1.5 g should be used. This amount cor- for 1 hr or so at about 1050 F before siev-
responds roughly to 15 to 20 particles ing. The moisture content of the catalyst
per 45-~ opening and depends in practice does not seem to be a critical factor since
upon the particle density and the size the per cent adsorbed is independent of
distribution. I t is recommended that the particle size.
amount of sample taken for analysis The ratio of net sample "recovered" to
should result in a distribution of not that charged to the stack of sieves fre-
more than 20 particles per opening for quently changes drastically. This de-
any one sieve. pends upon the amount of water in the
Table V I I illustrates the reliability of catalyst pores, the size and activity of
results when a 1-g sample is used com- the pores, and the relative humidity of
pared to that of a 3-g sample. In addition the atmosphere. Table V I I I shows that
essentially the same values are obtained
TABLE VIII.--EFFECT OF
MOISTURE CONTENT. TABLE IX.--EFFECT UPON PARTICLE
S y n t h e t i c c a t a l y s t B. A m b i e n t , 55 per c e n t SIZE DISTRIBUTION OF HEATING
relative humidity SYNTHETIC C A T A L Y S T T O 1050 F .
V a c u u m Y)ried, a Kumidified, Per Cent Finer Than Size

2.8 g T a k e n , 4.5 g T a k e n , Nominal Size,
Nominal Size Range, per cent in per cent in
size range size r a n g e Before Heating a After Heating a
>90 ............ 13.2 12.5 90 ............... 85.1 89.9

75 to 90 . . . . . . . . . 16.9 17.5 75 .............. 71.6 78.5
60 to 75 . . . . . . . . . 17.1 17.5 60 ............... 49.5 55.0
45 to 60 . . . . . . . . . 18.7 19.5 45 ............... 25.9 27.8
30 to 45 . . . . . . . . . 19.7 19.2 30 ............... 11.8 11.6
20 to 30 . . . . . . . . . 6.7 5.5 20 ............... 0.6 2.6
<20 ............ 7.7 8.2
Pore volume, ml
2.9 g r e c o v - 4.3 g r e c o v - per g .......... 0.84 0.77
ered ered
a Identical sample.
a 120 to 130 C, 10 to 20 c m HR.
(within experimental error) whether the
to obtaining identical values of size dis- sample is dry or nearly saturated with
tribution, within sampling and experi- water, but still flee-flowing, at the start
mental error, there is the added advan- of the determination. I t is recommended
tage of the shorter time necessary to that samples be allowed to adsorb some
terminate the shaking of the sieves. Er- atmospheric moisture prior to a determi-
rors arising from the change in weight of nation only to prevent agglomeration
the sieves during handling for weighing caused by static charges and to minimize
have been determined to be less than 0.1 changes in weight during weighing. Such
per cent of the total 1-g sample. a period cannot be specified definitely
because of different humidities and cata-
Pretreatmenl: lysts encountered. Since moisture content
In general, the pretreatment of a sam- is not critical, spreading the required
ple of catalyst depends upon the condi- amount of sample in a thin layer on a flat
tion of the catalyst and the use to be dish and allowing it to stand 15 to 30
made of the particle size data. Used cata- min in the room atmosphere prior to
lyst which is coated with carbonaceous sieving should suffice. Because the rate
material that might cause particles to ad- of weight change after 30 or 45 min is
not as great with "dry" samples as it is ative humidity, therefore static accumu-
with nearly "saturated" samples, it is lation was not too severe a problem. In
suggested that no water as such be added atmospheres of a lower humidity several
to the sample unless the amount neces- devices may be employed. Grounding the
sary to bring the sample to equilibrium sieves and humidifying the sample as
with the atmosphere has been previously specified in the method is quite effective.
established. Change in weight of the An antistatic agent such as Anstac-M or
catalyst in the first fraction weighed dur- Technistat A may be diluted and added
ing the total weighing period of 5 to 7 in such a manner that it coats the par-
rain would normally reflect only about ticles without causing them to adhere.
0.1 per cent in the value for that fraction. Introduction of a stream of humidified
If it is desired to determine the amount air into the sieves or enclosing the sieves
of shrinkage a fresh synthetic catalyst and shaker in a cabinet for humidity con-
particle undergoes after it reaches the trol is suggested when the ambient is dry.
temperature of the catalytic cracking A last resort would be to attach a strip
unit, the sample must be heated first to of metal coated with some radioactive
that temperature prior to humidifying material to the inner wall of each sieve.
and sieving. Table I X illustrates the con- However, adequate precautions must be
sequence of heating to 1050 F for 2 hr. observed to avoid personal contamina-
The sample from the initial sieving was tion or exposure.
recovered and heated to 1050 F before Mechanical deagglomeration with a
resieving. When the distributions are small rubber 0-ring on each sieve was
plotted, the curves show that a shrink- found to be effective. Because of possible
age of about 7 per cent has occurred in increased abrasive action on the micro-
the particle diameters. This was con- mesh, this practice is not recommended.
firmed by determining the pore volume
of the sample before and after heating.
Sieving Motion:
Natural catalysts do not show as pro- The sieve shakers commercially avail-
nounced a collapse of the particle at this able are designed to handle 8-in. sieves
temperature. and, therefore, are unnecessarily bulky
and powerful for a stack of 3-in. sieves,
Particle Agglomeration: each weighing about 80 g. The sieving
Static electricity generated by the fric- efficiency produced by two commercial
tion of silica-alumina catalyst particles shakers and by several experimental de-
rubbing together causes the particles to vices were investigated. The results of
cohere. The accumulation of static re- studies reported by DallaValle (8) and
sults in loss of sieving efficiency and er- also by Carpenter and Deitz (7) show
roneous values. Agglomeration and sieve that the amplitude and frequency of a
blinding due to static is more pronounced shaking machine affect the efficiency of
with some types of catalysts than with sieving. A few tests using pneumatic vi-
others. In testing the applicability of brators attached to a light frame contain-
micromesh sieves and the method of dis- ing the sieves did not prove as efficient
sipating static charges, it is essential to as the Rotap or Cenco-Meinzer shakers
make frequent use of a microscope to which have less frequency and greater
ascertain the state of agglomeration on amplitude. The oscillating rate (7200
the sieves. Magnification of 20 to 40 cpm) produced by the spring-type arma-
times is adequate for this purpose. ture of a magnetic jigsaw was likewise too
All of the sieving tests were conducted great to be effective.
in an atmosphere of 55 to 75 per cent rel- A Rotap shaker was modified by in-
38 SYMPosIuM ON PARTICLE SIZE MEASUREMENT
stalling 8-in. disks of ~-in. plywood with tain speed setting, the catalyst on some
3-in. depressions cut in the centers to sieves formed a pattern, covering a third
hold the micromesh sieves in the regular to a quarter of the area, and this pat-
8-in. supporting yokes. A Cenco-Meinzer tern moved in a rhythmic fashion over
shaker was modified to permit use of 3-in. the whole area. On other sieves in the
sieves by elevating the sieves and adding stack the pattern remained stationary.
additional weight to the vibrating plat- This latter is undesirable because sieving
form. This consisted of a 2-in. section of efficiency is lowered and blinding pro-
metal pipe, 3-in. inside diameter and 389 moted. However, by periodically chang-
in. outside diameter, machined to fit the ing the shaking rate during the sieving
sieve pan, which was loosely held inside period the catalyst may be caused to
the iron ring supplied with the shaker for move rhythmically over the entire siev-
use with 5-in. sieves. With this assembly ing area on all sieves.
TABLE X.--COMPARISON OF MICROMESH SIEVING FOR DIFFERENT

TYPES O F S H A K E R S (3 g S A M P L E ) .
Synthetic Catalyst C Synthetic Catalyst A Synthetic Catalyst B
Nominal Size Range,

Rotap [ Cenco Cenco Aeroshak Cenco
_ _ ~ S h a k e r Shaker Rotap Shaker Shaker Flask Shaker
Shaker
~90 ........................ 0.5 0.3 30.4 29.5 29.4 13.6 14.6

75 t o 90 . . . . . . . . . . . . . . . . . . . . . 0.9 [ 0.8 19.5 18.6 17.0 13.4 14.4
60 t o 75 . . . . . . . . . . . . . . . . . . . . . 3.6 3.5 23.5 23.4 23.7 24.3 22.2
45 t o 60 . . . . . . . . . . . . . . . . . . . . . 9.3 I 8.1 15.3 15.2 16.2 22.9 18.3
30 t o 4 5 . . . . . . . . . . . . . . . . . . . . . 26.3 26.2 9.8 11.0 11.6 14.1 14.1
20 t o 30 . . . . . . . . . . . . . . . . . . . . . 24.6 ] 25.0 1.3 1.7 1.9 8.3 10.1
~20 ........................ 34.8 36.1 0.2 0.5 0.4 3.4 6.2
Shaking time, rain ............ 35 40 35 3O 40

Hammer used ................ No Yes ...
the 3-in. sieves had essentially the same Except where noted, all sieving de-
motion as 8-in. sieves. scribed in this paper was done with the
A third device, the Precision Aeroshak, Cenco-Meinzer shaker because of its con-
an air-driven flask shaker for use in ex- venience and quietness.
plosive atmospheres was cursorily tried.
By clamping the stack of sieves at a slight Sieving Time:
angle to the reciprocating upright post Several factors appear to affect the
the sample could be shaken in an even terminal sieving rate or end point of siev-
layer over the surface of the sieves. Other ing. The time required to reach an equi-
similar devices might suffice as expedient librium state depends upon the extent
sieve shakers. Typical comparative re- of blinding during the early stages of
sults using these three shakers with the shaking. This in turn depends upon the
same set of micromesh sieves are shown amount of sample taken and the size dis-
in Table X. The pattern of catalyst distribution of the catalyst, that is, the ra-
tributed over each sieve surface during tio of number of close-fit particles to the
the shaking period was studied by nest- number of meshes in the pertinent sieve.
ing a transparent ring on top of the perti- The type of shaker may produce a char-
nent sieve. It was observed that when the acteristic movement of particles over some
Cenco-Meinzer shaker was used at a cer- portion of the sieve surface causing local
D A E S C H N E R E T AL ON P A R T I C L E S I Z E D I S T R I B U T I O N 39
blinding. This would reduce sieving effi- the type of sieving motion and the pro-
ciency and increase the length of time nec- vision for continuous movement of the
essary to reach the terminal rate. Reducing sample over all parts of the sieving sur-
agglomeration resulting from accumula- face, the only requirement for sieving
tion of static charges, shortens the sieving time appears to be that shaking be con-
time, as well as contributing to cleaner tinued until equilibrium conditions are
separation. The shape of the particles has reached. I t is essential to determine equi-
a slight influence on sieving rate; spheri- librium conditions by periodic weighings
cal particles tend to pass through an made near the onset of the terminal rate.
opening more readily than those of ir- I t is necessary that all sieves and con-
regular shape which must be oriented tents be weighed because the time neces-
several times before the least dimension sary to reach equilibrium may not be the
coincides with the mesh opening. Cata- same for each sieve in the set.
lyst particles are considered to be of such
a hardness that the terminal rate of siev- Calculating and Reporting:
In converting results based upon the
TABLE XI.--SIEVING RATE OF A calibrated size of a micromesh sieve to
3-g P O R T I O N O F S Y N T H E T I C C A T A L Y S T
G ON MICROMESH SIEVES.
some common reference size, it is neces-
sary first to convert the fractions to a
Weight Per Cent After cumulative basis as "per cent finer than"
Sieve Size,
the calibrated size and then plot these
min 10 min 15 min 20 rain 25 min
values as a function of the effective or
R e t a i n e d on: calibrated opening of the sieve. By inter-
86 . . . . . . . . . . . 18.( 16.31 15.71 15.31 1 5 . 2 preting a smooth curve drawn through
74 . . . . . . . . . . 7.~ 7.91 7.51 7.41 7.5 all points, the weight per cent finer than
58.5 . . . . . . . . . 22.( 22.61 22.71 22.5j 22.5
43 . . . . . . . . . . 25.I 25.91 25.91 26.0 t 26.0 the corresponding or standard reference
32 . . . . . . . . . . 13.~ 14.1j 14.41 14.51 14.4 size may be obtained. I t is assumed that
19 . . . . . . . . . . 7.7 8.3 8.6 s.s I 8.s the method of manufacturing cracking
P a s s i n g 19 . . . . . 4.3 4.9 5.2 5.5 5.6
catalysts produces a more or less bino-
mial distribution of particles according to
ing with the micromesh sieves is inde- size. Unless some selective classification
pendent of attrition. according to size distribution has been
The magnitude of any of these factors practiced, the plotted values should all
is not great and is difficult to determine fall on a nearly straight line or continuous
accurately because the sieving rate ap- smooth curve if the per cent is plotted
proaches the terminal rate gradually and on the probability axis of either logarith-
the terminal rate cannot be clearly de- mic or arithmetic probability paper.
fined for a wide variety of catalyst sam- A desirable consequence of evaluating
ples. An illustration of the amount of primary data by graphical form is that
time necessary to sieve a 1-g sample com- defective sieves and faulty sieving may
pared to a 3-g sample is shown in Table be detected. If a sieve has blinded during
VII. This table also shows the slight in- sieving or if the calibrated value is
crease in time required to sieve a sample greater than it should be, the plotted re-
of small particles over that for large par- sult for that sieve will be somewhat to
ticles. Table X I shows the sieving rate in the left of the smooth, uniform curve. If
5-min intervals for a catalyst sample of the value lies on the right of the curve, a
average particle size distribution. broken mesh or an excessive number of
Because the sieving time depends upon large openings is indicated.
40 SYMPOSlIy~ ON PARTICLE SIZE MEASUREMENT
A frequent industrial practice has been washed, they were dried in the standard
to use even increments of 5 or 10 u in manner used before sieving. The amount
referring to particle size distribution. I t through the bottom or finest sieve was
is recommended that values obtained calculated by difference. Typical results
from precision micromesh sieving deter- of limited comparative tests shown in
minations be referred to a decimal series Table X I I demonstrate that wet sieving
of micron diameters solely for conveni- is practical. The repeatability between
ence and to maintain a distinction from duplicate tests is believed to be very
similar results by woven-wire sieves. The good, considering the fact that there is
series of sizes, 45, 60, 75, and 90 u are no way for determining the terminal rate
sufficiently close to the designated values of sieving. Although a 2.5-g sample was
of woven-wire sieves for most practical used in these tests, it is believed that a
purposes. Values based upon meshes per 1- to 1.5-g sample could be wet-sieved in
linear measure should never be used be- a shorter time and with better precision.
cause of the ambiguity. This amount is consistent with that rec-
ommended for dry sieving.
TABLE XII.--DUPLICATE PARTICLE Wet sieving is particularly applicable
SIZE DISTRIBUTIONS OBTAINED ]BY
WET AND DRY SIEVING WITH MICRO- to catalyst particles which agglomerate
MESH (2.5 g SAMPLE). excessively during dry sieving and to
stack fines which are predominantly less
Per Cent Finer Than Size
than 30 ~. It was found that there was
Sieve Size, g Wet Sieving Dry Sieving less blinding during wet sieving than dry
sieving for these types of samples.
Test l Te~t 2 __Test
1 Test2
CLEANING AND PRECAUTIONS ]~OR USE
86 . . . . . . . . . . . . . . 89.4 87.8 88.5/87.8 Micromesh sieves are precision instru-
58.5 . . . . . . . . . . . . 59.0 57.7 62.5 [ 62.5
43 . . . . . . . . . . . . . . / 31.1/ 29.9 34.5 I 33.6 ments and must be treated as such. The
i9 . . . . . . . . . . . . . . 15.212.r 4.2 I 3.5 technique used for care and cleaning of
woven-wire sieves should not be used for
the more fragile micromesh sieves. Scrub-
WET SIEVING
bing with brushes for cleaning or the use
A few tests were made to determine of assay button brushes to break up ag-
the practicality of wet sieving with the glomerates on the sieves is to be avoided.
micromesh sieves. A small hole was A sable brush may be drawn gently at an
drilled near the upper edge of each sieve angle over the mesh during wet or dry
frame in the set to prevent the sieves sieving to reduce agglomerates but in no
from becoming air-bound. The set of case should the action be such that the
sieves and the sample were brought to a tips of the hairs are caught in the meshes.
standard condition of dryness in a vac- Several procedures for cleaning blinded
uum oven, and after weighing, the sample meshes have been investigated. Strong,
was washed through the top sieve of the concentrated blasts of air or jets of water
stack by means of about 200 ml of meth- will break the micromesh from the sup-
anol, or some liquid having low viscosity porting grid and are therefore to be
and surface tension, delivered in a jet strictly avoided. Vibration of an inverted
from a polyethylene wash bottle. The top sieve by means of a pneumatic vibrator
sieve was removed and the washing pro- in a dish containing a detergent solution
cedure applied to the next smaller sieve. of water or alcohol is moderately effective
After all sieves and contents had been but requires considerable time. Slapping
D A E S C I t N E R ET AL ON PARTICLE SIZE D I S T R I B U T I O N 41
or knocking a sieve smartly on a bench with over 50 per cent open area) when
top will spring or break the fine mesh. the configuration is exactly right to in-
By far the best method of freeing the duce resonance. It is therefore recom-
sieves of blinded particles is the use of mended that ultrasonics be used as the
ultrasonic cleaners. The effect of trans- best tool with which to clean the blinded
ducers delivering ultrasonic energy at micromesh, but that pilot tests be made
40 kc and 1 Mc per sec were investigated. to develop the necessary precautions.
A single sieve was placed upside down in Meshes which have become accidently
the cleaning tank containing a sufficient broken may be easily soldered with soft
amount of isopropyl alcohol and water to solder and a pencil-point iron. A low-
TABLE XIII.--REPEATABILITY OF MICROMESH SIEVES.
Per Cent of 3-g Sample on Nominal Mesh Size
Nominal Sieve Size, ~ Synthetic Catalysts Natural Catalysts
SampleA I SampleB 1SampleC Sampled I SampleE I SampleF
MICROMESH SET No. 2
90 . . . . . . . . . . . . . . . . 29.8 29.4114.6 14.71 0 . 5 0.31 6 . 3 6.4120.6 20.6118.7 18.4

75 . . . . . . . . . . . . . . . . 15.9 17.0114.4 12.71 0.9 0.8 / 6.4 6.7/11.0 11.01 9.1 9.2
60 . . . . . . . . . . . . . . . . 24.3 23.7122.2 21.91 3 . 2 3.5116.1 15.9120.4 20.4117.2 16.4
45 . . . . . . . . . . . . . . . . 16.5 16.2118.3 18.3 7 . 9 8.1129.5 30.2122.6 25.3117.2 16.7
30 . . . . . . . . . . . . . . . . II1.1 11.6/14.1 16.9/25.6 26.2/19.3 18.7117.0 14.8/20.5 20.6
20 . . . . . . . . . . . . . . . . 1.9 1.910.1 8.224.9 25.014.2 16.3 6 . 5 6.013.3 12.0
Pan ............... 0.5 0.4 6.2 7.337.0 36.1 8 . 3 5.7 2 . 0 2 . 0 3.9 6.7
M~c~o~sH S~T No. 3
90 ................ 29.5 27.6 13.2 11.8 0 . 4 0.1 5.6 6.1 18.4 18.7 16.7 17.2
75 . . . . . . . . . . . . . . . . 20.6 23.5 17.1 17.5 1.0 0.7 8.8 9 . 0 15.6 15.5 13.4 13.3
60 . . . . . . . . . . . . . . . . 19.8 18.3 17.3 18.3 2 . 6 2.4 12.9 14.2 i 15.3 15.7 12.6 12.6
45 . . . . . . . . . . . . . . . 15.3 16.6 18.9 19.4 7 . 4 7.1 19.9 20.0 19.2 18.5 16 5 16.7
30 . . . . . . . . . . . . . . . 12.4 11.3 19.2 19.0 26.7 26.2 28.5 28 5 22.1 21.8 22.6 22.6
20 . . . . . . . . . . . . . . . 1.6 1.6 6.7 5.5 22.6 22.0 12.3 12.1 7.1 6.4 10.8 9.9
Pan .............. 0.9 1 .O 7.6 8.5 39.3 41.4 12.0 19.') 2 . 3 3.4 7.2 7.8
S t a n d a r d deviation
of r e p e a t a b i l i t y . . . 0.8 0.9 0.5 0.8 0.7 0.6
cover the sieve completely. I t was found power binocular microscope is useful in
that at peak power of 50 w the 40-kc this connection. Self-curing resins and
transducer cleaned a sieve in less than plastic cements may also be used pro-
1 min, and the 1-Mc transducer required vided they adhere to the metal, are suffi-
5 to 10 min. Since cleaning by ultrasonics ciently hard, and do not dissolve in any
is a study in itself, optimum conditions solvent used for cleaning or wet sieving.
for cleaning without any onset of cavita-
tion damage was not fully investigated. R E S U L T S ON CATALYST SAMPLES
At some combination of power and fre- Precision micromesh sieves have been
quency it is possible to produce undesir- applied satisfactorily to a number of
able cavitation damage in certain loca- fresh and used synthetic and natural
tions of some sieves (for example those catalysts. Three fresh, synthetic catalysts
and three fresh, natural catalysts were ing to the calibrated sizes (shown in
selected for application studies because Table II) and the weight percentage
these are also under cooperative study by with respect to the reference size read
the American Petroleum Institute (API) from the curves; these values are shown
Committee on Analytical Research. in Table XIV. All determinations were
made on 3-g samples, before investiga-
TABLE XIV.--REPRODUCIBILITY OF tions were completed on the desirability
PARTICLE SIZE DISTRIBUTION BASED
UPON CALIBRATED MICROMESH
of a smaller sample, consequently the
SIEVES. ~ terminal sieving rate was not reached
until after about 40 rain. After the tests
Cumulative Per Cent Finer Than
Reference Size were completed it was noticed that the
20-~ sieve of set No. 3 allowed more
Synthetic I Natural sample to pass through than was con-
Reference Particle
Size, Catalysts Cataly~t_~
sistent with the calibration. A detailed
Sam-ISam-ISam-Sam- Sa - ISam- microscopic inspection revealed an im-
ple I ple [ ple ] pie ] ple ] ple
perfect or broken mesh which would
allow particles as large as 40 or 50 ~ to
AVERAGE OF 2 DETERMINATIONS U S I N G pass. This experience illustrates the value
MICnO~ESH SET N o . 2
of making periodic determinations of a
90 ............. 72.086.799.694.080.582.5
known sample to quickly reveal a mesh
75 ............. 51.2 71.5 98.5 86.0 66.4 70.5 failure.
60 ............. 29.2 49.8 95.2 70.2147.0 55.0
45 ............. 12.029.3185.544.025.036.2 Precision and Accuracy:
30 ............. 2.012.657.518.5 7.016.3
20 ............. 0.3 5.531.0 5.0 1.1 3.0 The estimated standard deviation of
repeatability, st, and reproducibility,
AVERAGE OF 2 DETERMINATIONS U S I N G sR, were calculated 5 to show the expected
MICROMESH S~T NO. 3
difference between duplicate determina-
90 . . . . . . . . . . . . 69.7185.8199.6 93.6 9.981.8
tions on a single set of sieves and the
75 . . . . . . . . . . . . 51.2171.4199.0186.2 7.0 70.4 difference in results between two sets of
60 . . . . . . . . . . . . 28.8150.5196.0170.0 8.555.0 sieves. The standard deviations for differ-
45 . . . . . . . . . . . . 11.2]29.0185.5145.0 6.435.6
30 ............ 2.413.3]58.0]20.0 8.2 15.8 ent sieve fractions are not strictly com-
20 b . . . . . . . . . . . 072634026 1.7 5.3 parable because of the wide distributions
I according to various sizes and samples
Standard devia- ]
t i o n of r e p r o - and because fractions obtained on one
ducibility .... 0.8 0.4] 0 . 3 l 0 . 6 0.8 0.3 sieve are not entirely independent of
those on adjacent sieves. The deviations
a Distributions obtained graphically from
d a t a s h o w n in T a b l e X I I I . have been averaged to give a rough single
b V a l u e s n o t u s e d in c a l c u l a t i n g s t a n d a r d figure as a measure of the precision. The
d e v i a t i o n b e c a u s e of a b r o k e n m e s h in 20-~
sieve of set N o . 3.
repeatability standard deviations shown
in Table X I I I are independent of the
These catalyst samples were sieved in type of sample. If they are summed over
duplicate on two sets of microscopically samples for the sieve size, quantities on
calibrated micromesh sieves. The distri- all sieves have standard deviations from
bution values in per cent on the nominal 0.5 to 0.8 with the exception that the
size sieves are shown in Table X I I I . quantity in the pan is of the order of 1.3
After averaging the duplicates and con-
5 A S T M M a n u a l o n Q u a l i t y C o n t r o l of M a -
verting to cumulative per cent finer than t e r i a l s , p. 14 a n d f o o t n o t e 1 (1951). ( I s s u e d a s
the size, the values were plotted accord- s e p a r a t e p u b l i c a t i o n A S T M S T P No. 15-c.)
DAESCI-INER ET AL ON PARTICLE SIZE DISTRIBUTION 43
per cent for the natural catalysts. This sieves except in the case noted for a
is not surprising since natural catalysts broken mesh. Although the data are not
are very irregular in shape and seem to sufficient for a firm reproducibility figure,
Fla. 5.--Examples of Separations Obtained with Micromesh Sieves for Different Catalysts (X55).
accumulate the greatest static charge the maximum acceptable difference be-
during sieving. tween two laboratories at the 95 per
The reproducibility standard devia- cent probability level, a rough estimate
tion according to samples, shown in of about 2 per cent finer than a size is
Table XIV, is likewise independent of indicated. This difference of 2 per cent
sample type and when calculated for of the sample also includes errors due to
sieve size shows no difference between sampling, plotting the results, and sieve
44 SYMPOSIUI~ ON PARTICLE SIZE M E A S U R E M E N T
calibration. Such a figure is considered tion results obtained by a hydrometer-

to be excellent precision compared to the sedimentation method with those by
precision apparently obtained by other micromesh sieving. The specific limita-
methods for determining particle size tions of the hydrometer method have
distritmtions. long been recognized, and it was thought
The accuracy of the method is difficult that by use of well defined distributions
to describe because of the irregular some of the limitations might be under-
shapes of catalyst particles, especially stood or even negated by cGrrelation
those of natural catalysts. The use of equations. The use of micromesh sieves
microscopic counting and measuring has as a fundamental standard for calibrating
been considered a fundamental method. woven-wire sieves was also investigated.
Loveland (9) presents an excellent de- Figures 6 and 7 illustrate the particle
scription of the use of the microscope size distributions obtained by these two
and difficulties encountered in this appli- methods compared with those by pre-
cation. Several fractions of some of the cision micromesh sieves for four of the
samples were examined and measured, catalyst samples.
where possible, with the microscope. The h y d r o m e t e r - s e d i m e n t a t i o n
Figure 5 illustrates several samples taken method, a modification of the Biddle
at random from the micromesh sieves and Klein (10) method studied coopera-
after the terminal sieving rate had been tively by the API Committee on Analyt-
reached. The spherical shape of the syn- ical Research, shows good correlation
thetic catalyst presented no problem in below certain sizes with some of the
microscopic measurement, but to de- samples. No specific reasons can be given
scribe the irregular, three-dimensional at the present time for the lack of cor-
shape of the natural catalyst particles in relation above certain particle diameters
one or possibly two dimensions is futile. for some samples, for example the syn-
Microscopic checks of the size range of thetic C catalyst sample. The compara-
synthetic catalyst from several micro- tive curves are shown only to illustrate
mesh sieve determinations showed that the confidence which may be expected
over 95 per cent of the number of parti- from hydrometer-sedimentation data and
cles in a fraction represented the cali- the difficulties which arise in attempting
brated sizes of the respective sieves. to derive correlation factors.
About 5 per cent were less than the sieve I t has been pointed out in the section
range and none larger than the range. on "Comparison with Woven-Wire
On a weight basis the small particles Sieves" that wire sieves would show a
represented from 1 to 2 per cent of the larger per cent finer than the sieve size
fraction. This confirms the experimental because of the wide tolerance in size of
number of 2.6 per cent shown in the openings. This is illustrated by the four
third column of Table IV. A few of these examples in Figs. 6 and 7. From these
particles much smaller than the range distribution curves it appears that the
may be seen in Fig. 5. Their presence in effective size of woven-wire sieves bears
the fraction may be due to static attrac- some constant relationship to the pre-
tion or they might have been tubercles cisely calibrated micromesh sieves. If it
broken from large particles after the is assumed that the distribution curves
fraction was removed from the sieve. for the synthetic A catalyst sample are
to be the basis for calibration, the effec-
Comparison with Other Methods: tive size of the woven-wire sieves may be
A limited amount of work was under- obtained by examining the micromesh
taken to compare particle size distribu- curves to determine the micron size
which corresponds to the same weight amount through .a sieve partially blinded
per cent as obtained for the woven-wire by that particular sample. Results for
sieve. With reference to the synthetic A the natural catalyst samples D and E
catalyst curves, the effective sizes of are not shown because of severe blinding
woven-wire sieves of 88, 74, 61, 53 and 43 on the 61-, 53-, and 43-u sieves.
become 93, 82, 68, 59 and 43 #, respec- Binding is much more severe in woven-
tively. If the per cent values obtained wire sieves than in micromesh sieves be-
with the wire sieves for the other three cause there is essentially only one size of
samples are plotted against these "cali- opening in a micromesh sieve to be
brated" empirical values and interpo- blinded by the number of close-fit patti-
100
SyntheticCatalystA~ /
90
80
y rometer-SedJmentation ////~/
-- C) MicromeshSieves #~ ~..
_ ~ Woven-Wire Sieves / ~7/V
7O
=k
~- 6 o
E
50 /
._ //~//L) y/~ $.vnthetl'c
Cata/yst
B
-,~ 4 o
//-/,
.30
20
10
I t I , ,l .... I i I I I I I I I
0.5 1 2 5 10 20 30 40 50 60 70 80 90 95
Per Cent FinerThen Size
FIG. 6.--Particle Size Distributions by Three Methods for Two Synthetic Catalyst Samples.
lated at reference sizes, the distribution cles in the range offered to the sieve,
results shown in Table XV are obtained. whereas in a wire sieve there is a range
In general, the results by the wire sieves of sizes of openings, due to the large al-
which do not blind agree very well with lowable tolerance and each size can be
those obtained by the micromesh sieves. blinded by close-fit particles in the frac-
The displacement of the value for the tion on that sieve. Furthermore, the
43-# wire sieve to the left of a continuous peculiar shape of the three-dimensional
uniform curve produced by results from openings in wire sieves, especially those
other sizes indicates excessive blinding. with twilled weave in the 61-, 53-, and
With some samples this is quite severe, 43-u sieves, contribute to greater blinding
therefore any "calibration" obtained by than the square openings in one plane
comparing results only reflects the characteristic of micromesh sieves.
CONCLUSIONS and conveniently followed with an ana-

It is evident from this investigation lytical balance and the degree of blind-
that electroformed, precision micromesh ing and agglomeration followed with an
sieves when properly calibrated are use- ordinary microscope.
100
90
80
/P /
70 /,' /I, , ' %
=L 60
/x7 I / v
~ 5o
.a I .#
--~
o
4O
a. 50
(.d//" ~// - - Hydrometer-Sedimentotion
20 /y / , D 0 Micromesh Sieves
J ~ Woven-Wire Sieves
10
I , , I .... I I I I I I I I I,,,,I , , I I t
2 5 10 20 504050607080 90 95 98 99 99.5
Per Cenf Finer Then Size
Fro. 7.--Particle Size Distribution by Three Methods for Natural Catalyst and a Fine Synthetic
Catalyst.
ful as a reliable primary standard for T A B L E X V . - - C O M P A R I S O N OF RE-

SULTS F R O M W O V E N - W I R E S I E V E S
determining the particle size distribu- C A L I B R A T E D BY P R E C I S I O N M I C R O -
tion of petroleum cracking catalysts. M E S H DATA W I T H R E S U L T S F R O M
They are characterized by the following M I C R O M E S H SIEVES.
significant features:
Per Cent Finer T h a n Size
1. Micromesh sieves are available over
the entire range of particle size distribu- Synthetic Synthetic Natural
tion of general interest in the testing of Reference Catalyst B Catalyst C Catalyst F
Particle
cracking catalysts. Size,
2. The uniformity of the openings is
such that a precision of 1 to 2 per cent . >.N
is easily attainable; the accuracy, for ~ N

spheroidal particles, is equal to that by 90 ....... 86.7 85.5 99.t3 99.6 82.5 82.8
microscopic measurement. 75 . . . . . . . 71.5: 70.0 98.5 98.6 70.5 69.5
3. The micromesh openings may be 60 . . . . . . . 49.8 50.0 95.2 95.0 55.0 49.5
45 . . . . . . . 29.3 26.5 85.5 83.5 36.2 24.0
reliably measured with a microscope.
4. Because of the physical size of the Data obtained by graphic interpolation at
sieves, the sieving rate may be precisely arbitrary sizes.
D A E S C H N E R ET AL ON 1)ARTICLE SIZE DISTRIBUTION 47
5. Compared to the use of woven-wire micromesh sieves should give satisfactory

sieves, the micromesh sieves require less service with a degree of confidence not
sample and less sieving time, and, be- heretofore attainable.
cause of the uniformity of openings which
are in a single plane, the micromesh Acknowledgment:
sieves blind less and give a more accurate
The authors wish to express their ap-
separation according to particle diam-
eters. preciation to the Buckbee Mears Co.,
The micromesh sieve m a y be consid- St. Paul, Minn., for their cooperation in
ered a delicate precision instrument; the development of micromesh sieves
therefore, the technique or t r e a t m e n t and to F r a n z Ucko in particular for his
used for woven-wire sieves cannot be efforts in producing the sieves and sup-
applied indiscriminately. However, in plying a description of the manufacturing
the hands of an experienced a n a l y s t the process.
R.EFERENCES
(1) H. R. Lang, "The Physics of Particle Size tion," Analytical Chemistry, Vol. 28, p. 332
Analysis," British Journal of Applied Phys- (1956).
ics, Supplement No. 3, Vol. 5 (1954). (7) F. G. Carpenter and V. R. Deitz, "Methods
(2) Symposium on New Methods for Particle of Sieve Analysis with Particular Reference
Size Determination in the Subsieve Range, to Bone Char," Journal o/Research, Nat.
Am. Soc. Testing Mats. (1941). (Issued as Bureau Standards, Research Paper 2143,
separate publication ASTM STP No. 51.) Vol. 45, p. 328 (1950).
(3) F. G. Carpenter and V. R. Deitz, "Glass (8) J. M. DallaValle, "Micromeritics, The
Spheres for the Measurement of Effective Technology of Fine Particles," Pitman Pub-
Opening of Testing Sieves," Journal of Re- lishing Corp., New York, N. Y., 2nd Edi-
search, Nat. Bureau Standards, Research tion (1948).
Paper 2238, Vol. 47, p. 139 (1951). (9) R. P. Loveland, "Methods of Particle Size
(4) K. D. Ashley and W. B. Innes, "Control of Analysis," Symposium on Light Micros-
Physical Structure of Silica-Alumina Cata-
lyst," Industrial and Engineering Chemistry, copy, Am. Soc. Testing Mats., p. 94 (1952).
Vol. 44, p. 2857. (1952). (Issued as separate publication ASTM
(5) H. A. Benesi, R. U. Bonnar, and C. F. Lee, STP No. 145.)
"Determination of Pore Volume of Solid (10) S. B. Biddle, Jr. and A. Klein, "A I-Iy-
Catalysts," Analytical Chemistry, Vol. 27, drometer Method for Determining the
p. 1963 (1955). Fineness of Portland-Pozzolan Cements,"
(6) W. B. Innes, "Total Porosity and Particle Proceedings, Am. Soc. Testing Mats., Vol.
Density of Fluid Catalysts by Liquid Titra- 36, Part II, p. 310 (1936).
DISCUSSION
MR. HAROLD H. HIRSCHJ--I should ported by a roller bearing and by slowly

like to ask the authors why they went to rotating it and applying alcohol from a
this technique for sieving rather than squeeze bottle, each sieve was flushed in
some air elutriation or liquid sedimenta- turn. Gentle stroking with a wet sable
tion process which seems to be more or brush and vibrating the sieves were ad-
less a standard, or more reliable method. ditional effective aids. We treated the
MR. H. W. DAESCHNER (author).-- sample and the sieves at some tempera-
As I mentioned, the popularity of the ture and humidity prior to sieving and
sieving procedure is the reason we con- then followed the same technique after
sidered it--everyone has at some time sieving. Fairly repeatable results which
used it. In the micromesh sieving pro- agreed with those by dry sieving were
cedure the apparatus requires a minimum obtained.
of space and time, it is not a costly deter- MR. HOOPER.--We have been doing a
mination to make, and we believe it is little experimenting with these sieves.
much more precise and reproducible The U. S. Naval Radiological Defense
between laboratories than any other Laboratory on the West Coast has been
procedure we have so far investigated. using these sieves and they are also being
Air elutriation and sedimentation meas- tried in a number of other places at our
ured by hydrometer or pipet are influ- suggestion. We have found in wet sieving
enced by type of sample and particle to below 20 ~ we have to go to suction
size range to a greater extent than, siev- for various reasons--time required etc.
ing. This was found to be true for catalyst We have not accomplished much with the
samples. problem but we are still working on it.
MR. PETER HoopEl~J--In the wet MR. ALAN R. LUmENS?--Have the
sieving, was it found necessary to use authors heard of the Pyramid sieves?
suction? These sieves have circular openings.
MR. DAESCHNg~.--We did not do too This type of sieve was developed in Hol-
much work on wet sieving. Suction pos- land and has greater structural strength
sibly would have helped; however, by than the woven sieve.
drilling a small hole in each supporting MR. DAESCHNER.--We examined the
ring to prevent air-binding, wash liquid Pyramid screens and found that their
carried particles through the mesh ade- method of making the opening produces
quately. We chose a solvent which had a a somewhat more jagged appearance.
very low surface tension and viscosity. In comparison with most of the sieves
One assembly tried consisted of mounting which we have worked with, including
the meshes in a funnel which was sup- those produced by Buckbee Mears, they
have more of the little particles of metal
1General Electric Co., Schenectady, N. Y.
2 Director of Research, Sturtevant Mill Co., 3 President, Lukens Laboratories, Inc., New-
Dorchester (Boston), Mass. ton, Mass.
48
DISCUSSION ON PARTICLE SIZE DISTRIBUTION 49
that were attached on the side of the particles passing rigid sieves and greatest
openings. The Buckbee Mears sieve also for soft particles passing flexible sieves
has this configuration to a very slight (that is, silk or nylon). This constant is
extent but is hardly apparent in the also greater for irregular particles. There-
figures shown. fore silk or nylon sieves will have sieving
MR. R. P. LOVELA14D.4---I have seen constants three to four times those for
large size screens, which might have equivalent metal sieves. Thus silk or ny-
been experimental, whose apertures were lon sieves will have much poorer resolu-
round and very smooth, but my question tion than metal sieves.
is more theoretical, assuming we had From a few preliminary trials it would
such perfect screens. appear that the electroformed sieves
I would like to ask whether keeping have lower sieving constants or hence
the holes in one plane and having them better resolution than the equivalent
perfectly circular and accurate would be woven sieves.
of virtue. I had always assumed it would. I feel very definitely that these electro-
After hearing Mr. Whitby's paper, I be- formed sieves have a place in test sieving,
gin to doubt it. I would like him to com- particularly in the sieves under 150 u-
ment on it. We have made no tests on round hole
MR. K. T. WHI~Bu would like to sieves.
compliment the authors on this very fine MR. DAESCttNER.--I wish to comment
work. I feel the quality of this work is that we have drawn up specifications
something which should be commended between the Buckbee Mears Co. of St.
particularly. Paul, Minn. and our laboratory for pro-
I did not mention in the presentation ducing meshes as large as 150 u and from
of my paper that some studies were made 20 # down to about 5 u in addition to
with silk and nylon cloth. At the time those discussed. They are of course rigid
these studies were made four years ago metal with square openings. M y suppo-
the electroform sieves were not available. sition is that round holes will blind much
We now have several of the finer ones in more rapidly than square or rectangular
the series and have made a few prelimi- openings with the consequence of lower
nary attempts at measuring the sieving efficiency.
constants and comparing them. The re- MR. DAESC~INER (by letter).--A re-
sults are very preliminary but the indica- c e n t l y obtained set of 12 micromesh
tions are that the constants are about one sieves covering the particle size range of
half those for a wire sieve of equivalent 5 to 150/z shows that the openings are
mesh which means that the sieving rates within 1 # of the nominal size; standard
would be about double. In region 2 the deviations of openings are less than 1
slopes of the curves were flatter which for the sieves above 45 ~ and about 0.2 #
means that the electroformed sieves for those of 45 # and less. The 5- and 10-#
would have better resolution. meshes were formed on rulings of 1000
The sieve material and the type of lines per inch with open areas of 6 and 17
particle influence the region 2 sieve con- per cent, respectively.
stant greatly. I t will be smallest for rigid I t was found that powdered materials
such as catalyst stack fines, sugar, flour,
4 Eastman Kodak Co., Research Laboratories, ground inorganic salts, portland cement,
Rochester, N. Y. clay, atomized aluminum, and finely pre-
5 Assistant Professor of Mechanical Engineer-
ing, Mechanical Engineering Department, cipitated resins and polymers could not
University of Minnesota, Minneapolis, Minn. be dry sieved if particles less than 45 #
50 SYmPosIuM ON PARTICLE SIZE MEASUREMENT
predominated, because of agglomeration. 5-~ sieves even though a third of the sam-
Wet sieving of 0.5 to 1.0 g with an ap- ple was below 5 #. Nearly all the samples
propriate polar liquid or hydrocarbon, mentioned showed a distribution in
such as heptane made polar with about agreement with the Hatch-Choate equa-
100 p p m of a dispersant, was found very tion. This is believed to be strong evi-
effective. No particular di~culty was ex- dence that the sieving technique em-
perienced in sieving through the 10- and ployed was sound.
S T P 2 3 4 - E B / A u g . 1959
M E A S U R E M E N T OF PHYSICAL P R O P E R T I E S OF C R A C K I N G CATALYSTS
A REvIEw oF THE WOR~: OF API COMMITTEE ON ANALYTICALRESEARCH
]BY Louis MITTELMAN I
SYNOPSIS
The Subcommittee on Measurement of Physical Properties of Cracking

Catalysts, of the American Petroleum Institute Committee on Analytical Re-
search, has been engaged for the past six years on a study of methods of meas-
urement of physical properties. A progress report is now in the draft stage and
will present recommended terminology, methods of measurement of density
and pore volume, and tentative methods of measurement of particle size by
sieving, liquid sedimentation, and air elutriation procedures. Studies are con-
tinuing on methods of measurement of surface area, refinement and correlation
of particle size procedures, applicability of the various methods to fluid hydro-
forming catalysts, and measurement of hardness and attrition of pelleted cata-
lysts.
Fluid cracking catalysts include both such as density, porosity, surface area,
naturally occurring clays and syntheti- and particle size, as well as by chemical
cally manufactured substances. They are nature and source. The same physical
prepared and used as finely divided bulk characteristics are utilized in many sys-
mixtures with particle sizes ranging tems for correlation of laboratory and
downward from a usual maximum diam- pilot plant data with observed effective-
eter of approximately 100 ~. Within the ness in use. Thus it is important that
past fifteen years the use of fluid cata- laboratory measurements of such physi-
lytic cracking processes has been ex- cal properties be made with precision.
panded to the point where fluid cracking Unfortunately, standardized methods
catalysts represent one of the largest vol- of measurement of these properties do
umes of catalytic substances used in in- not exist. The many manufacturers' and
dustrial operations. refiners' laboratories have developed or
Fluid cracking catalysts are described adapted widely varying methods with the
in sale and purchase specifications in result that data reported by different lab-
terms of their physical characteristics oratories can rarely be correlated or di-
rectly compared. In some instances even
Tidewater Oil Co., San Francisco, Calif.; the terminology, particularly that relat-
Chairman of Subcommittee on Measurement of ing to density measurements, has been so
Physical Properties of Cracking Catalysts of the
API Committee on Analytical Research. affected by the different measuring tech-
51
Copyrights 1959 by ASTM International www.astm.org
52 S Y M P O S I U M ON P A R T I C L E SIZE MEASUREMENT
niques that the same words have an en- In this way the working panels pre-
tirely different meaning to different in- pared new methods for dry sieving, wet
dividuals. sieving, liquid sedimentation and air elu-
In recognition of the existent confu- triation. The procedures were then sub-
sion, the Committee on Analytical Re- jected to round-robin tests on reference
search of the American Petroleum Insti- samples of new and used natural, syn-
tute appointed a Subcommittee on thetic, and mixed catalysts.
Measurement of Physical Properties of The data from the first round of sieve
Cracking Catalysts on M a y 13, 1952. The tests showed fair repeatability but very
Subcommittee, whose members are repre- poor reproducibility, leading to a suspi-
sentatives of the laboratories, both of cion of discrepancies between sieves. A
catalyst manufacturers and petroleum re- second round, in which two sets of sieves,
finers, was assigned the task of reviewing one for dry and one for wet sieving, were
the terminology and the methods in use, shipped in turn to each participating lab-
of cooperatively trying those methods oratory, proved that acceptable agree-
which appeared most promising, devel- ment in results could be obtained with
TABLE I.--RESULTS OF MICROMESH SIEVING TESTS IN EIGHT

SEPARATE LABORATORIES.
Maximum Deviation from Mean, per cent

Type of Catalyst
On 90-t~ On 75-~ On 60-/~ )n 45-,~ On 30-~ On 20-~
Sieve Sieve Sieve Sieve Sieve Sieve On Pan
Synthetic A ................ +1.4 +1.8 --1,0 +0.7 +0.7 +0.2 :~0.1

S y n t h e t i c 13 . . . . . . . . . . . . . . . . +1.1 +1.6 --1.4 • --0.9 +1.2 --0,9
Synthetic C ................ -0.2 --0.3 --0.5 --0.5 :~1.8 +0.8 +1.7
Natural D ................. -1.0 +1.3 --0.6 --1.5 +2.1 --1.4 --1.5
Natural E ................. +1.2 +0.7 +0.8 --1.2 --1.4 +0.8 +0.5
Natural F .................. +1.2 -0.6 --1.2 ~:1.1 +0.5 --1.3 +1.0
oping new or revised techniques where either the dry or wet procedures provided
necessary, and recommending to the in- one set of sieves was used by all partici-
dustry definitions and methods of meas- pants.
urement which may be suitable for im- At this point the subcommittee's at-
mediate use or eventual standardization. tention became focused on the problem
One of the major problems confronting of improving sieves and sieve calibration
the subcommittee was the discrepancies methods. The National Bureau of Stand-
between particle size analyses as reported ards was asked to consider the problem of
by different laboratories. By means of a calibration and the possibility of prepar-
questionnaire circulated to the labora- ing samples of mixtures of glass beads of
tories of the members of the Committee known size ranges which could be used to
on Analytical Research, it was found that calibrate sieves. This program is now un-
a wide variety of sieving, sedimentation, der way at the Bureau and it is hoped
and air elutriation methods were in use. that standard reference mixtures of glass
Copies of many of these methods were beads will ultimately be available.
obtained and working panels were organ- At the same time a new sieve material
ized to study them and to prepare pro- came to the attention of the subcommit-
cedures which would combine the best tee. This is a nonwoven screen made by
features of each. electrodeposition in such a manner that
MITTEL1VIAN ON CRACKING CATALYSTS 53
square openings are formed in one plane. Lack of correlation, or discontinuity be-
In another paper of this symposium, 2 the tween the sieve and sedimentation data,
properties and method of use of this new and inconvenience of the mixed proce-
material, which has been named "micro- dure, led to consideration of a sedimenta-
mesh," have been described. tion technique applicable to the entire
Samples of three synthetic and three size range of the sample. The procedure
natural catalysts were subjected to round- utilizes a mold-blown hydrometer and
robin tests with micromesh sieves in eight does not require preliminary sieving.
laboratories. Sieves used by two of the As a result of the subcommittee work,
laboratories had been calibrated by there are now available a micromesh siev-
microscopic measurement, the remaining procedure, a liquid sedimentation
I I I I I Sed~'~e.y~tio.m' I II I
70
I I I I ] I IY~I/ Wov~,,-WZ~e
Ory Sieves
I
.o 5 0
4O
30
10
2 5 10 20 5 0 4 0 5 0 6 0 7 0 80 90 95 98 99
Per cent
Fro. 1.--Davison T S - 5 5 API Reference Catalyst.
ing six were calibrated by use of standard procedure, and an air elutriation proce-
samples which had been established by dure, each applicable to the entire sam-
sieve tests with the two sets calibrated ple.
by microscopic measurement. Figure 1 shows a comparison of the
Maximum deviation from the mean for averages of cooperative results obtained
each size measurement on each of the six by woven-wire dry sieving, liquid sedi-
samples is shown in Table I. mentation and air elutriation on a fresh
The first liquid sedimentation work synthetic catalyst. Micromesh sieve re-
was conducted on the fine portion of the sults obtained by one laboratory are also
sample after separation by dry sieving. shown.
2 H. W. Daeschner, E. E. Seibert, and E. D. Figure 2 shows similar data on a re-
Peters, "Application of Electroformed Precision generated natural catalyst sample and,
Sieves for the Determination of Particle Size
Distribution of Cracking Catalysts," p. 26 of in addition, results obtained with woven-
this publication. wire wet sieving.
54 SYMPOSIUM ON PARTICLE SIZE ~/[EASUREMENT
It is emphasized that the data repre- cability of the various methods to fluid
sented by these figures were obtained in hydroforming catalysts. Work so far
separate programs designed to test each completed indicates that the micromesh
of the individual methods. The woven- sieving and air elutriation procedures for
wire sieves had not been calibrated. The particle size can be satisfactorily applied
results of the air elutriation method were to these materials.
dependent upon an empirical factor in- A progress report of the subcommittee
tended to provide agreement with one is now in draft stage. It will present rec-
80 ISedimentat~onj
60
t .
o
.,~ 50
4,0
3O
20
10
1 2 5 10 20 3 0 4 0 5 0 6 0 7 0 80 90 95 98 99
Per cent
FIG. 2.--Used Filtrol SV 6679 API Reference Catalyst.
particular set of woven-wire sieves. ommended definitions of terms used in

Therefore, the curves cannot be consid- describing density, pore characteristics,
ered a measure of the degree of correla- and surface area of fluid catalysts and
tion which might be obtained with the recommended procedures for measure-
various methods. They do, however, in- ment of bulk density, fluid/zeal density,
dicate that fair correlation may be pos-
skeletal density, and pore volume. The
sible.
Other current projects of the subcom- report will also include tentative meth-
mittee include methods of measurement ods for determination of particle size by
of hardness and attrition of pelleted cat- sieving, liquid sedimentation, and air elu-
alysts and an investigation of the appli- triation techniques.
DISCUSSION
MR. K. T. WIIITBy.I----I should like to I t was mentioned t h a t a report would

ask w h a t air elutriation m e t h o d is used be issued soon on various methods of
here. particle determinations. Will t h a t be
MI~. H. W. DAESCHNEI~3--The air available to others and how m a y a copy
elutriation procedure used in this s t u d y of the report be obtained?
was essentially the P. S. Roller m e t h o d 3 MR. B. J. HEINRICI-I~ (for the author).
b u t with modifications proposed b y G. Yes, this report is now in process of
L. M a t h e s o n ~ to reduce a t t r i t i o n and being prepared and within the next 60
dissipate electrostatic agglomeration. days the Division of Refining of the
These modifications were confirmed b y American P e t r o l e u m Inst. as well as the
F. E. I v e y 5 who further proposed the catalysts manufacturers who are mem-
use of a correction term based on a com- bers on this subcommittee will be letter
pacted density figure of the sample in ballotted. This is a progress report pre-
computing a " t r u e " size basis. Such a senting preliminary versions of methods
m e t h o d is now k n o w n as the Corrected which are expected to be the bases for
Air Elutriation (CAE) procedure. There development of standards in the Ameri-
m a y be other modifications of which I can Petroleum I n s t i t u t e for contractural
a m unaware because we did not t a k e p a r t relations dealing with purchasing of cata-
in this phase of the work. lysts. This is one case where the petro-
MR. DONALD PASTER.L-In the filter leum i n d u s t r y is the consumer. I t should
field we supply glass beads in various eventually be a s t a n d a r d both with re-
grades. If these are not available from spect to definitions, terms and methods
other sources we a t F r a m Corp. do sup- of measuring the physical properties of
p l y glass beads in 10-u increments from cracking catalysts. T h e r e p o r t can be
a p p r o x i m a t e l y 15 ~ on up to 60 #. obtained from the American Petroleum
1Assistant Professor of Mechanical Engineer- Inst.
ing, Mechanical Engineering Department, Uni- I do w a n t to t h a n k Mr. Daeschner for
versity of Minnesota, Minneapolis, Minn. answering these questions t h a t were
2Chemist, Shell Development Co., Emery-
ville, Calif. directed a t me.
s p. S. Roller, "Measurement of Particle Size MR. HAROLD H. HIRSCH.S~I have
with an Accurate Air Analyzer: The Fineness
and Particle Size Distribution of Portland Ce- been wondering w h y the a u t h o r did not
ment," Proceedings, Am. Soe. Testing Mats., also use the Sharples micromerograph to
Vol. 32, Part II, p. 607 (1932); Journal, Am. cross check the different screen tech-
Ceramic Soc., Voh 20, p. 167 (1937).
4G. L. Matheson, "Modifications in the niques. So far this device has not been
Roller Analysis for the Determination of mentioned for analyzing particle size dis-
Particle Size Distribution," presented at the tributions. I have not personally used
27th Annual Meeting of the API, Nov. 10,
1947. this instrument, b u t it is m y understand-
5 F. E. Ivey, Jr., "The Particle Size Analysis ing it gives v e r y reliable results. Among
of Fluid Cracking Catalysts," Petroleum Re-
finer, Vol. 30, Nos. 6, 7 and 9 (1951). Phillips Petroleum Co., Bartlesville, Okla.
GSupervisor, Applied Research, Fram Corp., s Powder Metallurgist, General Electric Re-
Providence, R. I. search Lab., Schenectady, N. Y.
55
its valuable features is an arrangement tion below about 20 ~. In 189 hr sedimen-

for deagglomerating powder clumps just tation in isopropyl alcohol at about 80
before the analysis takes place. F one can obtain the distribution down
MR. DAESC~NER.--The Micromero- to 15 ~. Below that the quantities are
graph was not cooperatively investigated generally rather slight and we were not
because very few laboratories had it, and particularly interested in breaking the
those that did found that it was not too fraction down to any finer sizes.
applicable to catalysts which accumu- MR. HUNT.--Does not the hydrometer
lated a very high static charge during the method fail when attempts are made to
test. The method is essentially air sedi- determine particle sizes as large as 90 #,
mentation through a long column of dry because of the very short sedimentation
nitrogen atmosphere onto a servo bal- time?
ance pan. It was found that some cata- MR. DAESCHNER.--Two methods were
lysts would be recovered on the pan to tried: the first on the so-called subsieve
the extent of 40 per cent, and others to sample. In this method, the sample was
70 per cent. The fraction recovered ap- sieved through an 88-~ sieve and that
pears to decrease as the particle size de- portion used for the determination. How-
creases; antistatic additives relieve the ever, most samples of catalysts have but
situation only slightly. It was difficult a small fraction above 90/~ and it was
to determine what happened to the found that by taking a whole sample we
portion that was not recovered and what could obtain a distribution comparable
particle size that portion represented. to that of the sub-sieve sample. In about
Undoubtedly much work could be done 30 sec time of sedimentation, all the por-
with this instrument to improve its ap- tions above 90 ~ had settled out, so no
plicability since it has many factors distribution above that was obtained.
recommending it. There is apparently no influence on the
MR. CHARLES M. HUNT.9--The hy- sedimentation rate of the smaller parti-
drometer method seems to have been cles due to the presence of a moderate
used for comparison in both of these last amount of larger particles. By using a
two papers and with particle sizes ex- more viscous sedimentation liquid dis-
tending up to about 90 it or thereabouts. tributions of the coarser fraction may be
Do either of the authors happen to obtained.
have an idea what the sedimentation MR. HARRY F. OGDEN, JR.l~ want
time for that general particle size range to thank Mr. Hirsch on his kind remarks
would be? on our instrument.
MR. DAESCHNER.--Yes, we did ex- I would like to point out that we do
tensive work with the sedimentation have several of these instruments being
method. About 1 to 189 hr was suffi- used by petroleum people for catalyst
cient to determine the range of primary distribution curves and we are able to
interest. We were not particularly in- get down to essentially 5 ~ in short
terested in getting the precise distribu- periods of time in the neighborhood of 5
to 10 min.
9 Chemist, National Bureau of Standards,
Washington, D. C. lo Sharpies Corp., Philadelphia, Pa.
S T P 2 3 4 - E B / A u g . 1959
Preg*ented at the
S y m p o s i u m on Light Microscopy
Held at the Fifty-F.ifth Annual Meeting
American Society for Testing Materials
New York, N. Y., June 25, 1952
METHODS OF PARTICLE-SIZE ANALYSIS 1

:By R . P . LOVELAND2
Particle size is a generic term and em- COUNT METHOD

braces a wide range of sizes of matter. Principle:
In this discussion it will be limited to
those sizes that will pass t~arough the The principle underlying the deter-
common commercial sieves. Of the many mination of the average particle size by
methods for determining particle size, the count method is simple. A volume of
only a few are fundamental, that is, do fluid containing a known weight of dis-
not require calibration by other methods. persed material is taken and the number
The microscopic method is one of these of particles in it are counted under the
few. This discussion will be restricted microscope. The weight of material is
to this method. Although in the liter- then merely divided by the number of
ature its only value is stated to be as particles to obtain the weight of the
a calibration method for other methods, average particle, ~). If the density is
and it is more laborious than some other uniform throughout the particle disper-
methods, nevertheless it is being used as sion, the volume of the average particle
a routine method of measurement in is obtained by dividing the average
many places. Measurement of the image weight by the density of the dispersed
of a particle with a rule seems very di- w
material, ~ = - . In practice, if the
rect compared with the measurement of p
a physical property correlated with the material is a powder, the known mass is
size and it gives a sense of validity. obtained by weighing it out, and if it is
an already dispersed suspension, by
Two General Microscopic Methods: chemical or physical analysis. Tl~/e ma-
terial must be uniformly dispersed in a
There are two general microscopic vehicle and made up to a known volume.
methods for the determination of particle An aliquot of this volume is then taken
size: (a) the count method, with which and the number of particles in it counted.
the average particle size can be obtained, There will be experimental error in the
and (b) the direct measurement and results, but at this point there are no
classification of each particle whereby serious limiting assumptions, such as the
the frequency of the distribution of the one that is introduced by the shape fac-
various sizes can be obtained, that is, tor. It is preferable therefore to leave
the size-frequency curve. the expression of the average partMe
1 Communication No. 1499 from the Kodak Research
size as is, that is, as the mass of the
Laboratories. average particle or as its volume. How-
2Research Laboratories, Eastman Kodak Co., Roches-
ter, N, Y. ever, it is frequently desired to express
57
58 SYMPOSllr~ ON PARTICLE SIZE MEASUREMENT
particle size by a linear dimension. It is came the paraboloid condenser, followed

necessary to assume some shape at once by the cardiold dark-field condenser, and
if a linear measure is to be used, and it is finally dark-field condensers became
usually expressed as a diameter; that is, available that allow the use of oil-im-
the assumed shape is usually that of a mersion objectives with full 1.30 N.A.
sphere. This assumption may or may not completely inside the cone of illuminating
be very accurate and the difficulties light.
usually begin at this point. Incidentally, The constituent of "ultramicroscope"
this measure is the D diameter of Perrot is present in dark-field illumination be-
and Kinney (1)3 and of Henry Green (2). cause of the difference between the re-
This count method is also the so- solving power and the detecting power
called "ultramicroscope method," first of the microscope. The resolving power is
a limitation in making measurements of
microscope images according to the well-
k
known ratio, (2~N. A.)' but the detecting
power, merely to see whether a particle
is present or absent, is limited by an
entirely different set of factors: difference
in refractive index, contrast, and il-
lumination intensity. It has been stated
(3) that the presence or absence of
particles can be detected down to a
diameter of 5 m~ in an efficient dark field.
However, the dark field is not efficient
for very fine particles if there are some
coarse ones present, because of this
factor of contrast and the scattering of
large amounts of light by the large par-
FIG. 1.--Zsigmondy Ultramicroscope. ticles. Since many more fine particles
are included in the count method than
applied by Zsigmondy using his method would ]3e included by measurement in a
of dark-field illumination (Fig. 1). By size-frequency determination, it is not
this method, a volume of suspension is surprising that the average particle size
observed by looking down a microscope obtained by the count method is usually
at a ribbon of light entering the suspen- smaller than that from a size-frequency
sion from one side through a slit. But determination. In fact, one of the weak-
since the only light observed will be that nesses of this method is that, below
scattered at right angles, a very intense resolving power, at least, extraneous
light source is required for this method particles, that is, dirt, cannot be dis-
of illumination. When light is scattered tinguished from those belonging to the
by a suspension, the greatest fraction is system under observation. The count
scattered forward in the same direction method for determination of average
as the original beam and more efficient particle size, however, is not tied to
dark-field illumination devices have been dark-field illumination nor to the deter-
designed to utilize this principle: First mination of the size of very fine particles.
3 The boldface numbers in parentheses refer to the It probably is not used sufficiently under
llst of references appended to this paper, see p. 85.
LOVELAND ON PARTICLE SIZE 59
low-power bright-field conditions, when one remainder. Then by use of nomo-

only the average particle size is wanted. graphs that he provides, it is possible to
identify the exact distribution applicable
Method of Counting: and hence the average number of par-
When dark-field illumination is used, ticles per square, ~. This procedure is
the field appears like the night sky, full of so much faster than the usual count
stars but with a grid of squares super- method that many more particles can
posed on it, as one looks down the be counted in an equal time and, since
microscope. The latter must correspond the accuracy is proportional to the square
to known areas by calibration. A depth root of the number counted, more ac-
dimension along the microscope axis curacy is obtained in equal time. That is:
may be necessary to determine the vol- 1
ume, or the particles from the aliquot Error (in ~ ) - ~ . . . . . (2)
volume may now be lying in one plane.
The particles per unit area of field may where:
now be obtained by simple count. How-
ever, this is difficult to do if the particles N = total number of zones counted and
are in Brownian motion, and it is not so = true average number of particles
efficient as the snap count method. For per zone.
this method, the dilution must be s u c h Practical Methods and Techniques:
that by instantaneous observation one
can note whether there are none, 1, 2, 3, One means of reducing operator fatigue
etc., particles per square. What is wanted resulting from prolonged use of this
is the average number of particles per method is the use of binocular observa-
square, that is, the average number of tion in the microscope or projection of the
particles per aliquot volume of the field as in a Euscope. Electronic counting
original sample. (S) is even easier and is much faster.
I~ 1932, Tippett (4) proposed a most The exact technique involved depends
useful modification of this snap count largely on the method of holding the
method. The frequency of occurrence of sample that is being counted and on the
particles per square is expressed by the method of determining the elementary
famous Poisson probability law. volume of the sample. This method
--8
varies with the order of the particle size.
m e- ~ ........... (1) If the particles are relatively large, the
grating can be engraved on the slide and
the elementary volume is determined
where:
physically by causing an excess to over-
n~ = frequency of s particles per zone flow from the cell in the slide. The
and particles frequently sediment into a
r~ = average number of particles per single layer. Examples of such cells are
zone (observed). the Sedgewick-Rafter cell with a depth
Hence, it is only necessary to determine of 1 mm and the haemacytometer type
one parameter, ~, to identify the exact of cell with a depth of 0.1 ram.
mathematical expression that applies to If the suspension is one of very fine
the case under consideration. Tippett particles, the Zsigmondy ultramicro-
advises making snap counts as usual of scope may be used. Here the depth of the
0, 1, 2, and 3 grains observed per square sample volume is that of the ribbon of
but throwing all higher frequencies into illumination, as determined by the slit.
60 SYMPOSlIY~ ON PARTICLE SIZE MEASUREMENT
The latter can be temporarily revolved so be solved and the meetings chiefly dealt
that what is normally the depth dimen- with suggestions for accomplishing this.
sion can be determined by measurement Some type of electronic memory or cal-
across the field. The limits are not sharp culating device will normally be included.
and therefore the dimension is not so Most designers hoped to measure size
accurate; moreover, this instrument lacks distribution as well as concentration of
illumination efficiency, as already men- the particles. For instance, some methods
tioned. This method, however, is the allow a sharp and adjustable limit to the
most convenient one for many samples, smallest particles included in the count.
especially aerosols, and the cleansing If the whole process is very rapid, Cooke-
of the cells is not so difficult as it is in Yarborough suggested that a series of
competing methods. counts could be made with a constantly
An ingenious solution of the sample decreasing lower limit of included particle
problem for the ultramicroscope, includ- size so that the cumulative size-frequency
ing determination of the elementary distribution would be obtained. Roberts,
volume, is in greatly diluting the sample Young, and Causley (8) have since de-
and moving the liquid under the micro- scribed further development of their
scope so that a large volume is put "flying spot microscope" for particle
through, which now can be independ- counting. They split the beam with a
ently and accurately measured by simple birefringent crystal into two polarized
means. The depth of the cell below the beams giving adjacent spots that control
objective should be limited to the depth two separate phototubes.
of focus. With this procedure, the scin- The quartz cell that is sold for use
tillations of light produced by individual with the cardioid condenser is usually
particles can be observed and recorded by recommended for dark-field counts (as it
an electronic counter. Great claims (5) is in the ASTM report on this method
have been advanced for the speed and by Allen (9) and his committee). A com-
accuracy of this method; for example, mercial cell hasa depth of 2 ~, and the top
that it takes 0nly a few minutes to make and bottom are not plane parallel. The
a determination. author had some cells polished so that
A more efficient electronic method is they were plane parallel and had a depth
one which possibly may become the of 10/~ and he also obtained similar cells
simplest of all to operate even though it from Zeiss before the last war. The per-
necessarily involves very elaborate and .centage error of depth determination
expensive apparatus. This is the auto- using these was appreciably less. The
matic counting of particles, lying in a method generally recommended for de-
field, by a scanning beam of very minute termining depth of these cells is by dif-
cross-section, utilizing television prin- ferehtial focusing of the microscope. Our
ciples. There are at least four different experienco substantiated Allen's state-
types of methods for doing this. Two ment that the reproducibility of the
meetings held in England on this subject method is poor because the eells could
have been reported upon by Walton (7), not be reassembled accurately to the
who appended a valuable bibliography. same depfh and with the top and bot-
Some speakers reported instruments that tom plane parallel. Also, the determin-
were in operation; others that instru- ation of depth is slow. It should be pos-
ments were under construction. How- sible to determine the depth quickly,
ever, for satisfactory general application each time the cell is assembled.
some fundamental problems have yet to The contour and channeled spectrum
L O V E L A N D ON PARTICLE SIZE 61
interferometers are two instruments cases lies within ~. The pattern of the
with which in a few minutes not only the
parallelism of the top and bottom of the interferometer is then marked on the
ceil can be determined but also the depth top of the cell with a sharp crayon, and
of the cell. Before observation in the the ceil is transferred to a channeled
interferometers, the bottom of the as- spectrum interferometer where its depth
sembled cell is quickly painted black on at a given point within the marked band
the bottom with a thick film that later can be determined within a few minutes.
can be pulled off easily. The cell is then The principles of the channeled spec-
placed on a contour interferometer of trum interferometer, Fig. 4, and its ap-
A H-3 lamo
B
E )Lens
C Pinhole with diffuser
D Wratten 77A filter
LJ
/ i j I ~" "~" ~
I
-~ .~ f 1 / t ~ ' ~
I
-i
[
A B c D E
FIG. 2.--Contour Interferometer.
the type shown in Fig. 2, where parallel plication to the rapid determination of
monochromatic light is reflected down the depth of the assembled quartz cell
Onto the cell. Examination is made with just before a particle count has been
a 48-ram objective. Sometimes a dust described by Gamble and Pfund (10).
particle is included on one side and causes However, they used it with transmitted
a wedged cell, Fig. 3(c). The width of illumination so that a semireflecting
each band represents a difference in mirror of platinum had to be plated on
k the cell surfaces. The equations can be
depth of ~ which, with the mercury green re-derived to fit the measurement of the
line, is 0.55 p. Obviously, a cell assembled depth by reflected light. This method is
thus is of no use, but assembly can be considerably more convenient when the
repeated until a good one is obtainedl cell is filled with liquid; it requires no
Fig. 3(a). Most of the area in these two semitransparent metal plating. The cell
62 SYMPOSlIIM ON PARTICLE SIZE MEASUREMENT
FrG. 3.--Interference Pattern. Three cell assemblies,
FI~. 4.--ChannelSpectrum Interferometer

with its temporary black bottom is I n this photographic method, the depth
placed under the microscope illuminated of the cell must be small to include all
by white light through a vertical il- particles, although they need not be in
luminator, and the image beam is fed perfect focus. The use of dark-field or
into a spectrometer. A second line spec- bright-phase illumination allows detec-
trum such as that obtained with a tion when particles are not in perfect
hydrogen arc is used for wavelength focus.
calibration. Upon looking into the spec- Another problem is that of cleaning
trometer, the white-light spectrum can the quartz cell, especially when many
be seen crossed with many black lines. samples are to be counted.
The number of black lines between two
Coating Method:
predetermined wavelengths of the spec-
trum are counted. The thickness of the In these Laboratories, the samples are
cell is obtained by multiplication of this now prepared for particle counts by
number, n, by the factor, F, previously coating on plates. This has proved the
determined. best method, especially when there are
many samples for analysis. Only aqueous
t = gn--X~ - n . F .... (3) dispersions have been coated by this
X0 -- X~ method. The principle is again simple. A
definitovolume of the suspension is coated
where:
over a definite area on plate glass slides
g = refractive index of liquid in cell, that are exactly 2 by 5 in. Only the area
n = number of dark lines between X0 under the microscope need be deter-
and X=, and mined, the depth factor having dropped
t = thickness of assembled cell. out. Since plates are dry and permanent
The count method using the quartz many may be made at the time of
cell has disadvantages, one of them being sampling and counted at convenience. If
the Brownian motion which the fine the simple equipment needed is readily
particles exhibit during counting. La- available, actually less time is consumed
guarta (11) (1943) and~others have sug- per sample.
gested interrupting the illumination A constant area of coating must be
beam to the microscope with a pendulum obtained since it is one of the constants
and have declared that snap counts are in the formula for concentration and
easier to make thus in the presence of average particle size; errors in the latter
Brownian motion. The Kodak Labora- will be proportional to errors of the
tories have successfully used a xenon coating. To maintain the constancy,
flash lamp to stop the motion; the par- there must be either no edge defect or a
ticles can then be counted directly from constant one. One difficulty is that the
the photographic negative. A series of coating solution may wet to the edge but
such negatives on roll film, one for each withdraw variably upon drying. To
field, is most convenient. There is overcome this, a c9ating solution should
insufficient exposure for a dark-field be used which will set first and then dry.
picture at very high magnification with A 1 per cent solution of de-ashed gelatin
present xenon arcs. Lower magnification is used in these Laboratories.
at high aperture on 35-mm film, which is The coating method is successful only
used for projection during counting, or when a skilled coating technique has been
use of objectives giving bright phase used and excellent equivalent areas ob-
contrast should eliminate this difficulty. tained. By equivalent area is meant the
64 SYMPOSIIJ~ ON PARTICLE SIZE MEASUREMENT
area equivalent to the one which would be good wetting agent. A solution of a com-
obtained if the coating were of commercial, nonionic wetting agent, Pluronic
pletely uniform concentration to its very F-68, is satisfactory for this. There is
edge which might not coincide with the also a rigidity factor. If a little Diolin
edge of the glass. Some wedging at the (12-hydroxyoctadecyl alcohol) is in-
edge is obtained invariably, although it cluded in the coating solution, the coat-
may be very small. The equivalent area ings show less tendency to withdraw from
is determined by making grain counts in t h e edges in drying. The Diolin must
checkerboard fashion over the plate for first be solubilized in Pluronic solution
calibration. The special factors involved before the two are added to the coating
are principally (a) cleaning of the slides, solution. But the slightest excess of Dio-
(b) skill in coating, and (c) formula for lin, as determined by a permanent tur-
spreading. bidity, causes the formation of repellency
Cleaning the glass plates so that they spots; this determines the upper limit
will wet uniformly and yet not be of its concentration.
etched requires care. Although a solution
of potassium dichromate and concen- PREPARATION OF SAMPLES
trated sulfuric acid is usually recom- Microscopists, whether they are biolo-
mended, it is really very poor for the gists or chemists, agree that the prepa-
purpose. Few people realize how strongly ration of the samples is the most im-
chromic oxide is adsorbed to glass. After portant and the most time-consuming
plates cleaned with this solution have phase of microscopy and requires the
been washed in tap water up to 15 rain, most expert knowledge of the field.
a poor dark-field is obtained in strong In this paper, the preparation of
illumination because of the haziness pro- samples for the count method of particle
duced by the residually adsorbed salt. size determination has already been
We now use a 2 per cent solution of potas- discussed briefly. But before determina-
sium persulfate (K~S~Os) in concentrated tion of size-frequency distribution is
sulfuric acid. It is a remarkable cleansing discussed, this important subject of
solution but must not be used longer sample preparation deserves greater con-
than 2 to 5 min, because of the danger of sideration.
some micro etching on even selected The subject may be classified and sub-
glass. The persulfate solution loses its divided in either of two ways:
efficiency after it has more than 5 per 1. By the as-received condition of
cent water in it. After 2 or 3 rain in the samples, dry or in suspension.
acid, tile plates, which are usually held 2. By the dispersion vehicle used,
in an all-glass rack, are washed in tap aqueous or nonaqueous.
water for only a few minutes, given a The aqueous method has already been
distilled-water rinse, and dried in a warm discussed to some extent; vehicles are
oven in a desiccator over Drierite. If needed such as gelatin or polyvinyl
transferred to a dry glass rack, they alcohol from a high-viscosity vinyl ace-
usually dry within 30 rain and can be .tate (V80).
stored in the desiccator if the latter is
free from grease. The desiccators are
Dispersing Agents:
made from museum jars with a glass or A dispersing agent is usually needed. A
plastic cover fitting by gravity on the few general principles regarding these
well-ground top. must be kept in mind. There are four
The coating formula must contain a types of dispersing agents, which belong
to the general type of surface-active pounds are usually listed and discussed
agents: under the former classification.
1. Anionic The microscopist searching for a dis-
2. Cationic persing agent for a nonaqueous system
3. Ampholytic (internally linked) will find less pertinent literature on this
4. Nonionic subject, although there are several
It is well known that the first and papers (IS, IS, 17) listing results with
second types cannot be mixed and nor- various compounds in this application.
mally should not be used in the same It is not surprising that using different
solution. While the first type is more powders and different vehicles Kodak
common, the second is sometimes Laboratories found the effectiveness of
preferable. For instance, the best dis- agents to be in a different order from
persions of rouge in polyvinyl alcohol that listed by Damerell, el al. (16, 17).
were obtained with Triton K-60 (cat- In this case, oleic acid and the lauryl
ionic) as the dispersing agent. A quick ettler of polyethylene glycol have been
determination of the natural charge of found to be among the best general dis-
the particles in an electrophoresis ap- persing agents for nonaqueous systems
paratus can be helpful in selecting the and are among the agents tried first on
dispersing agent, if such equipment is new systems. The latter compound is a
readily available. nonionic agent, many of which are help-
If extensive work with many different ful in nonaqueous systems.
kinds of materials is to be undertaken, Some beta-ines, which belong to class 3,
the worker should become at least have been found to be among the best
generally familiar with the subject of dispersing agents in certain aqueous
surface-active agents. A good short re- systems.
view, principally covering types 1 and 2 Aqueous Mounts:
listed above, is given by Snell (12). An
When a microscope sample is prepared
excellent alid much more comprehensive
from an aqueous system using polyvinyl
treatise is that by Schwartz and Perry alcohol as the vehicle instead of gelatin,
(13). Since most surface-active agents the smear or coating can also be dried
may have to be obtained commercially down to a film. It is advantageous to
under their trade names, a list, such as observe such samples without a micro
that furnished by McCutcheon (14), of cover glass. Oil-immersion objectives can
the type and characteristics of most of be used directly on such dry coatings
the commercial surface-active agents ac- with negligible deterioration of the
cording to trade names, is of great service. image. For observation with a high, dry
All good dispersing agents are prob- objective, metallographic objectives are
ably wetting agents. However, the best most suitable if the correct tube length
general wetting agents are often not the for the objective is used, since such ob-
best dispersing agents. Conflicting state- jectives are corrected for use without
ments have been given concerning the cover slips. The objectives that are cor-
rected for infinite tube length are not so
relationship between the characteristics
easily used; the others can usually be used
suitable for these two functions. On the
with a metal spacing ring.
whole, a very close relationship can be Sometimes a liquid mount is more con-
expected between good detergents and venient or more valid, especially when
dispersing agents, and the available corn- the sample arrives as an aqueous dis-
66 SYMPOSIIY~ ON PARTICLE SIZE MEASUREMENT
persion. When the sample arrives as an baryta, the addition of 0.15 g of

aqueous dispersion of oil droplets, the Duponal WA in the 5 ml of stock solution
simplest procedure in this laboratory gave excellent dispersions that jelled in
has proved to be that of pressing a drop 5 min. Excellent slides of well-dispersed
of the sample, diluted if desirable, be- samples have been made by this method.
25
tween a microscope slide and a cover The refractive index of the mount, n , ,
slip and making photomicrographs of it is also 1.43.
at 1000 X magnification by phase micros- With liquid or wet gel mounts, it is
copy, using a xenon flash lamp (exposure advantageous to ring the cover slip with
1 a protective adhesive, that is, a thermal
time, 3 - ~ set). Sharp images of the
cement, not only to make a permanent
vibrating droplets are obtained, but if mount but to prevent flow to one side
the oil droplets are very fine they will through local evaporation. Manual ring-
rarely lie in one plane. Such photomicro- ing of the cover slip with melted sealing
graphs can be made on a horizontal mixture using a nichrome rod flattened at
bench with a vertical stage without one end has been found quite satisfac-
difficulty. tory. When many such samples are made,
Stoppage of Brownian motion in an it is more convenient to stamp the sealing
aqueous mount by the gelatin of the compound around the cover slip with
mounting medium is the more common the end of a metal tube. The following
method. Glycerin jelly (n~5 = 1.43) is formula proposed by Fant (ls) cools to
much used in biological preparations. a relatively hard seal:
Glucose with relatively fresh pectin (such 4 parts anhydrous lanolin
as Certo) is a satisfactory and fast- 8 parts rosin
jelling mixture and can be added to some 1 part dry Canada balsam
aqueous systems without otherwise dis- The ingredients are melted and mixed.
turbing them. The resulting gel has very Abopon (glycerin bori-phosphate, n~'
weak tensile strength and cracks easily = 1.44) is especially useful as an aqueous
under the cover slip. This tendency can mounting medium, since it jells to a
be reduced by using corn syrup instead stiff glass and is colorless. In fact, it is
of glucose. It can also be reduced by the transparent down to and including a
addition of a little glycerin to the wavelength of 254 m~ and is one of the
formula, but with baryta, at least, this few satisfactory mounting media that
causes some clumping of the particles. can be used for photomicrography with
A stock solution is made as follows: far-ultraviolet light.
Glucose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 g
Water ............................. 10 m l Viscous Shear as a Dispersing Agent:
Dispersing agent .................... x g
Often the problem in sampling is to
After the sample is thoroughly dis- disperse the material of the sample uni-
persed in some of this stock solution, formly to its individual particles without
fresh pectin (Certo) is added: breaking them to still smaller individuals.
G l u c o s e s t o c k solution . . . . . . . . . . . . . . . . 5 ml This must be done by controlled physical
Cert~ .............................. 3 ml work. In 1926 Wiegand (19) made an
The setting time, somewhat affected important contribution when he milled
by the concentration of the dispersing samples of zinc oxide in rubber. This was
agent, can be adjusted by altering the followed up by Allen (20) in 1930 and
proportions, which are quite critical. For Gehman and Morris (21) in 1932, who
L O V E L A N D ON P A R T I C L E SIZE 67
developed what has become a recognized tube by an amount considerably larger

and recommended method. Viscous shear than any individual particle. The wooden
seems to be the ideal force to tear clumps roller or the toothpick is a very important
apart without breaking down the par- specification, as can be illustrated with
tides. Deciding that this principle could an example. Calcium tungstate forms
be indefinitely generalized, we used cel- exceedingly brittle crystals. When these
Fla. 5.--Laboratory Mill for Dispersion by Viscous Shear.
lulose acetate dope and similar viscous were prepared by dispersing on a slide
sticky materials with excellent results. with a glass rod or rubber policeman, in
This principle can be used in a laboratory some vehicles the crystals were largely
mill or the sample can be milled by hand broken up (Fig. 6(a)). I t was then de-
with a toothpick in a concave micro- cided to use wood as a softer material
slide. The mill shown in Fig. 5 uses a and to paint the dispersion onto the final
wooden rod s clearing the precision glass
slide with a brush. As a result, the broken
4 It is worth while insuring that the rod is very straight,
as by cutting it in a lathe, and that the clearance is rela- crystals were a negligible fraction (Fig
tively small. The liquid vehicle must wet the rod so well
that it tends to stick to it. 6(b)).
68 S Y ~ o s i z r ~ ON PARTICLE SIZE MEASUREMENT
I.
Nonaqueous Dispersions: piastieizers have been chosen from

During an ASTM cooperative project, those useful with a given polymer so
a microslide was sent to the Kodak Labo- as not to ~ lower the refractive index.
ratories of zinc sulfide dispersed in bal- The plastieizers somewhat increase the
sam. After glancing at it through the wetting action toward glass. When a
microscope, we were forced to put it away preparation without plasticizer is stored,
for some weeks before undertaking the the cover glass may snap off after weeks
analysis. When a powdered sample is or months of 'storage, because brittleness
dispersed in a solution of resin, then of the polymer increases with time.
mounted between a glass slide and its In all cases, the preparation is made
cover slip, the center of the preparation with a partial polymer that can be pre-
may contain solvent for a long time. In pared ahead of time and kept for days
fact, after some time, the particles in or even weeks in the refrigerator. The
this case were found to have become foo monomer is polymerized to a suitable
clumpecLto allow use of the sample. Be- viscosity to allow effective viscous shear
cause of this incident, we have adopted and less contraction in preparation of
T A B L E L - - R E S I N S S U I T A B L E FOR M O U N T I N G M E D I A F O R M E D B Y P O L Y M E R I Z A T I O N .
Polymer Plasticizer, Plasticizer

Polymer Plasticizers
% per cent %
Polyvinyl acetate . . . . . . . . . . . . . . . . . 1.466 Acetyl triethyl citrate 1. 468
Polyisobutyl methacrylate . . . . . . . . . 1.477 Castor oil (water-white) 1.477
Poly n-butyl methacrylate . . . . . . . . . 1,483 Butoxy ethyl phthalate 1.482
Polyethyl methacrylate . . . . . . . . . . . 1. 485 Dibutyl phthalate 1.490
Polymethyl methacrylate . . . . . . . . . . 1.50 Diethyl phthalate 1.502
Bioplastic a .. b. . . . . . . . . . . . . . . . . . . . 1.554 Aroclor 1242 1.628
Paraplex P-43 . . . . . . . . . . . . . . . . . . . . 1,556 Aroclor 1242 1.628
V i b n n 142 c . . . . . . . . . . . . . . . . . . . . . . . 1.581 Aroclor 1242 1,628
Polystyrene . . . . . . . . . . . . . . . . . . . . . . . 1.60 Aroclor 1242 1.628
or
a-chloronaphthalene 1. 633
a Sold by Ward's Natural ScienCe Establishment, Rochester, N. Y.

b Sold by RShm & Haas, Philadelphia, Pa.
c Sold by The Naugatuck Chemical Co., Naugatuck, Conn.
polymerization of a solvent rather than the powdered sample and then, after
evaporation as a means of setting or incorporating the sample and mounting
solidifying our nonaqueous mounting it between slide and cover glass, the
media. polymerization is "carried on until a
solid mount is obtained. The best dis-
Use of Polymers: persion is obtained when the subsequent
polymerization is as rapid as possible. For
The choice of polymer (see Table I)
this reason, an accelerator and more
is largely governed by the refractive
catalyst are added at this stage. Dispers-
index of the sample, since there should be
ing agents also may be incorporated.
a reasonable difference in refractive index
Oxygen and many metals are inhibitors
between the sample and the mounting
of polymerization to greatly varying
medium if sufficient contrast is to be ob-
deg?ees.
tained. The ability to wet glass some-
The chief disadvantage of this method
times affects the choice. The polymers is the difficulty of getting a finely pow-
in the table are listed in the order of their dered sample into a single plane. The
increasing refractive index, but unfortu- viscosity of the dispersion, after the
nately this also seems to be the order of incorporation of the sample by milling,
the decreasing wetting of glass. The can be reduced by addition of consider-
7O Sgm~OSltr~ oN PARTICLE SIZE MEASLrREMENT
able monomer (containing catalyst), but the concavity of a hanging drop slide. If the
this has usually caused clumping during dispersing agent is a solid, a drop of concen-
polymerization, probably due to exces- trated solution of the agent in monomer is
sive shrinkage. used.
(3) A relatively large amount of the vis-
The sample can b e dispersed in a
cous partial polymer is gradually added. The
mechanical mill or by a toothpick on a samqle is carefully and thoroughly milled on
slide. The latter technique will be used in the slide for an appreciable time (at least 5
the following description. min.). Experience shows that a principal
source of clumps in the final sample is due to
(la) Thepartial polymer is made from the material at the edge entering the final sample
monomer, containing the catalyst, in an after little participation in the milling ac-
Erlenmeyer flask. The most generally Used tion.
catalyst is. 1 per cent benzoyl peroxide which (4) Incorporate just enough monomer
has been found to be effective in all cases containing 5 per cent catalyst to bring down
listed in Table I. The usual precautions dur- the viscosity to that suitable for mounting.
ing handling and storing of organic peroxides (5) If a small drop of ,an accelerator 5 is
must be observed in the case of all the incorporated at this point better dispersions
catalysts. In particular, the catalyst and the are usually obtained.
accelerator must not be mixed with each (6) Transfer a drop of this mixture to an-
other directly; such a mixture might explode. other slide; put on a cover slip at once and
The catalyst is kept in the refrigerator. press down gradually with a clean rubber
(b) The monomer containing the catalyst stopper or pencil eraser. Put in a strong slide
is heated carefully in a beaker of warm water press and then in the oven or on a hot plate.
with a thermometer as'a stirring rod. An- The temperature should be as high as 100 C
other beaker of ice water must be available. if not injurious to the sample. The mount
The conditions of initial polymerization dif- should seem solid at the end of 15 rain or
fer markedly among the different monomers; less.
a record should be made of the temperature
relation as experience is gained. All mono- The calcium tungstate sample used
mers show an initial incubation period when for the example in Fig. 6(b) was mounted
little seems to happen. The velocity of poly- in n-butyl methacrylate with no special
merization, once it has started, varies greatly dispersing agent.
but is correlated with the temperature rise.
Suggestion: Remove tl~e flask from the hot Miscellaneous Methods:
water if the temperature reaches 80 C. At
90 C plunge the flask into ice water. Some other speciM methods are im-
(c) Cooling must start before the desired portant, such as the use of an impinger
viscosity is reached. Rotate the flask slowly for sampling aerosols, especially at-
in the ice water to avoid the incorporation of mospheric dusts. Such a sample shoots a
air bubbles in the liquid. jet of the dusty air or other aerosol
(d) Evacuate the resin with a water-jet against the microscope slide prepared to
aspirator. The flask must not be shaken un- retain the particles. An instrument with
til the bubbles apparently stop coming off multiple jets that seems efficient was
and then only gentIy at first.
described in 1945 by M a y (22). He states
(e) For storage, keep the flask in the re-
that it will collect particles from 1.5
frigerator. It should be allowed to warm up
to 50 ~ in diameter.
somewhat before use to prevent condensa-
An analogous method for sampling
tion of water in the sample.
liquid suspensions is to shoot an atomized
(2) The powdered sample, which is taken
mist of the suspension onto a surface
on the broad end of a toothpick, is thor-
oughly wetted by triturating with a small their5 Accelerator B supplied by lt~hm & Haas for use with
Paraplex resins was found to be generally satisfac~
drop of the dispersing or wetting agent in tory.
that has been prepared for wetting by Therefore, in the determination of the
the liquid. Backus and Williams (23) and size-frequency distribution in the tail
Cravath, Smith, and Vinograd (24) have of the distribution curve, the numbers
found this to be an excellent method to will be very small, and the error will be
prepare specimens for electron microg- large when the departure from sphericity
raphy, but, in principle, it could be is great, as, for instance, with rectangular
employed for sampling very fine particles particles.
for photomicrography.-Another method Any accurate measurement, involving
which has been much used for sample the actual movement of the stage equiva-
preparation for electron micrography is lent to the length of the particle or of the
described in detail for photomicrog- tube equivalent to its depth, as is done
raphers by Miller (25, 26). This consists at low magnifications with the traveling
in melting the sample in a plastic, such microscope, avoids certain fundamental
as nitrocellulose, and dropping it on a optical errors. In 1932, Dunbar (28)
surface of renter. The thin skin is picked applied this to the measurement of fine
up by a microscope slide directly from particles; he used two interferometers,
below. one to measure lengthwise movements
along the direction of the stage and the
DIRECT MEASUREMENT AND CLASSIFICA- other to measure depth by the movement
TION OF MICROSCOPE IMAGES of the objective.
A direct classification method, which
Visual Method: has staunch adherents, is the comparison
A size-frequency analysis can be made of the sizes of particles with standard
by direct measurement and classification areas that may be a series of circles en-
according to size of the images of par- graved on an eyepiece reticle. A rela-
ticles seen by looking directly at the tively recent type advocated by Fairs
sample slide through a microscope. A (29) is shown in Fig. 7. Accurate evalua-
linear scale on a reticle in the eyepiece tion and classification of size is claimed,
can be used, if it has excellent contrast even for irregular particles, by balancing
and if the particles are brought up to it, areas lying outside of the circle circum-
one by one, by means of a good mechani- ference with those required inside to
cal stage. It is more usual to use the filar equal the encircled area. Fairs states
micrometer for this. Although a rotating that the true Stokes sedimentation diam-
stage can be used, almost invariably eter is achieved in spite of the nature of
only one dimension is measured and this the "shape factor."
lies along one direction, that is, Martin's
diameters. This method is excellent for .Projection of Image:
measurement of spheres. If the particles When measuring particle size by the
are not spherical, Martin's suggestion microscopic method it is advantageous to
(27) was that the line used in measuring do so on a projected image. Dunn (30)
the size be drawn in one direction so as has been stressing this point since 1930,
to divide the area of ~the image of the Brown (31) since about 1935; the latter
particle in half. He claimed that if a has constructed a special apparatus that
sufficient number of the randomly scat- seems to be generally available. With any
tered particles are measured, the same method that involves measurement ove~
sizes will be found as if they were spheres. a protracted period, as this does, con-
However, the number involved is the venience is important to the operator
number of particles in one class-size. and often to the results. Well-designed
SYMPOSIUM ON PARTICLE SIZE MEASUREMENT
72
remote controls to the microscope are of standard areas, to the method of
necessary for full advantage of this image projection with considerable ad-
method. We think the operator should vantage. Although the images in his
sit at a sloping desk-like surface and view case are lying within the central grid of
images projected from below. In this way, his reticle and are only mentally trans-
the operator can quickly and easily ferred in comparison with the standard
3Z 23
16 II 8. ~ 7
00o *o'z'
I
9
45
16 NO.I NO, 2
O ; ;;~, ~.., 0
16 23
32
A
o=,r~
8 9
N::.~.~t ~ 468910
$ 6 0II I~'(")
~13
ioo.:
IllillI I
4689 I0 OII 12~ 1 3
NO. 3
C O
Fic. 7.--Fairs' Reticles for Eyepieces.
follow the orientation of the particles circles at the edges of the field, it is also
with his rule to obtain their best measure. possible to make a plate bearing a graded
Kasai (3z) t~/as formulated a complete series of circles, hexagons, and other
system in which all nonspherical par~ appropriate shapes and to slide the
plate about the plane of the projected
ticies are considered as ellipses and their
image and thus actually to superpose the
major and minor axes are measured. outlines of the standard areas on the
Fairs has extended (33) his system of particle images being classified. This was
classification, in which the image areas first done in these Laboratories by R. H.
of the particles are compared as series Lambert.
LOVELAND ON. PARTICLE SIZE 73
Photomicrographic Method: is more appropriate to the order of the

particle size.
We prefer to add the extra step of The photomicrographic method has a
photomicrography to the projection serious disadvantage over the visual
method. Photomicrographic negatives method in that the focus is determined
of the sample at exactly 2500X magnifi- at the time the photograph is made and
cation are made and put into an enlarger. it is impossible to focus up and down on a
An operator, who sits before a trans- particle during i~tsmeasurement. Usually
lucent sloping surface, views them at this is a drawback only when the particles
exactly 4X further magnification. This are coarse with respect to the magnifica-
surface consists of tracing paper held tion used because of other fine particle s
down by suction so that a pencil can be in the field. It does mean, however, that
used on it indiscriminantly. New sheets the slides must be made with special care
are available for each field. This en- so that the particles will all be in one
largement may seem to give overmagni- plane.
fication, but with measurements at
10,000X, 1 ~ in the sample becomes 1 cm Determination of Magnification:
and with electron micrographs at The procedures for the projection and
100,000X, 10 mg on the original sample photomicrographid methods are dis-
becomes i mm, so that treatment of the cussed in detail in the ASTM tentative
data is greatly facilitated. recommended practice E 20 - 51 T3 Spe-
The photomicrographic method has cial emphasis need only be given here to
some important advantages. Most im- the determination of magnification. This
portant is that the desired contrast can is partly because an error in the direc-
be almost always obtained by use of the tions exists in literature frequently given
photographic contrast (~/). This means as reference for this method and also
that the numerical aperture can be in- because it has been demonstrated that
dependently set as high as desirable for errors in magnification constitute one
b e s t resolution and that that wave- of the chief causes of discrepancies in
length nan be used which is the best results between laboratories. An investi-
for resolution or for differential absorp- gation made before the war in Kodak
tion in the sample. For instance, an Laboratories showed that t h e r e were
apochromatic objective, N.A. 1.30, is errors in the. commercial stage microm-
used routinely in these Laboratories with eters available at the time that were
monochromatic mercury radiation of a greater than other errors of the method.
wavelength of 436 mg or 365 mg. The Fortunately, some very accurate stage
far-ultraviolet wavelength (254 m~) can micrometers are now available. Estab-
be used if desired. The use of electron lishment of ekact magnification for the
micrographs for particle-size measure- negatives for particle-size measurement
ment also fits easily into this system. It is best done by determining the magni-
seems desirable, however, to rectify the fication in the image plane, at various
magnification of the electron micro- positions on the bench. Magnification
graphs, which may or may not be a is not simply proportional to the bench
position of the camera back, in spite of
convenient value, by making photo-
some statements in the literature to
micrographs of them to give exactly the
Tentative Recommended' Practice for Analysis by
100,000X mentioned before upon pro- Microscopical Methods for Particle Size Distribution of
Particulate Substances of Subsieve Sizes (E 20-51 T),
jection or some other magnification that 1952 Book of ASTM Standards, Part 3, p. 1574.
74 SYMI~OSIIJ~ ON PARTICLE SIZE MEASUREMENT
that effect. It is, however, simpler and viewed at an included angle of about
more accurate to utilize the bench 120 deg, so the observer is looking
positions rather than to measure the partly around the particle. It is instruc-
bellows draw from the eyepiece, to which tive to view a small glass bead or mi-
length the magnification is simply pro- crosphere under varying microscopic
portional. It is most satisfactory to conditions. Beside the above effect, the
plot the bench position versus the magni- microsphere also acts as a lens, and it is
fication on a graph at a sufficient scale. very difficult to determine the correct
If positive oculars are used, there is a focus and size. The above considera-
linear relation between magnification tions have to do with the subjective
and bench position, but the line does criterion of the correct edge which will
not pass through the zero point of the be discussed later. When taking actual
bench scale unless this happens to cor- measurements, the most reproducible
respond accurately to the eyepoint, criterion has proved to be taking the
which would be unusual. With negative outermost "best" focus of the edge.
amplifiers, the relationship between In the measurement of regular par-
bench position and magnification is not ticles, it is necessary to follow the orien-
even linear, which would require that tation of the particle in the field with the
the tube length be changed accurately measuring rule. With a triangular crys-
and continuously with each shift of the tal, for instance, only its altitude gives a
camera back. simple and correct linear measure of its
size. It was in a study of regular crystals
Shape Factor in the Technique of Measure- that we discovered that the systematic
ment: departure from the assumption that they
were spheres or circles led to very large
The greatest problem in the actual
errors that were not diminished by the
measurement of many particles is caused
number of particles measured. In this
by the various shapes that they may
case, Martin's method of statistical
have. The simplest case for microscopy
is that in which the particles are thin diameters is completely inapplicable.
If the projected areas of the particles
tablets regular in shape, that is, circles,
are measured and the expression of size
squares, triangles, or hexagons. In this
is left in units of "projective area," the
case, the size can be adequately expressed
shape factor is no longer a problem.
as a single linear dimension. This is also
Only when making comparisons of
true of regular, three-dimensional figures
particle size outside of the routine system
(spheres, cubes, tetrahedrons, etc.), al-
is it necessary to convert the expression
though these may not be lying so that
of particle size from terms of projective
the adequate linear dimension can be
area to those of the diameter of equiva-
readily measured; but when its depth
lent spheres.
dimension is of equal importance, an-
It is a fortunate circumstance that the
other trouble enters. A small particle
log-normal formula applies to the size-
observed at high aperture through a frequency distribution of most subsieve
microscope is being viewed at a high in- dispersions that are formed by precipi-
cluded angle that is not normally used tation or comminution:
in viewing nonmicroscopic objects. If an
objective of N.A. 1..30 is used to observe y=N
a particle embedded in a medium with
a refractive index' of 1.5, it is being where y is the frequency and x the size
attribute, such as projective area or 2. Areas of the particle images may be

diameter of each particle. compared with standard areas either
This formula can be put into a etched on eyepiece reticles, as in the
generic form: Fairs method, or on glass rules. In this
case, it is wise to have a set varying
y = A,,x~e -k~ln~-'~n)~ dx . . . . (5)
according to the shape of the particles
Here n is any integer and is used both as if several well-defined and different
an exponent of x and as a designation shapes occur. 1%. Lambert (Kodak Lab-
of the accompanying parameters. It is a oratories) made such a rule photo-
unique characteristic of this formula graphically with a series of circles, tri-
that only the parameters of the formula angles, hexagons, etc., in rows on an 8 by
need be changed (34) when the expres- 10-in. plate.
sion of particle size is converted from 3. Graph-like cross-hatching can be
diameters to areas, or conversely. superposed on the images, and the
The reduction of the raw data from a squares around the periphery can be
particle:size analysis is discussed in the counted. This method is very slow and
ASTM tentative method E 20. 6 Applica- tedious but apparently is often used.
tion of the log-normal formula wars first 4. Another method for the determina-
applied by the author to particle-size tion of the projective areas of particles
analysis in 1927 (34) but was reviewed is to draw around the outlines of the
in 1947 (35) as applied to the size-fre- images, cut them out, and weigh them.
quency distributions of the particles of Mainland (37) compared this method
photographic emulsions. The graphical with that of counting the cross-hatched
determination of the parameters was squares, and S c a m m o n and Scott (38)
discussed in 1948 (36). compared it with the use of a planimeter.
There are a number of methods for All three investigators concluded that
determining the projective areas of this was the better method in each case.
particles as seen through the microscope S c a m m o n and Scott advocate the use of
or as projected upon the screen: Kodaloid as a sheet material. W e have
1. Rules are applicable to the meas- found that the outlines can be traced
urement and classification of regular through very thin Kodaloid with a hot-
shapes as mentioned above. The rule point etching tool as rapidly as they
should read directly in units of projective could be drawn with a pencil and the
area. When the rules are on glass and the "cutout" is made simultaneously.
~mages are projected from below, no 5. Determination of the areas of the
parallax occurs. This system has been projected images by planimeter has been
applied to the size-frequency analysis of declared to be poor, and it is too slow
the crystals of photographic emulsions. for routine use, but we have found it to
If the corners of the particles are trun- be a very accurate method and have
cated, as by solvent action, a subtraction
used it as the fundamental basis for
is necessarily involved. In this system
calibration of other methods. A panto-
two steps are required: a shape classifi-
cation is made and then the size classifi- graphic planimeter is used in our
cation for each shape. In practice, the laboratory. It must be remembered that
shape classification is quickly made for one is really measuring controlled fric-
each particle, and the operator then tion, so that the surface on which the
reaches for the rule applicable to the wheel rolls and slides must be stand-
particle shape to be measured. ardized, but it need not be the same as
SY~IPOSIIYM ON PARTICLE SIZE MEASUREMENT
76
that on which the images are photo- rent is produced and the sector wheel closes
graphed or projected. down until the two beams are again equal;
6. Measurement of projective areas by the turning 6f the diaphragm is a measure of
a photoelectric c~ll is an almost ideal the size of the obstruction. It is most simply
measured on a Veeder counter or rotating
method since automatically, if the
scale and more elaborately on a series of
particles are totally absorbing, their Veeder counters denoting size ranges. With
shadow is the projected area, irrespective this instrument, a series of apertures can be
of the intricacy of the outline, and the measured as readily as a series of area ob-
shape of the particle. A null instrument structions.
400
380
360
%
340
320
300
280
]
b
p\,,,\
O
260 4/
O
o 240
CL
220
200
//
180
g 160 !/
140 !
LL
,2o / / ..["
,oo
s0
//
/
6O j
4O
2O
I I , , P , ] , I ~ t I ,
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Meen Closs Size, Dierneter, t~
FIG. 8.--ASTM Cooperative Test on Size-Frequency of Iron Oxide.
is being used in our Laboratories that A S T M COOPERATIVE PROGRAM:

is based on the following principle: SIzE-FREQUENCY DETERMINATION
Light beams from two sides of a concentrated
source are sent on diverse and independent I n the 1942-1945 period some pre-
paths but meet again to form an image of pared slides of dispersed powders were
the source superposed accurately and at circulated among the laboratories of the
identical magnification. A rotating-sector members of the particle:size committee
mirror cuts accurately through this image
~nd sends a light from each beam alternately of A S T M under the sponsorship of its
to a vacuum-tube photocell. The latter, in chairman, Dr. C. E. Barnett. The size-
turn, is connected through an a-c amplifier to frequency distributions were determined
a servomotor that either opens or closes a by these various laboratories. AS shown-
sector diaphragm in one of the two beams. in Fig. 8, the results for an iron oxide
If the two beams produce equal illumination
powder were only fairly consistent. N o t e
at the photocell, the a-c amplifier and the
motor are unaffected, and nothing happens. that all of the distributions have the
However, when any obstruction is intro- same mode and that one of them is
duced into the measuring beam, an a-c cur- appreciably different from the others.
LOVELAND O N P A R T I C L E SIZE 77
The analytical results for the zinc dust same modal frequency, which removes
are in poor agreement (Fig. 9). The the effect of the extra particles at the
sample contained many fine particles extremes.
extraneous to the original sample and The causes for the marked discrepan-
400
380
360
340
320
3O0 --
x.o,A
OLob B
/ \~,
i
280 I I//'''',,
00 260 . . . . . .-.-. +LobD
~LabC
0 240 "~Lob E :: "
~, 220
200
i8o
~eo \\\\. ~/
~4o
120 \X\ / : /x f ~ \" ~"
~- I00
80
6O
'-.-. ./ I,.!"V "\ \",,
40
20
.,. r--r--. ; , , . , . , . , . T. .,. ~ .--7-:-~~__
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Meon Closs Size, Diometer,,~
FIG. 9.--ASTM Cooperative Test on Size-Frequency of Zinc Dust.
400;
380
360
340
3ZO X Lob A
300 \ 0 Lob B
~, 2 8 o \ 4~Lob C
260 ......... +LobD
i 240
220
.- 200
\
\ "..Lob E
o 180
J:l 160
E 140
,2o
Joo
80
6o
40
2O
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Meon Closs Size, Diometer,/~
FIO. 10.--ASTM Cooperative Test on Frequency Values Adjusted for Equality of Modes.
Laboratory A included them all in the cies in these results may be listed as
measurements, which were made at high follows:
aperture. Most of these fine particles 1. Mistakes.
were omitted by the other laboratories 2. Differential selection of "dirt."
3. Magnification, calibration, and use.
or were not resolved (Fig. 10). These 4. Resolving limit.
various size-frequency distributions are 5. Differences in edge definition and
best compared by bringing them to the subjective criteria.
SYMPOSIUM ON PARTICLE SIZE MEASUREMENT
78
The factor of magnification has al- stancy fails as the limit of resolution is
ready been mentioned but is emphasized approached, that is, at the head of the
b y these results because it was decided size-frequency curve.
that the pronounced discrepancy in the The author and his coworkers, nota-
results of Laboratory D was due to an bly 3. J. Duane, undertook a two-part
error in magnification. Before the war, investigation of this whole field of size-
Schuster 7 and Loveland independently frequency determination: (a) a study of
questioned the authenticity of commer- the relative effects of optical and photo-
cial stage micrometers and each ex- graphic factors on apparent size and (b)
amined as many micrometers as possible. a measure of the discrepancy between
Both had almost identical experience and the apparent v e r s u s the true size. The
found an alarming variation in the com- first investigation is practically complete.
mercial stage micrometers. Since the The second involves cooperation among
war, Richardson (39) has made an ex- several of the members of the particle-
tensive investigation of the production size committee of the ASTM and '.'s
of micrometers and other rulings by still in progress. A brief description of
interferometric control and calibration. this second investigation will be given
As a result, accurate micrometer rulings first.
are now available in this country. We expect to utilize the extreme re-
The fifth factor is probably the most solving power of the electron microscope
troublesome and is the most frequent and also the very accurately known
among individual particle:size analyses. magnification and reproducibility of the
photomicroscope. To accomplish this,
APPARENT VERSUS " T R U E " SIZE the same crystals are photographed with
The true edge of a thin tablet type of both th~ electron microscope and the
particle may be considered to be an photomicroscope, the crystals being
infinitely thin line. But lack of resolu- embedded between the two operations,
tion, alone, will broaden this line to a so that the highest numerical apertures
k can be used with the photomicroscope.
band of width (2 N.A.) which, at a The magnifications with the photomicro-
wavelength (k) of 435 m/z and N.A. scope are known accurately from a
1.30, would be 0.17 ~ wide; at 10,000X, Bureau of Standards ruling and have
this is 1.7 mm as measured on the easel. been independently checked interfero-
Only one half of this widening will occur metrically. In this particular case, there-
on one side of the line. But unlike the fore, the magnification for the electron
measurement of distance using the ruled microscope is known just as accurately.
lines of a grating, particle size must be By utilizing the higher resolution of the
measured between the opposing edges latter and a series of particles of de-
creasing size taken with both types of
of the particles. Therefore, at very high
microscope, it should be possible to
magnifications, particles will seem larger
plot apparent v e r s u s " t r u e " size to the
than their true size. Accordingly, for
limit of resolution of the photomicro-
some time an increment has been sub-
tracted from the measurements made ih scope.
The nature of the~cest obiect is o f great
these Laboratories. This has been a con-
importance. In fact, it has already been
stant value, b u t - p r o b a b l y this con-
mentioned that the photomicroscope
7Mary Schuster, unpublished report at meeting of views a particle at !.3 N.A. with an
Subcommittee 11 of ASTM Committee E-I on Methods of
Testing. included angle of about 120 deg, whereas
the electron microscope views it with scanned by a microdensitometer at 40)<

nearly parallel light. Therefore, spheres,
magnification, through the kindness of
such as those of polystyrene, would be a
Perrin and Altman, of these Laborato-
poor choice of test object for a mutualries. Now, theoretically, a very sharp
examination with these two instruments.edge should be represented by a vertical
line on these microdensitometer graphs.
Very thin hexagonal platelets are almost
ideal, especially if made of a conducting
In practice, one obtains an S-curve that
material, since the linear dimension isincludes the one which is representative
identical and unequivocal with the two of an emulsion and its processing. How-
instruments. Hexagonal platelets, if ever, if the true width is known inde-
perfect, have three pairs of parallel pendently, these vertical straight lines
sides. The crystal is first examined with
can be drawn in, and in this case there
a vertical illuminator to be sure that was a criterion for their correct location.
it is perpendicular to the axis of ex- It was therefore possible to study the
amination, since a tilt would introduceeffect of optical and photographic factors
an error. Jelley discovered (40) that the
on the nature of this edge as represented
"bright silver" which Ltippo-Cramer b y the S-curve and its position relative
(41) had obtained by reduction of silver
to the true edge.
salts with metal under acid conditions The test objects were thin strips of
was made up of thin, hexagonal crystals,
glass mounted under a cover slip. They
and this method is the basis of our pres-
were made from parallel plate glass about
ent technique. We can produce thin 1 ram' thick, cut, ground, and polished
crystals that vary in size from hexagons
so that the original surfaces were now
8 v high to thin needles with sides the sides of a test object,, assuring their
separated by less than 0.1 ~. Eight being parallel, and so that its width was
microns is a size that can be measured accurately known, although that was
unequivocally with the photomicro- later independently checked with a
scope and with the electron microscope traveling microscope. These test objects
on the 2 by 2-in. plates. We expect to were made of different thicknesses, one
have a series of 2 by 2-in. negatives, being as thin as possible so that its
each having at least part of one of thethickness would be negligible. Glasses of
large crystals in the field and one crystal
different refractive indices were used,
including a Kodak glass of n,20 = 1.88.
of successively smaller size down to and
below that size corresponding to the By using different mounting media,
limit of photomicroscopic resolution. the difference in refractive index could
These will be compared by measurements be made any value up to 1.88.
with photomicrographs that include the Photomicrographic negatives were
same fields. made at a magnification of 50X, either
the 32 mm or the 16 mm objective being
EFFECT OF OPTICAL AND PHOTOGRAPHIC
used, according to the numerical aperture
FACTORS
desired. Different magnification/N.A.
The principle of the method used by ratios were studied, including those
Duan.e and Loveland in the first phase representing high magnification. For the
of this investigation was as follows: technique of determining the position
Photomicrographic negatives were made of the true edge of our test object, given
of a test object of known width having its correct width, we are indebted to
parallel sides. These negatives were F. H. Perrin, who used this technique
80 SYMPOS~ ON PARTICLE SIZE ~IEASUREMENT
for another purpose. The long micro- Effect of Photographic Factors:

densitometer trace across the whole Photographic factors have a definite
test object was folded in two to super- effect upon the apparent size of the
pose the traces of the two edges and was image, but it is less than has often
creased at the middle. This established a been charged for the photomicrographic
base for measuring one half the known method. Little more will be done here
true width to each side, at which point a than to list the results and give a limited
vertical line was drawn. These lines discussion of them.
could be compared with the vertical Exposure of the negative has an ap-
S-curve, which represented the actual preciable effect. That the apparent size
edge on the trace. becomes smaller with increase in ex-
posure can be noted from Fig. 11.
immersion Medium I.OnD
Spectroscopic Plate IV-O Gamma = 5.0 Each curve is a trace across one edge of
Negative M48146
32ram Objective NA=O.IO the image of the test bar on a negative, and
2.8 the exposures of the negatives range from
Exposure of Negative
that which would normally be considered
a= 3sec
2.4 b= 4 sec d underexposed to some that would be nor-
c= 4.5 sec r mally considered overexposed. The interior
d= 5sec
of the test object would be represented on
2.0 b
this graph at the left of the vertical line rep-
resenting the true edge. The abscissa units
| 1.6 on the graph represent dimensions in milli-
a
meters on the trace which is 40 times that
on the negative and 10 times that on the
0 pictured images when they are measured.
O.S Note the crosses on the graph which

represent completely independent mea-
0.4 surements of the width of the test object
made by an operator with some ex-
i i i i L ~ i perience. The projected images of the
0-4-2 0 2 4 6 8 I0 12 14 16 18 negatives at 4X enlargement were
Oistonce on Trace from Geometric Edge, mm measured as usual for particle size
ll.--Effect of Exposure on Apparent
FIG. analyses, with a linear millimeter glass
Size. Bar test object. Bright-field.
rule observed thrgugh a magnifying
A study of this type is slow and ex.- glass. This study can give only relative
effects. We have many such graphs
tremely detailed. The results have there-
varying with gamma and other factors,
fore been voluminous. However, some
but the exposure relation is similar in
general conclusions can be drawn. Most all of them. Figure 12 shows that, on
important, the study confirmed the fact the whole, the apparent size decreases
that the apparent size is larger than the linearly with increasing log E, which
true size--at least with the standard means that the largest relative effect
method of transmitted illumination. is at the lowest exposures.
The extent of this difference in practical Effect of development can be studied
work will depend upon the second phase by utilizing photographic gamma as a
of the investigation already described. measure of development. Apparent size
E I0
E
g
"o
"' 8
o
.r-
(,9
E Lower
o 4 Aperture
2
9 •=0.8
0 ~ - 9 9
9 Geometric edge Higher
~ Y=~. 0 & Aperture
&
~-2
~3
I I I I I I I I
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Log Exposure Time
Fzo. 12.--Displacement of Measured Edge from True Edge.
~.0
2.5
"~ 2.0
a
I.O
0.5
0
16 12 8 4 0 0 4 8 12 16
Distance from Arbitrary Fiduciol Marks'on Trace, mm
FIG. 13.--Effect of Exposure on Apparent Size Silver Bromide Crystals ( X 2500).
8_9 S~POSIIYM ON PARTICLE SIZE ~ E A S U R E M E N T
usually increases with increasing gamma, and includes the independent measure-
but the effect is not as great as with ments of the images made on the en-
variation of exposure, and the latter is larger by the technicians. The result is
easier to control. It is only necessary to purely relative, but it is consistent with
hold the development reasonably con- those of the test object. Moreover, the
stant. same rules seem to hold for electron
The best general\procedure proved to micrographs. However, this part of the
be to hold the background density of the investigation is much less complete.
2.5
Exposure of Negoti
0 = 3 sec
b= 4sec
2.0 C= 5 SeC
1.5
o. 1.0
0
0.5
0 -12 - I 0 , - 8 - 6 - 4 -2 0 +2 4 6 8 I0
Distonce on Troce from Geometric Edge, mm
FIG. 14.--Eitect of Exposure on Apparent Size. Bar test object. Dark-field.
negative constant at a reasonably con- Effect o/Optics and Illumination:

stant photographic gamma. We chose a The objective aperture is the most
background density equal to 2.0. The important factor, as might be expected.
apparent size seems to vary linearly with The limiting aperture must apparently
the background density. The background be considered from two viewpoints:
can be kept constant fairly readily by 1. The aperture governs the limit of
photometry of the image plane. In most resolution, according to the well-known
routine work, it is possible to maintain a wavelength:aperture ratio, ;~/(2 N.A.).
constant background density by holding 2. The aperture is important in an
the exposure and development constant. absolute geometrical sense; that is, it
When studying these photographic affects the factors of subtense, of con-
effects on actual particle-size negatives, trast, of flare and possibly other factors,
we chose hexagons of silver bromide all of which, in turn, affect the apparent
with their three sets of parallel sides. size. This second effect seems to continue
A'result in one case is given in Fig. 13 through varying apertures with no
break at the limit of visual resolution. does not influence the ratio of apparent
Therefore, this component is independent versus true size. But the nature of the
of the N.A./magnification ratio. More- errors of measurement varies so much
over, there apparently is no complete with the refractive index that it is easy
break when the condenser aperture to understand how some investigators
equals the objective aperture, although have thought that it affected the ap-
this has yet to be confirmed. As expected, parent size. It is essential to obtain the
the width of the edge varies with the "correct focus." As is well known, the
ratio: width of the edge shadows increases with
condenser aperture the difference in refractive index. This
objective aperture is an important psychological factor.
An investigation using dark-field il-
It is obvious that at high magnifica-
lumination, which was started to measure
tions, Where much greater apertures are
the effect of wide apertures, was con-
required, flare is a much greater factor
tinued for its own sake because of the
1.4 interesting results. The edge criteria are
Dark-Field Illumination
very different; the peak density is now
1.2 Max.N.A.of Condenser I.(3 inside the "true edge." Independent
\ Max. N.A. of Objeclive O.I
\ measurements on the projected images
E t.o ,,
E \ still give an apparent size that is too
large, but the difference is now smaller
:9 0.8 o ~ ~
3 and might well be considered negligible
| 0.6,
in many cases. This can be seen in Fig.
0.4 ~ 14.
The width of the edges is affected by
~0.2 the central stop of the dark-field con-
denser, and if the central patch is de-
I I I I h
o 2 ; ; ;',8 ,6 creased in size, the relation becomes
Central StopDMmeter, mm very critical when nearing the size that
FIO. L~.--Effectof Dark-Fie|dStopDiameter would just occlude the objective aper-
on EdgeWidth.
ture (Fig. 15).
than at lower magnifications. This
became apparent in comparing the ESTABLISHMENT O1~ VISUAL CRITERIA
results obtained with our test object with BY TRAINING
those obtained from photomicrographs These test objects provide a case
of particles at high magnification that where the true width can be known while
were used for routine measurements. We the measure of a size is being deter-
therefore made a study of this factor. By mined. The question arose whether the
introducing flare, we could make the technicians could not be trained to
curves of our test object like those of the measure the true width directly, that
crystals taken at high powers. This is, to change their subjective edge
factor increased the scatter of our in- criterion to that specified by the known
dependent visual measurements, as width. With bright-field illumination,
might be expected.
t . . .
the true width specified an image where
The refrachve radices of the object the density was equal to 0.11, which is
and its mounting media are extremely on the toe of the reproduction curve
important. However, with all other where the density gradient is nearly
factors constant, the refractive index zero. The reproducibility of the width
84 SYMPOSIUM ON PARTICLE SIZE MEASUNEMENT
measurements with this criterion was the analysis as a whole. The required
exceedingly poor. In the cases used for correction in absolute terms depends, of
test, the image was measured at a point course, on the unfinished second portion
0.5 mm beyond this correct edge when of the investigation already described.
the usual criterion was used, making Photomicrographic negatives bearing
the test object about 1 mm wider. With images of the test crystals used in the
dark-field illumination, the true edge was investigation, for which microdensitom-
well within any reproducible edge eter traces exist, are useful aids in
criterion. However, it was only 0.3 mm training new operators. The criterion of
the edge as that most reproducibly
inside of the normally measured edge
measured is also that which is normally
on the enlarger, which made the test
chosen. The use of these test objects
object only about 0.6 mm too wide as has allowed us t o eliminate the small
normally measured. personal variations that occurred in the
It is best therefore in particle-size edge criterion more effectivel)~ than was
analysis to use the most reproducible done by verbal instruction of a novice
edge criterion and then to make a cor- by an experienced operator. It is, of
rection between apparent and true size, course, especially valuable if skilled
if the discrepancy is ~vithin the error of operators are not available.
REFERENCES
(1) G. St. J. Perrot and S. P. Kinney, "The (14) J. W. McCutcheon, "Synthetic Deter-
Meaning and Microscopic Measurement of gents," Soap and Sanitary Chemicals, Vol.
Average Particle Size," Journal, Am. Ce- 25, No. 8, p. "33 (1949); No. 9, p. 42
ramic Soc., Vol. 6, No. 2, p. 417 (1923). (1949); No. 10, p. 40 (1949).
(2) Henry Green, "The Effect of Non-Uni- (15) E. K. Fischer and C. W. Jerome, "Pigment
formity and Particle Shape on 'Average Dispersion with Surface-Active Agents,"
Particle Size,' " Journal, Franklin Inst., Industrial and Engineering Chemistry, Vol.
Vol. 204, p. 713 (1927). 35, p. 336 (1943).
(3) H. Heywood, "The Scope of Particle Size (16) V. R. DamereU, K. Gayer, and H. Lauden-
Analysis and Standardization," Supple'- slager, "Effect of Surface-Active Agents
ment, Transactions, Symposium on Parti- upon Dispersions of Sifica in Xylene,"
cle Size Analysis, Institute of Chemical Journal of Physical Chemistry, Vol. 49, No.
Engrs., Vol. 25, p. 15 (1947). 5, p. 436 (1945).
(4) L. C. H. Tippett, "A Modified Method of (17) V. R. Damerell and M. J. Vogt, "The Ef-
Counting Particles," Proceedings A, Royal fect of Surface-Active Agents upot~ Disper-
Society, Vol. 137, p. 434 ~1932). sions of Lead Monoxide in Xylene," Jour-
(5) F. T. Gucker, Jr., and C. T. O'Konski, nal of Physical Chemistry, Vol. 52, No. 2,
"Electronic Methods of Cotmting Aerosol p. 363 (1948).
Particles," Chemical Reviews, Vol. 44, p. (18) "Sealing Fluid Mounts," Watson's Micro-
373 (1949). scope Record, No. 33, p. 23 (1934).
(6) B. Deryagin and G. Vlasenko, "Flow (19) W. B. Wiegand, "Rubber Compounding as
Method of Ultramicroscopic Measurement an Aid to Conservation," Canadian Chemis-
of Particle Concentrations of Aerosols and try and Metaphysics, Vol. 10, p. 251 (1926);
Other Disperse Systems," Doklady Akad- India Rubber Journal, Vol. 73, p. 31 (1927).
emii Nauk SSSR, Vol. 63, p. 155 (1948). (20) Raymond P. Allen, "Method of Making
(7) W. H. Walton, "Automatic Counting of Micro Sections of Rubber Stocks," Indus-
Particles," Nature, Vol. 169, March 29, trial and Engineering Chemistry, Analytical
1952 p. 518. Also C. Lagercrantz, 3cta Edition, Vol. 2, p. 311 (1930).
Physiologica Scandinavica, Vo[. 26, Supple- (21) S. D. Gehman and J. C. Morris, "Measure-
ment 93. ment of Average Particle Size of Fine Pig-
(8) F. Roberts, J. Z. Young, and D. Causley, ments," Industrial and Engineering Chemis-
"Flying Spot Microscope," Electronics., try, Analytical Edition, Vol. 4, p. 157
Vol. 26, p. 137 (1953). (1932).
(9) 1~. P. Allen and G. S. ttaslam, "Report on (22) K. R. May, "The Cascade Impactor: An
Study of Microscopic Count Method of Instrument for Sampling Coarse Aerosols,"
Particle Size Measurement," Proceedings, Journal of Scientific Instruments, Vol. 22,
Am. Soc. Testing Mats., Vol. 35, Part I, No. 10, p. 187 (1945).
p. 497 (1935).
(10) D.L. Gamble and A. H. Pfund, "An Inter- (23) R. C. Backus and R. C. Williams, "The
ference Scheme for Measuring the Cell Use of Spraying Methods and of Volatile
Depth of a Siedentopf Ultramicroscope Suspending Media in the Preparation of
Counting Chamber," Journal, Optical Soc. Specimens in Electron Microscopy," Jour-
Am., Vol. 23, p. 416. (1933). nal of Applied Physics, Vol. 21, p. 11
(11) E. M. G. Laguarta, "A Modification of the (1950).
Count Method for Determination of Parti- (24) A.M. Cravath, A. E. Smith, J. R. Vinograd,
cle Size," Kolloid-Zeitschrift, Vol. 102, No. and J. N. Wilson, "Preparation of Electron
3, p. 268(1943). Microscope Specimens for Determination
(12) F. D. Snell, "Surface-Active Agents," In- of Particle Size Distributions in Aqueous
dustrial and Engineering Chemistry, Vol. 35, Suspensions," Journal of Applied Physiol-
p. 107 (1943). ogy, Vol. 17, p. 309 (1946).
(13) A. M. Schwartz and J. W. Perry, "Surface- (25) L. B. Miller, "Dispersion of Pigments and
Active Agents, Their Chemistry and Tech- Fillers for Microscopical Examination,"
nology," Interscience Publishers, New Paper Trade Journal, Vol. 116, p. 39 (1943).
York, N. Y. (1949).
(26) L. B. Miller, "Dispersion of Powders for Analysis of Size of Particles, Parts I and
Microscopical Examination," Transactions, II," Journal, Franklin Institue, Vol. 204,
Am. Microscopical Soc., Vol. 61, p. 302 pp. 193, 377 (1927), Communication No.
(1942). 300.
(27) G. Martinetal., "Researches on the Theory (35) R. P. Loveland and A. P. H. TriveUi,
of Fine Grinding, Part I," Transactions, "Analysis of Particle Formation and
Ceramic Soc. (England), Vol. 23, pp. 61- Gl'owth by Size Frequency Determinations
118 (1923-1924). of the Silver Halide Precipitations of
(28) C. Dunbar, "Interferometer Microscope," Photographic Emulsions," Journal, Phys.
Journal of Scientific Instruments, Vol. 11, and Coll. Chem., Vol. 51, p. 1004 (1947),
p. 85 (1934). Communication No. 1096.
(29) G.L. Fairs, "The Use of the Microscope in (36) R. P. Loveland, H. M. Menihan, and A. P.
Particle Size Analysis," Chemistry and H. Trivelli, "Analysis of the Particle-Size
Industry, Vol. 62, October 2, 1943, p. 374. Distribution of the Grains Producing a
Photographic Image," Journal, Franklin
(30) E. J. Dunn, "Microscopic Measurements
for the Determination of Particle Size of Institue, Vol. 246, p. 459 (1948), Commun-
Pigments and Powders," Industrial and ication No. 1175.
(37) D. Mainland, "The Technique of Estimat-
Engineering Chemistry, Analytical Edition, ing Small Irregular Areas in Biological Re-
Vol. 2, p. 59 (1930). search with Notes on the Tests of Ac-
(31) C. R. Brown and W. P. Yant, "A Micro-
curacy," Journal of Anatomy, VoI. 63, p.
projector for Determining Particle Size
Distribution and Number Concentration of 345 (1928-1929).
(38) R. E. Scammon and G. H. Scott, "The
Atmospheric Dust," Report of Investiga-
Technique of Determining Irregular Areas
tion No. 3289, U. S. Bureau of Mines, 8 pp.
in Morphological Studies," Anatomical
(1935). Record, Vol. 35, p. 269 (1927).
(32) K. Kasai, "The Determination of Particle
(39) C. H. Brumley and D. Richardson, "An
Size of Powdered Particles," Scientific
Electro-Optic Crystal Interferometer,"
Papers, Inst. Phys. and Chem. Research Journal, Optical Soc. Am., Vol. 40, p. 800
(Tokyo), No. 242, pp. 135-183 (1930). (In
(1950).
German). (40) E. E. Jelley, "Structure of the Developed
(33) G. L. Fairs, "Developments in the Tech-
Silver Image as Revealed by the Electron
nique of Microscopical Examination," Microscope," Journal, Photographic Soc.
Journal, Royal Microscopical Society, Vol. Am., Vol. 8, June-August, 1942, p. 283.
71, Part 2, pp. 209-222 (1951). (41) Liippo-Cramer, "Kolloidchemie und Photo-
(34) R. P. Loveland and A. P. H. Trivelli, graphie," Kollold-Zeltschrlft, Vol. 14, p. 186
"Mathematical Methods of Frequency
(1914).
DISCUSSION
MR. E. J. DUNN, JR.1--The author's but as I stated, the error is apparently a

remarks on particle size are, naturally, of constant one, making its relative im-
great interest to National Lead Co. where portance greater as the particle size
much microscopical work on pigments is goes down. We have done some things
done. The remarks on mounting es- on an absolute basis, but they are in-
pecially were of interest in that they complete yet.
described a practice of using a piece of If I should plot apparent versus true
wood which is a softer material than a size, if it was theoretically correct I
glass rod. The National Lead Co. ex- would get a straight line at 45 deg.
tended that principle a little further. We obtained part of such a plot which
Our microscopist uses a finger for could be represented as another curve
this purpose. The finger pressure and the above the correct one and parallel to it.
tremendous amount of viscosity shear I cannot report at present on the
obtained as the solvent leaves the slide second phase of this investigation. I
makes an excellent way of obtaining think that as the limit of resolution
good dispersion. I t is a simple procedure is approached the line (true versus
that seems to work in a great many apparent size) curves away, and so the
media; it has been considered very satis- answer--the only one I can give--is
factory at National Lead Co. that the discrepancy between true and
What are the effects" of the various apparent size is probably going to be
errors in either dark- or light-field work absolutely negligible as you go to large
on the average particle-size measure- enough particles, but as you go down
ment? Where class intervals in a fre- into small particles of high magnifica-
quency distribution count are taken tion, I do not think it is negligible. You
logarithmically, such as 0.75 to 1.0 t~ are asking a question that can only be
and 1 to 1.5 #, would the errors of meas- answered by knowing the absolute re-
urement throw many particles out of lationship between the apparent and the
one interval into another to result in a true size, and we have not learned this yet.
different distribution, or is the average Mr. D u i N . - - T h e author mentioned
error of measurement as it totals up a that in the count method there is a pro-
relatively small one--a 5 or l0 per cent cedure for electronically counting par-
error? ticles such as are mounted in the cardioid
M R . R. P. LOVELAND ( a u t h o r ) . - - W e cell. Such particles are normally under
usually use an arithmetic classification, constant Brownian movement, and
because of this would not the counting
1 Research Laboratories, National Lead Co., Brooklyn,
N.Y. have to be an instantaneous proposition?
87
88 SYM_POSlI~ ON PARTICLE SIZE MEASUREMENT
MR. LOVELAND.--There are only two method, it could be concluded that

fundamental electronic methods as far as usually shape factors are so important
I know. The first type which I men- that very precise determination of
tioned uses a slit ultramicroscope and actual diameters would seem to be of
also a large volume of liquid sample. somewhat less importance.
There we must have great dilution of our Is there a relationship between shape
sample, and the fluid containing the factors and the required accuracy on the
particles passes under the microscope measurements of actual diameters?
and the flashes caused by the individuals MR. LOVELAND.--I tried to avoid the
are electronically counted. With enough shape factor. It is one of the most com-
dilution no matter how quickly the parti- plex parts of the work. The interest
cles come, unless two are going absolutely that a given group has in particle size
simultaneously--which-will constitute is usually pretty specific and will usually
an error not accounted for by dilution-- determine what dimensions they must
an electronic method can catch them. have, but I am very sure that a good
This method just moves free particles in a many people are using and making a
liquid. determinations of particle size as diame-
The other, much more elaborate ters where it is not obligatory, but it has
method, and, I think, one of very great just become habit with them to deter-
potential value, uses a slide with the mine or express particle size in terms of
particles in position as if for photo- a linear dimension, or something involv-
micrography and counts them electroni- ing it.
cally by scanning the area. I assume We are lucky, photographically speak-
these instruments are going to cost ing; the projective area of a particle in a
$50,000 and up. This method has been photographic emulsion is the important
applied to blood counting, and there is a size attribute that it presents to the
great deal of pressure for its develop- light, but surface volume and projective
ment for that very reason. area are measurements that are inde-
MR. C. J. CALBECK.2--In a method for pendent of shape factor.
making silica replicas of particles which I quite agree that the minute you get
is expected to be useful to electron into that subject you have to simply
microscopists, silica is evaporated onto hold a symposium on the shape factor.
the particles dispersed on a plastic film, If the shape is a sphere, you can do
which is subsequently dissolved, leaving something about that, as you can about
the particles encased in silica shells and any regular shape--cubes, spheres, any
supported by the continuous silica film regular shape of any kind. But the
between the particles. In many cases, it minute you get to your irregular shapes,
is then possible to dissolve the particles; you have simply got to make arbi-
leaving the shells as replicas of the trary or measured allowances for such
particles. Since these shells are semi- dimensions as you are talking about.
transparent to electrons, stereoscopic Therefore, I merely made a plea to
electron micrographs can be obtained. the people, who, I think, include a rather
From study of the three-dimensional large group, that are not interested neces-
views of particles afforded by the sarily in shape factors to avoid them
altogether by expressing particle size
Member of Technical Staff, Bell Telephone Labora-
tories, Murray Hill, N. J. in mass, area, or volume units.
RECENT DEVELOPMENTS IN THE HYDROMETER METHOD

AS A P P L I E D TO SOILS
BY EDWARD E. BAUER1
The method of test for grain-size the hydrometer reading can be assumed
analysis of soils, A S T M Tentative to give the density of the suspension at
Method D 422, 2 was extensively revised the volume center of the immersed portion
in 1954. The technique was originally of the hydrometer (Fig. 1). He proposed a
developed by the Bureau of Public Roads symmetrical bulb having a rather large
(I) 3 following the suggested use of an volume in comparison to the volume of
hydrometer by George Bouyoucos in the immersed portion of the stem so
1927 (2). The A S T M first published a that for all practical purposes the volume
tentative method of test covering this center of the immersed portion can be
procedure in 1935. Following some assumed to be midway between the two
changes in 1938 the method was adopted ends of the bulb. Casagrande also pro-
a s A S T M standard in 1939. Two re- posed the use of scale graduated in
visions that were more or less editorial specific gravity values based on water
in nature were included in the standard at 68 F.
in 1951. I t is the purpose of this paper When work began in 1953 by Com-
to discuss the changes that were made mittee E-1 on Methods of Testing,
in 1954. on the preparation of the Tentative
Specifications for A S T M Hydrometers
Hydrometers: (E 100), 4 (Fig. 2) A S T M Committee
Bouyoucos who in 1927 (2) first pro- D-18 on Soils for Engineering Purposes
posed the use of an hydrometer (Fig. 1) was represented. The Bureau of Public
in connection with grain-size analysis of Roads had done some experimental
fine-grained soils made use of the then work on the design of an hydrometer
current shape of hydrometer bulb and a specially adapted for use in suspensions
stem graduated in grams of soil colloids of soils, and their recommendations
per liter of suspension based on a specific were written into the new hydrometer
gravity of soil particles of 2.65. The specification (Designated 151 H with
hydrometer was calibrated at a tem- stem indicating specific gravity and 152
perature of 67 F. The original Bouyoucos H with a stem indicating grams per
scale was copyrighted. liter) .5
Casagrande in 1934 (3) showed that The tolerances permitted for these
new hydrometers are small. One manu-
i Professor of Civil Engineering, University
of Illinois, Urbana, Ill.
: Tentative Method for Grain-Size Analysis 4 Tentative Specifications for ASTM Hy-
of Soils (D 422- 54 T), 1958 Book of ASTM drometers (E 100- 57 T), 1957 Supplement to
Standards, Part 4, p. 1119. Book of ASTM Standards, Part 3.
3 The boldface numbers in parentheses refer 5 Requirements for the hydrometers are tt, e
to the list of references appended to this paper. same in AASHO Method T 146 - 54.
89
90 SYMl~OSlU~ ON PARTICLE SIZE M E A S U R E M E N T
facturer has the bulbs blown in a mold made by Bouyoucos. A number of

and specially selects the tubing for the laboratories are known to have pre-
stem in order to meet the requirements. pared correction charts or tables for
While the cost of the hydrometer is the older hydrometers, an item that is
not necessary with the new hydrometer.
SPECIF,C
GRAVI'r v
---I-- ~,S
.ITLR
I-
Z
I.O00 SP. G, ,ZEF
OG~
I.O00 -- ,
,
1.010--
z :~ o :5
It<
1.020 - -
l~l~ ~-- t~
-, Ul I
L 030 - -
r OI
ol
I--Q
U
-'i <.~
- -
----J
1 . 0 5 0 - -
IX
! .
FIG. 2.--New Soil Hydrometers, as Specified

in Specifications for ASTM Hydrometers (E
100 - 5 7 T ) . 4
B A
FIO. 1.--Hydrometers in the Original Air-Dispersion Equipment:
Method. Hydrometer A is the Bouyoucos Hy-
drometer and Hydrometer B is a Streamlined Bouyoucos (2) proposed the use of the
One Suggested by A. Casogrande. mechanical device commonly called a
malted milk mixer to create a suspension
increased due to the close tolerances, of soil particles in water, and this device
the hydrometers are interchangeable with a special stirring paddle and dis-
in use. Savings due to this feature more persion cup are specified in the ASTM
than offset the increased initial cost. method of test. The malted milk mixer,
The grams per liter scale has been rotating at a very high rate of speed,
calculated on the same basis as the may pulverize some of the particles,
specific gravity scale, whereas the original especially when there are soft particles
Bouyoucos scale depended on tests present.
BAUER ON HYDROMETER METHOD AS APPLIED TO SOILS 91
The Bureau of Public Roads (I) in of the original cup A was slightly greater
describing the method of test in 1931 than for cup B, a simplified design.
called for 5, 10, or 15 rain of dispersion Either cup may be used, however, in
with the malted milk mixer, depending the ASTM and American Association
upon the plasticity index of the soil. of State Highway Officials (AASHO)
When ASTM Method D 422 was issued methods.
as tentative in 1935 the dispersion time Air pressure used with the Wintermyer
was reduced to 1 rain for all soils. One cups is 20 psi. Length of dispersion
minute of dispersion may degrade certain depends on the plasticity index of the
soils while in other cases 1 min may soil. For plasticity index values under 5,
HANOLEAND
HAN04_E
PRESSURE AND VENT
GAGE
CROSS SECTION
NEEDLE CUP A
VALVE
iONI'AINER
L,ONTAINER
~ASE,
AIR
A~R air HOt,E$ AIR TUBE LUNN~bTION
,~AIR PASSAGE PPLY
I12 "
CUP S
CUP A CROSS SECTION
CUP B
FIG. 3.--Wintermyer Air-Dispersion Cups as Specifiedin ASTM Method D 422.2
not be sufficient to disperse many of the the time is 5 min; for values 6 to 20,
more cohesive soils. the time is 10 min; and for values over
The Bureau of Public Roads reported 20, the time is 15 rain.
in 1948 the development of two air-jet Chu and Davidson (5) developed the
dispersion cups (4) shown in Fig. 3. simplified air-jet dispersion apparatus,
These are sometimes known as Win- shown in Fig. 4, named by the developers
termyer cups. Test data produced a soil-dispersion tube. The tube is
during the development program and designed to fit into the sedimentation
subsequent check tests indicate: (1) cylinder specified by both ASTM and
That the degrading action of the air-jet AASHO. As a result, soaking of the soil
dispersing cup with dispersing periods sample and the subsequent agitation
up to 20 min is no greater than that of can all be done in the sedimentation
the high-speed stirring device with a cylinder, eliminating several transfers
1-min dispersing period. (2) Use of the of the soil-water mixture. For silty and
air-jet dispersing cup results in more clayey soils the recommended air pres-
efficient dispersion of the clay fraction sure is 25 psi and for sandy soils 10 psi.
of plastic soils than is obtained with The dispersion period is 5 rain. The
the high-speed stirrer. (3) The efficiency optimum amount of soil water mixture
92 SYMpOSllnVt ON PARTICLE SIZE MEASUREMENT
for dispersion is 250 mt. Chu and David- furnished by 5 ml of a normal solution
son report that comparative tests in- in a liter of suspension.
dicate their tube and the Wintermyer Based on this report, use of sodium
cup give a comparatively high degree silicate was written into the ASTM
of dispersion without significant de- and AASHO methods.
gradation. This equipment is not in- Bauer in 1938 (7) reported on tests
cluded in ASTM Method D 422. he had made which showed that sodium
silicate was not always the best agent
Gage to use and that the optimum amount
of agent to use varied with different
soils.
d with Tyner noted in the progress of work
r Hose
Sliding ressed on the fixation of various forms of
Device .=
Escape phosphate that considerable dispersion
occurred when the soils were shaken with
dilute sodium metaphosphate solutions.
Following a study involving 28 soils
Brass he reported in 1939 (8) that "sodium
metaphosphate gives promise of ful-
:1 Gloss filling the need for a dispersing agent
eler Jar
capable of dispersing a wide variety
of soil types, many of which cannot be
" B r~ S~ satisfactorily dispersed for mechanical
analysis by the pipet method in a single
operation."
)n Head
Inclined Tyner indicates that the sodium meta-
s at the phosphate was effective in dispersing
Directh soils having a relatively high calcium
Air Inj,
carbonate content. The author recently
made a grain-size analysis of a sample
of limestone dust used as mineral filler
FIG. 4 . - - C h u and Davidson Air Dispersion in asphaltic concrete. The test was
Tube.
performed in accordance with ASTM
Since soaking of the sample can also Method D 4 2 2 - 5 4 T . No check test
be done in the cylinder, a number of was made by any other method. Results
transfers of the soil-water material are show the dust to be an extremely fine
eliminated. material so far as filler is concerned,
Dispersing Agents: an indication that the dust was highly
Thoreen reported in 1933 (6) that dispersed. There is some show of interest
"extensive tests with various defloc- on the part of asphalt paving technol-
culating agents showed sodium silicate ogists in the grain-size distribution of
to be the most effective for maintaining materials used as filler. The hydrometer
separation of the dispersed soil particles method is a possible method of analysis
in suspension." Other agents used in should such specification requirements
the study were potassium hydroxide, be needed.
sodium carbonate, and sodium oxMate, Tyner in a footnote in his article (8)
for which test results were given. The writes that E. M. Crowther of Rotham-
degree of normality was equal to that stead made a statement in 1938 at
BAUER ON HYDROMETER METHOD AS APPLIED TO SOILS 93
Helsinki, Finland, that with sodium variety of sodium metaphosphate up to

hexametaphosphate "it was possible two months had no harmful effect.
to perform mechanical analysis of a
large group of soils by sedimentation Maximum Size of Particle:
in very hard water." This author re- There is some difference of opinion
cently made check tests on a local soil concerning the maximum size of particle
using both Champaign-Urbana tap water for the soil sample used in the sedimenta-
having a hardness of approximately
tion procedure. When the tentative
300 ppm and demineralized water,
method was first adopted in 1935, pro-
securing essentially the same hydrom-
vision was made to use only that portion
eter readings for the same intervals of the soil which passed a No. 10 sieve.
of time. Differences were small and
No change has been made in this re-
not consistently in the same direction.
quirement, but there are requests to
Here is a detail of procedure that should
replace the No. 10 sieve with one of the
be investigated further, since use of
following: No. 4, No. 40, or No. 200.
tap water will decrease the cost of a
In certain laboratories an initial
test and at the same time be more con-
separation of the soil is made on the No.
venient.
4 sieve for other tests. No further separa.
Wintermyer and Kinter reported in
tion need be made to secure the sedi-
1954 (9) the results of an extensive
mentation sample if particles up to
series of tests on a broad selection of
that size are permitted. Other labora-
soils using a large group of dispersing
tories would like to use the minus 40
agents representing a wide range of
fraction because that is the portion of
chemical properties. They reported that
the soil used in the liquid and plastic
"sodium polyphosphate and sodium
limit tests. Still others feel that the
tripolyphosphate were highly and about
minus 200 fraction should be used. Their
equally effective for all the experimental
reason is that the two portions of the
soils representing many of the great
grain-size accumulation curve secured
soil groups of Continental United States.
from sedimentation and from sieving
Two others, sodium hexametaphosphate
do not fit together properly in every
and sodium tetraphosphate, were only
case unless a minus 200 fraction is used
slightly less so. None of these four phos-
in sedimentation. Preparation of a
phates was effective with laterite, a
minus 200 sample involves more over-all
soil of the tropics. This soil was highly
time and work, but there are laboratories
dispersed with trisodium phosphate
that have worked out satisfactory details
and tetrasodium pyrophosphate, which
of procedure. In view of the unrecon-
were generally ineffective with members
cilable requests, the original provision
of the other soil groups."
for a sample retained on the No. 10
Chu and Davidson reported favorably
sieve has been retained
in 1954 (I0) on the use of sodium mela-
phosphate as a dispersing agent and I t might be well to mention here
that there was practically no difference that all the plus 200 particles (74 ~)
in the dispersing effect of six different are settled out of the suspension before
varieties of sodium metaphosphate; that the 2-min reading is taken. For the
the degree of dispersion is nearly in- condition where about 90 per cent of a
dependent of the amount of dispersin~ 50-g sample is in suspension when the
agent used in the range of 20 to 120 ml 2-rain reading is taken, the grain size
of 0.5 N solution; that aging of one is of the order of 29 or 30 # at the level
94 SYMI'OSIII~ ON PARTICLE SIZE M E A S U R E M E N T
at which the density is read by the where:

hydrometer. D = diameter of particle, ram,
If all the large particles are settled n = coefficient of viscosity of sus-
out before the first reading is taken, pending medium, poises,
what difference can it make if they are L -- distance from the surface to the
included in the sample? The sectional level at which the density of the
group of Subcommittee R-3 on Physical suspension is measured, cm,
Characteristics of Soils of ASTM Com- G = specific gravity of soil particles,
mittee D-18 has data that when particles G1 = specific gravity of the suspending
larger than the No. 200 sieve are added medium, and
to the suspension following dispersion K = constant depending on the tem-
with either the mechanical or the air- perature of the suspension and
dispersion equipment the hydrometer specific gravity of soil particles.
readings are not affected. When the
larger particles are included with the Prior to 1954, a table of diameters
sample to be dispersed with the dis- appeared in ASTM Method D 422 for a
persing equipment, there appears to selected series of time intervals, T, for a
be some degradation of these larger constant value of L of 32.5 cm, for a
particles. When per cents were figured value of G of 2.65 and a value of n of
based on the minus 200 fraction of the 0.0102 poises. Values of L were never
sample, the values in some instances as much as 32.5 cm, values of G and n
were over t00 per cent for one or more were rarely those assumed. I t was
of the early readings. An explanation necessary therefore to prepare tables
is that the larger particles were de- or graphs of correction factors to apply
to the tabulated values of D. Corrected
graded.
values of D were often very much smaller
Calculations: than the value taken from the table.
Results are expressed as percentage This caused many persons to feel that
values for particles smaller than certain the diameter values were not accurate.
diameters. For each hydrometer read- In the formulas for P and D, certain
ing, the percentage of soil remaining items are constant for the series of
in suspension at the level at which the readings constituting a test and certain
hydrometer is indicating the density items vary with the readings. In the
of the suspension is calculated together calculation section of the 1954 revision,
with the diameter of the largest particle setting up the formula for D in this
that could have been at the surface of manner is an important detail. The two
the suspension at the beginning of numbers (30 and 980) never change,
sedimentation and which has settled values of n and 61 depend upon the
to the level at which the hydrometer is temperature of the suspension, and the
indicating the density of the suspension. value of G is constant for the soil used
The percentage value is calculated ~// 30 n
in the same manner in the revised method in the test. Values of 980 (G -- G1)
as in the original. The formula for the were calculated by Bauer and reported
specific gravity hydrometer appears in 1937 (n), for a range of temperatures
in a slightly different form. of 16 to 30 C and for a range of specific
The diameter of particle is based on gravities from 2.35 to 2.90. A table of
Stokes' law, expressed as: these values is included in the revised
method.
D -- 980(6 -- 62) T The sedimentation cylinder now has a
B A U E R ON H Y D R O M E T E R M E T H O D AS APPLIED TO SOILS 95
requirement that the inside diameter into one, named the composite correc-
shall be such that the 1000-ml mark is tion. Values are determined experi-
36 • 2 cm from the bottom on the in- mentally by preparing a solution of
side. With specific size requirements water and dispersing agent in the same
for both the hydrometer and the sedi- proportions that prevail in a sedimenta-
mentation cylinder, it is possible to tion analysis, bringing the solution to
compute with sufficient accuracy the several temperatures spanning the range
value of L based on average values. A expected to prevail in actual testing,
table of such values is given in the re- and taking readings with the hydrom-
vised method. eter. This composite correction is
To make the calculation for D, it is subtracted from the original hydrom-
necessary to know the specific gravity eter reading.
value G for the soil particles, the tem- The correction factor, a, for taking
perature of the suspension, and the time care of soil specific gravities other than
interval. Values of K and L are taken 2.65 is the same as in the previous method
from tables, and the calculation for D and must be used when the grams-per-
may be made using a 10-in. slide rule. liter hydrometer is used.
The value L is divided by T using the
A and B scales, the square root being SUMMARY
indicated on the D scale. Without The revised method of test incorpor-
ascertaining the value of the square
ates a number of new features that fa-
root, it may be multiplied by K, using
cilitate performance of the test, improve
either the C or CI scale.
Formulas for P, percentage of soil, the accuracy of the test results, and sim-
are based on use of distilled or de- plify calculations. The new requirements
mineralized water. Use of the dispersing for hydrometers call for instruments that
agent causes the hydrometer readings are sufficiently uniform to be inter-
to be greater than with water alone. The changeable. By placing necessary size
soil hydrometers are calibrated at 20 C requirements on the sedimentation cyl-
(68 F) and use of the hydrometers at inder, a table of effective depth values
other temperatures produces incorrect has been included in the published
readings due to expansion or contraction method. Provision was made for air-
of the bulb. Manufacturers of hydrom- dispersion equipment that produces less
eters graduate the stems to be read degradation of soil particles. A new
at the bottom of the meniscus formed chemical dispersing agent is required
by the liquid on the stem. Readings that gives better dispersion for a wider
of soil suspensions must be taken at variety of soils. The procedure in con-
the top of the meniscus, thus introducing nection with calculations has been
a small error. simplified, including the elimination of a
All these correction items can be put number of correction factors.
REFERENCES
(1) A. M. Wintermyer, E. A. Willis, and R. C. the Colloidal Content of Soils," Soil
Thoreen, "Procedures for Testing Soils for Science, Vol. 23, No. 4, April, 1927, p. 319;
the Determination of the Subgrade Soil and "The Hydrometer as a New Method
Constants," Public Roads, Vol. 12, No. 8, for the Mechanical Analysis of Soils,"
Oct., 1931, p. 197. Soil Science, Vol. 23, No. 5, May, 1927,
(2) G. J. Bouyoucos, "The Hydrometer as a p. 343.
New and Rapid Method for Determining (3) Arthur Casagrande, "Die Araometer-
96 SYMPOSIUM ON PARTICLE SIZE ~/[EASITREMENT
methode zur Bestimmung der Kornvertei- Testing Mats., Vol. 38, Part II, p. 575
lung von B6den und anderen Materialien," (1938).
Julius Springer, Berlin, Germany (1934). (8) E. H. Tyner, "The Use of Sodium Meta-
(4) A. M. Wintermyer, "A New Soil-Dis- phosphate for Dispersion of Soils for
persing Apparatus for Mechanical Analysis Mechanical Analysis," Proceedings, Soil
of Soils," Public Roads, Vol. 25, No. 5, Science Soc. of America, Vol. 4, p. 106
Sept., 1952, p. 102. (1939).
(5) T.Y. Chu and D. T. Davidson, "Simplified (9) A. M. Wintermyer and E. B. Kinter,
Air-Jet Dispersion Apparatus for Mechani- "A Study of Dispersing Agents for Particle-
cal Analysis of Soils," Proceedings,Highway Size Analysis of Soils," Public Roads,
Research Board, Vol. 32, p. 541 (1953). Vol. 28, No. 3, Aug., 1954, p. 55.
(10) T. Y. Chu and D. T. Davidson, "Defloc-
(6) R. C. Thoreen, "Comments on the Hy- culating Agents for Mechanical Analysis
drometer Method of Mechanical Analysis," o[ Soils," Bulletin No. 95, Highway
Public Roads, Vol. 14, No. 6, Aug., 1933, Research Board, (Laboratory Analysis of
p. 93. Soils), p. 15 (1954).
(7) E. E. Bauer, "A Study of Deflocculating (11) E. E. Bauer, "Hydrometer Computations
Agents Used in the Particle-Size Deter- in Soil Studies Simplified," Engineering
mination of Soils," Proceedings, Am, Soc. News-Record, Vol. 118, May 6, 1937, p. 662.
DISCUSSION
MR. L. T. WORK.I~I have appreciated MR. ALAN R. LUKENS.2---~'or how
greatly the work on the hydrometer that long a period of time do you wait to
has been done so carefully and so thor- allow all air bubbles to rise above the
oughly by the author. effective level of the hydrometer? As you
The question I ask is of a research know, the presence of air bubbles will
nature. Has anything been done with change the specific gravity of the sus-
nonfoaming detergents in lieu of the pension.
phosphates to wet the material? MR. BAUER.--We proceed with the
MR. E. ]~. BAUER (author).--No, not test according to a predetermined sched-
t h a t I know of. The Bureau of Public ule. Air dispersion equipment is used in
Roads made quite an extensive study of some instances and we proceed im-
dispersing agents. In the testing we have mediately to put the suspension in the
done at the university, we have not been sedimentation cylinder and add the ad-
bothered to any extent with foaming. ditional water to bring the suspension up
MR. WORK.--I was afraid that if you to the 1000-ml level. Then we have a
tried any of the regular detergents they minute of shaking end over end, after
would be foaming ones, like the shampoo which we start the series of hydrometer
detergents, and so on. The nonfoaming readings. The Bureau of Public Roads in
ones would probably not trouble you and their report in PubNc Roads (4) indicates
they might do a very good job. that their test results with the air dis-
MR. BAtlEI~.--We have used the persion equipment are the same as with
sodium metaphosphate. A number of the mechanical device. As far as I know
laboratories making a great m a n y routine they did not do any checking against the
tests are using Calgon, for instance. The pipet method or any of the other older
Bureau of Public Roads has never, to m y methods. We have not noticed any dif-
knowledge, reported any difficulty with ficulty with the air-dispersion device.
the commercial detergents tried in its MR. LUKENS.--Apparently I did not
laboratory.
2 President, Lukens Laboratories, Inc., New-
x Consulting Engineer, New York, N. Y. ton, Mass.
DISCUSSION ON HYDROMETER METHOD AS APPLIED TO SOILS 97
make myself clearly understood in my MR. BAtmR.--The ASTM method of

question. test requires that the hydrometer be
As one immerses the hydrometer, placed in the suspension about 20 to 25
during the test procedure, the bulb of the sec before the reading is due. We have
hydrometer comes to rest a certain dis- noticed that we do get variable readings
tance below the surface. The percentage at times, or that two successive readings
by weight of particles of a given size do not seem to be in agreement with each
depends upon the specific gravity of the
other, but the variations are small. You
fluid and that of the proportion of par-
may have suggested the reason for these
ticles being tested. A fluid, due to reten-
variations.
tion of air bubbles, may have a false
specific gravity. I t is advisable to wait MR. LUKENS.--Have you ever noticed
until all air bubbles are above the hy- an accumulation of very small air bubbles
drometer bulb level before making a upon the hydrometer?
reading. MR. BAUER.--No.
S T P 2 3 4 - E B / A u g . 1959
S E D I M E N T A T I O N PROCEDURES FOR D E T E R M I N I N G
P A R T I C L E SIZE D I S T R I B U T I O N
BY W. F. SULLIVAN1 AND A. E. JACOBSEN~
SYNOPSIS
The theory underlying the application of sedimentation procedures for
particle size distribution is presented. Modifications of the theory to satisfy
the several types of sedimentation techniques are described. Consideration is
given to the various experimental techniques, particularly to the advantages
and disadvantages of each. Experimental results are presented for the entire
subsieve range.
Information on the subsieve particle size distribution of finely divided materials is

of major importance in physicochemical studies, since many of the properties of in-
terest are dependent on the state of subdivision. It is also of importance to industry,
as for example in evaluating large scale grinding and particle size separation equip-
ment. In the pigment industry, in particular, it is essential that particle size distribu-
tion be closely controlled, since the optical and rheological properties of pigmented
systems are often strongly varying functions of particle size.
Although many methods for determining subsieve particle size have been de-
veloped, some of these yield only an average diameter for an assumed particle shape.
The measurement of surface area of a powder allows the diameter of a spherical or
cubical particle having an average surface to be determined. In principle, light scat-
tering, sedimentation, and light or electron microscopy provide information from
which a complete particle size distribution may be derived. Determination of scat-
tered light intensity as a function of angle must usually be performed at very low
concentrations of suspended material and unless other conditions are favorable, such
as the ratio of refractive index of the particle to suspension medium and the ratio of
particle diameter to wavelength, there is practical difficulty in evaluating the scat-
tering data. Light and electron microscopy can provide valuable information on par-
ticle shape, but counting procedures are tedious and tend to give distributions which
are displaced to smaller particle diameters than are the true distributions. On the other
hand sedimentation procedures have widespread application because of their con-
venience and the fact that particle size distributions obtained therefrom can be cor-
related with the phenomenon or apparatus under study.
1 National Lead Co., T i t a n i u m Division, Research Laboratory, Sayreville, N. J.
98
SULLIVAN AND JACOBSEN ON SEDIMENTATION PROCEDURES 99
PRINCIPLES OF SEDIMENTATION
DISTRIBUTION FUNCTION
Particle size distribution may be characterized by a distribution function F(D)
which is defined by the equation
dr = F(D) dD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
where:
d6 = weight fraction of particles having a diameter between D and D + dD, and
D = particle diameter of an equivalent Stokes' sphere.
The distribution function characterizes the distribution as it exists in the medium
under study. In some cases it may have a simple mathematical form--for example it
may be Gaussian. This usually occurs when the particulate material has been sub-
jected to physical treatment, such as grinding, and the resultant size distribution is a
reflection of the nature of this treatment. Explicit forms of the distribution function
have been given by many authors (1,2,3) 2 and have the advantage that, after a few
experimental points have been obtained to determine which form is applicable, the
balance of the distribution curve, F(D) versus D, can be obtained by extrapolation.
Without prior knowledge of the form of the distribution function, it is best to obtain
sufficient experimental data to determine its form with the desired degree of preci-
sion.
Instead of determining the distribution function itself, it is often more convenient
and precise to plot particle size data as a cumulative curve, f0 Dm F(D)dD versus Dm,
where the integral represents the weight fraction of particles between size with diame-
ter 0 and a particular size with a diameter Dm. I t is always possible to obtain F(Dm)
from f0 Dm F(D)dD by differentiation.
APPLICABILITY OF STOKES' LAW

The range of particle size covered by sedimentation procedures is from about 0.1
to 44 ~ (No. 325 sieve). Stokes' law, which is the basis of all sedimentation proce-
dures, describes the steady state settling of spherical particles by
FI = 3~-,TDv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
where:
F/ ---- frictional force,
-- coefficient of viscosity of the suspension medium, and
v -- velocity of the particle in the Suspension medium.
This law has been found experimentally to be valid for particles as large as 50 #
(4,5) when the coefficient of viscosity is of the of order of 1 centipoise (water). Lamb
(6) has given as a condition for the upper limit of validity of Stokes' law the equation
d~D
R = --v < 1................................. (3)
where:
R = Reynolds' number, and
d, = density of suspension medium.
The boldface numbers ha parentheses refer to the list of references appended to this paper.
Eisner (7) has verified this equation experimentally and also determined the amount
of drag on spheres at Reynolds' numbers greater than one. Equation 3 is useful for
estimating the upper limit of validity of Stokes' law in media of high viscosity where
experimental verification has generally not been undertaken. Berg (8) has made use
of the equation in this fashion. At the lower end of the particle size scale, Stokes'
law has been used to describe the motion in fluids of particles as small as ions and is
apparently valid in this region. In determining particle size by sedimentation pro-
cedures, however, there is a lower limit of about 0.1 ~ which will be discussed later.
The effect of the concentration of solids on the validity of Stokes' law has not been
investigated systematically, although by experimentation Martin (9) was able to es-
timate that Stokes' law was applicable up to about 3 per cent solids for titanium
dioxide particles suspended in water. Most investigators have used solids contents
between 1 and 3 per cent.
GRAVITATIONAL SEDIMENTATION
Sedimentation methods are performed under the influence of either gravitational
or centrifugal force. When exposed to a gravitational field, a particle accelerates and
approaches its steady state velocity asymptotically. Berg (8) has calculated that un-
der the usual conditions for performing gravitational sedimentation, the time to reach
99 per cent of the steady state velocity is less than 1 sec. This time of acceleration
may therefore be neglected and we may write
h
v = -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)
t
where:
h = distance from surface to a point in the suspension, and
t = time.
In this and subsequent sedimentation equations Brownian motion is neglected.
By combining Eq 4 with Eq 2 and equating the gravitational force on the particle
to the frictional force, the well-known equation
j// 18nh (5)
Dm= (d~ -- d,)gt,~
results,
where dp = density of particles, and
m = subscript referring to particular values of D and t, assuming that 7, h,
d~ and d~ are held constant. Equation 5 gives the diameter of an equiv-
alent spherical particle which has settled through a height h in time tm.
Particles with diameters greater than Dm have settled through this height
in times less than tm.
Method Based on the Change in Concentration at a Given Level:

Two sedimentation procedures are possible for determining particle size distribu-
tion of polydisperse systems. The first of these has been called the incremental method
(9,10) and consists of periodically determining the concentration of solids at a given
level. This principle has been used in the Andreasen pipet method (4,21), hydrometer
methods (4,5), Berg's diver method (8)~ and the Kelly sedimentation tube (11). If the
SULLIVAN AND JACOBSEN ON SEDIMENTATIONPROCEDURES 101
concentration is defined as the mass per unit volume, Eq 1 m a y be written as

dc
-- = F(D) dD .................................. (6)
Co
where:
dc = the concentration of particles having a diameter between D and D + dD, and
co = the total concentration (total mass divided by total volume).
If a given mass of particles having a diameter between D and D + dD is trans-
ferred by gravitational sedimentation from a thin shell at the surface of distance S
and thickness AS to a thin shell at the distance h and thickness Ah, there is no change
in separation of the particles and therefore no decrease in concentration. Equation 6
m a y then be written as
dc(S, D) dc(h,D)
F(D) dD . . . . (7)
Co Co
where:
dc(S, D) = concentration of particles having a diameter between D and D + dD
at S, and
dc(h, D) = concentration of particles having a diameter between D and D + dD at
h originating from AS at S.
Since only those particles are contained in Ah with diameters equal or less than D,~
and since F(0) = 0, integration of Eq 7 gives
D,~ f0 emde(h, D)
fo F(D) dO (S)
Co
where cm = the total concentration at the time t,~ at the height h, or
fo D'~ F(D) clD = cm

-- m = 1,2,3, ....................... (9)
Co
Method Based on the Accumulation of Material at a Given Level:

The second method which has been called the cumulative method (9,10) is based
on the determination of the total weight fraction sedimented at a definite height as
a function of time. The sedimentation balance, first developed by Od6n (12,13), em-
ploys this principle. If the per cent sedimented is defined by the equation
w8
loo x #~ = ~ x lOO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1o)
where:
p,~ = total weight fraction sedimented,
W8 = weight sedimented, and
W~ -= total weight,
then Od6n has shown that
:/ F(v) = (1 - p:) + t= (eP m = 1, 2, 3,. . . . . . . . . . . . . (11)

Jo \dt/m
Instead of obtaining the distribution function by differentiation of the cumulative

curve, it may be obtained from the second derivative of the p,, versus tm curve (12,13)
as
F(D~) = - D ~ \dt~lm m = 1, 2, 3,. . . . . . . . . . . . . . . . . . . . . (12)
CENTRIFUGAL SEDIMENTATION
Comparison of Gravitational with Centrifugal Sedimentation:

Since the settling time, as given by Eq 5, becomes excessively long for commonly
used values of the parameters 7, h, dp, and d~, the usual lower limit of particle size
determinable by gravitational sedimentation is about 1 tL. This is the main reason for
the use of centrifugal sedimentation for determining particle size distribution in the
region below 1 tL. There are, however, other factors which preclude the use of very
long settling times in cases where the time required to complete the determination is
of no importance. These factors are the Brownian movement and convection due to
vibration or temperature gradient.
The differential equation for the rate of change of concentration under these con-
ditions for a monodisperse system has been given by Jost (17) as
o~ ~(o~ ) o (vc~ . . . . .(13)
o5 = \ox2 + .... o-~ .....................
where:
~3 = diffusion coefficient,
c = concentration, and
x = a rectangular coordinate.
The mean square of the displacement X 2 due to Brownian movement is related
to the diffusion coefficient by
X2
g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (14)
and, on the basis that Stokes' law is valid, then

4kTt
X2 .................................. (15)
6zrnD
where:
k = Boltzmann's constant, and
T = absolute temperatures (Kelvin).
holds (IS) from which the diffusion coefficient may be calculated in terms of the
equivalent particle diameter. Knowledge of the external influences would in prin-
ciple allow the solution of Eq 13 to be determined, but unfortunately the effect of
vibration and temperature gradient are not known precisely in particle size work.
There is no doubt, however, that convection due to vibration is the more serious
factor, particularly in centrifugal sedimentation where vibration results from slight
unbalance of the centrifuge arms. I t is the opinion of workers in this field
(14,15,16) that vibration imposes a lower particle size limit of about 0.1 ~ and that data
obtained in this region are not sufficiently precise to justify the differentiation neces-
sary to obtain the distribution function F ( D ) . Convection due to temperature gra-

dient can be minimized with thermostatic temperature control of the order of 0.01 C.
Assuming that convection due to vibration and temperature gradient have been
minimized, it is possible to calculate the effect of the Brownian movement on gravi-
tational settling by Eq 13. For one dimensional motion in the direction x this equa-
tion reduces to
Oc c9~c Oc
-- = E)-- -- v--. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (16)
Ot Ox~ Ox
Solutions have been given by Ftirth in Jost's book (17). These have the form shown
in Fig. 1 and demonstrate clearly that, in the settling of monodisperse particles of suffi-
ciently small size, the Brownian movement causes loss of sharpness in the boundary
which increases with time. If one is interested in the approximate effect of the Brown-
TABLE I.--APPROXIMATE EFFECT OF

BROWNIAN MOVEMENT ON THE GRAVI-
TATIONAL SEDIMENTATION OF RUTILE
IN WATER.
D,/La Time, hr ~ / ~ , cmb h, cmc
(}.2 . . . . . . . . . . 24 1 (}.0(}6 (}.69 S r

0.1 .......... 24 0.989 0.17 E
0.1 .......... 48 0.12 I 0.34
o
Ol . . . . . . . . . . I 9o jol j o~
P a r t i c l e d i a m e t e r of a n e q u i v a l e n t S t o k e ' s
sphere.
b F r o m E q 15 w i t h k = 1.38 X 10 -18 e r g s
o Distance X h
p e r d e g C, T = 298 K e l v i n , a n d y = 8.94 X 10 -8
poise. FIG. 1 . - - E f f e c t of B r o w n i a n M o v e m e n t o n
c D i s t a n c e f r o m s u r f a c e ~o a p o i n t in t h e sus- t h e G r a v i t a t i o n a l S e d i m e n t a t i o n of V e r y Small,
p e n s i o n ; f r o m E q 5 w i t h d p = 4.20 g p e r c u cm, Monodisperse Particles.
d , = 0.997 g p e r c u e m a n d g = 9 8 0 c m p e r
see p e r see.
Jan movement, the tedious numerical evaluation resulting in the curves of Fig. 1
may be avoided by comparing the square root of the mean square displacement given
by Eq 15 with the distance settled given by Eq 5. Table I contains values for the
sedimentation of rutile in water.
These calculations which neglect the effect caused by the bottom of the sedimen-
tation vessel show that the displacement caused by Brownian movement is negligible
for futile particles larger than 0.2 u, but not for 0.1 u particles. The effect of the
Brownian movement has also been calculated by Heywood (29) on the basis of equa-
tions developed by Berg.
The advantage of centrifugal sedimentation over gravitational sedimentation in
minimizing the effect of Brownian movement is apparent from Eq 15 which shows
that the mean square of the displacement due to Brownian movement is proportional
to time. By application of a centrifugal force many times larger than gravitational
force, the time necessary for particles to move a given distance is decreased and con-
sequently the ratio of displacement to distance settled is also decreased.
In summary, centrifugal sedimentation has the advantages over gravitational
sedimentation in decreasing the excessive time necessary to settle particles less than
104 SgMPosiulvl ON PARTICLE SIZE MEASUREMENT
2/~ and of minimizing the effect of the Brownian movement. On the other hand vi-
bration is harder to eliminate and the apparatus is not as easily maintained at con-
stant temperature.
Theory of Centrifugal Sedimentation:

The equations of motion of a particle of diameter D moving in a centrifugal field
and obeying Stokes' law have been derived by Kamack (16). For the radial motion
he obtained the differential equation
dOr 187 dr
~dt + (d~ - d.,)D2 dt co~r = 0 . . . . . . . . . . . . . . . . . . . . . . . . . (17)
where:
r = distance from the center of rotation to a point in the suspension, and
co = angular velocity in radians per second.
As with gravitational sedimentation, the initial acceleration of the particle rapidly
decreases so that Eq 17 becomes
187 dr
~r = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . (18)
(dp -- d,)D ~ dt
which can also be readily obtained by equating the frictional force on the particle
to the centrifugal force. Integration of Eq 18 results in
D = a/ 187 In r/S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (19)

'V (d, -- d.)~o~t
where S = distance from center of rotation to surface of suspension.

This equation, first obtained by Svedberg and Nichols (19), is analogous to Eq 5.
I t may be noted that in centrifugal sedimentation the particles are continuously ac-
celerating and moving apart as they traverse radial paths.
Methods Based on the Change in Concentration at a Given L e v e L - - I f a given mass of
particles having a diameter between D and D + d D is transferred by centrifugation
from a thin shell at the surface to one in the body of the suspension, the concentra-
tion is decreased. Since concentration is inversely proportional to volume at constant
mass, we have
dc(r, D) (S + AS)2 -- S~
........................... (20)
dc(S, D) - (r + &r) ~ -- r 2
where:
dc(r, D) --- concentration of particles having a diameter between D and D + d D
at r originating from AS at S,
dc(S, D) = concentration of particles having a diameter between D and D + d D
at S,
AS = thickness of shell at S, and
Ar = thickness of shell at r containing all the particles originally in shell AS.
Elimination of S and S + AS by Eq 19 results in
&(r, D) exp r 2(d, - d~)D"~t 1

dc(S, D) ~_ i~ ..l . . . . . . . . . . . . . . . . . . . . . . . . (21)
SULLIVAN AND JACOBSEN ON SEDIMENTATIONPROCEDURES 105
I t should be noted that Eq 21 is valid no matter which variables of centrifugation

are changed to transport the particles from distance S to distance r. B y introducing
the distribution function from Eq 6 in which dc is identical with dc(S, D) there re-
suits
F(D) dD -- co d*)D~c~-] dc(r, D) . . . . . . . . . . . . . . . . . . . .
1 exp 12(dp ---1~ (22)
Solutions of this differential equation m a y be written in which the integration

limits are functions of any of the centrifugal parameters, but only two solutions are
of practical interest. The first, called the variable time method, is obtained by evalu-
ating at t = tm. Since only those particles are contained in &r with diameters equal
or less than Dm and since F(0) = 0, then
foDmexpl--2(dp---d-~)D2c~
c ' ~ d c-] ( r ' D ) 1 8 7 ............... (23)
Substitution of Eq 19, evaluated at t = t,~ and D = D ~ , into Eq 23 results in
f oDm exp [ - (2 in r/s)D2/Dm~] F(D) dD = Cm

-- m = 1 2, 3. . . . . . . . . . . . . (24)
Co
I t is not possible to obtain an exact solution for

fo F(D)dD as in Eq 9 for gravita-
tional settling. This is primarily caused by the dilution due to the radial paths trav-
ersed by the particles and the dilution resulting from the differences in acceleration of
particles in a layer of finite thickness.
The second solution of Eq 22, called the variable height method, results by evalu-
ating at h = hn = rn -- S, again taking into account that only those particles are
contained in &rn with diameters equal to or less than D~. Then we m a y substitute
Eq 19 into Eq 22 obtaining
1
F(D) dD = -- exp [2 In rJS] dc(r,,, D) . . . . . . . . . . . . . . . . . . . . . (25)
Co
Integration yields
fo c-o -S- dc(r,,,D) n = 1, 2, 3,. . . . . . . . . . . . . . (26)
where Dn is obtained from Eq 19 evaluated at r = rn 9 Both Eqs 24 and 26 have been

obtained by K a m a c k (16).
I n practice most centrifuge tubes are cylindrical in shape rather than sector-shaped.
On the assumption that the particles striking the side walls of the tube cause no ap-
preciable error in sedimentation, derivations similar to the above give
fo Dm exp [ - (ln r/S)D~/Dm 2] F(D) dD = Cm

-- m = 1, 2, 3. . . . . . . . . . . . . . (27)
Co
for the variable time method, and
= - dc n = 1, 2, 3,. . . . . . . . . . . . . . . . . . (28)
6o
for the variable height method.
Methods Based on the Accumulation of Material at a Given LeveL--These have been

the most widely used methods in centrifugal sedimentation. Equations for sector-
shaped tubes were first given by Romwalter and Vendl (20) who obtained for the
variable time method the equation
Pm= fo
D,,~ R2
(
R2 ~ S 2 1 -- exp [ --
2(d,. -- d~)D~.,~t~
187 J/
F(D) dD +
f) ,~
F(D) dD
m = 1, 2, 3,..(29)
where R = distance from center of rotation to bottom of suspension.
I t has not been possible to derive an exact solution for the integral F(D)dD
f0~176
from Eq 29. Brown (14), however, showed that for the variable height method an
exact solution was possible. He obtained the equation
fo~ F(D) dD = (1 -- p,) + 2S~ ~ , n = 1, 2, 3. . . . . . . . . . . . (30)
where D~ is obtained from Eq 19 evaluated at S -- S~ and r -- R.

If the centrifuge tubes are cylindrical in shape rather than sector-shaped and if the
errors caused by particles striking the sidewalls are neglected, the above equations
are modified to
r ~176
P" = J0 R -- S (1 -- exp I -- 18rl .J/ + f Jo,~
~
m = 1,2,3 . . . . . . . (31)
for the variable time method, and
F(D) dD = (1 -- p,~) + (R -- S,,) dp n = 1, 2, 3 , . .......... (32)

f0 n
for the variable height method,

DISCUSSION OF E X P E R I M E N T A L PROCEDURES
GRAVITATIONAL ~V~ETHODS BASED ON THE CTffANGE IN CONCENTRATION

AT A GIVEN LEVEL
The basis of these methods is Eq 9 in which the various cm are determined experi-
mentally and the corresponding D~ calculated from Eq 5.
Andreasen Pipet Method (4,21):

I n this method small samples are removed from the suspension during sedimenta-
tion and the concentrations determined analytically or by evaporating an aliquot to
dryness and weighing. The method has been widely used because results are obtained
with relatively simple apparatus. I t has been subject to m a n y modifications, some
of which are quite recent (22,23).
I n spite of its wide use, there are disadvantages to the pipet method. At the low
concentrations necessary to insure the validity of Stokes' law, a relatively large sam-
ple must usually be removed to determine the concentration with sufficient precision.
This means that a numerical correction must be made of the settling height as sedi-
mentation progresses. More serious, as was pointed out by K6hn (24), is the fact that
the thickness of the layer removed is often greater than 1 cm and that a considerable
disturbance is introduced into the steady settling state.
Berg's Side Pipet Method (8):

This is a variation of Andreasen's method in which a sample is removed with a
special pipet from a side arm fastened permanently near the bottom of the sedimen-
tation vessel. Although Berg has used this method for determining the size distribu-
tion below 20 #, the apparatus appears to be still subject to the same limitations as
the Andreasen apparatus.
Hydrometer Method:
This method was developed by Bouyoucos (25), Jarrett and Heywood (26), Klein
(27), Schweyer (28), and others. I t is assumed that the difference in density between
suspension and suspension medium is proportional to concentration and that the
hydrometer measures the density at a given level somewhere near the center of the
hydrometer. The position of this level is somewhat indeterminate and, since the hy-
drometer sinks as sedimentation progresses, the position is not constant. Removal
and reinsertion of the hydrometerSnto the suspension is also disadvantageous because
of disturbance of the steady settling state.
Berg's Diver Method (8):

Small glass divers of different densities are immersed in the suspension and assume
equilibrium positions at the level of equal suspension density. In this method, on the
assumption that concentration is proportional to the difference in density between
suspension and suspension medium, concentration is determined as a function of both
height and time. Since divers of radii less than 1 cm have been used, the uncertainty
introduced in the height is not too large. A disadvantage is that the diver is usually
not visible in the suspension and must be moved laterally into view with a magnet or
located with a search coil (26).
Manometric Methods:
The Kelly sedimentation tube (11) was one of the first to employ this method. A
manometer filled with suspension medium and attached to the sedimentation vessel
at a known distance beneath the surface of the suspension was used to record the
density changes at this position. Differential manometers (26) have also been used
similarly. These methods have the serious limitation that the changes in level of the
manometric fluid are small, even when the manometer is inclined, so that the pre-
cision is generally low. Gessner (4) has also shown that there is mixing of the fluids
at the junction of the manometer fluid and the suspension medium, thereby making
the density determination at this point questionable.
Photometric Methods:
The decrease in intensity of a light beam traversing the suspension at a given level
forms the basis of this method. While a relatively narrow beam of light can be used
and disturbance of the suspension is held to a minimum, the method has the serious
disadvantage that the relation between the extinction coefficient and concentration
is generally not known over a wide range of particle size. Where this relation has been
determined empirically for a given material in a given size range, the method is con-
venient and reliable (30,31,32). 8
GRAVITATIONAL METHODS BASED ON THE ACCUMULATION OF MATERIAL

AT A GIVEN LEVEL
The basis of these methods is Eq l l in which the pm and ~- are determined

m
experimentally and Dm calculated from Eq 5. The sedimentation balance for deter-

mining pm was first developed by Odin (12,13). Since pm is determined as a function
of time, ~- is usually determined from the slope of the curve. For this purpose
m
Eq l l is written as
fo D~ F(D) dD = 1 tangential intercept (33)
Modifications including the use of automatic registration of the pm versus t,~ curve
were made by Od6n (33) and others (34,35,40). Jacobsen and Sullivan (34) used a cy-
lindrical cup to avoid loss of sedimented material and, by introducing a buoyancy fac-
tor, were able to avoid the long wait necessary to obtain complete sedimentation oc-
curring in suspensions having an appreciable fraction of particles of size less than
1 #. Thus, in determining p~ of Eq 10, application of Archimedes' principle gives
l
W, 1 - d,/dp (W, --Wto) . . . . . . . . . . . . . . . . . . . . . . . . . . . (34)
where:
Wt = weight on the balance arm at time t, and
W t o = weight on the balance arm at time to.
The total weight sedimented includes the mass of all particles in a right circular
cylinder having an area equal to that of the base and a height equal to the height of
the suspension above the base, and is given by
W ~ Co X Abh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (35)
where Ab = area of base.
Other methods in which the fraction sedimented is determined manometrically
have been reviewed by Cadle (3).
With a well-constructed sedimentation balance, movement of the pan (or balance
cup) during weight registration can be kept very small, so that disturbance of the sus-
pension is practically negligible. If, in addition, the particle size analysis is done under
vibrationless and constant temperature conditions, the method is almost free of ob-
jections. There still remains an uncertainty caused by layers of suspension directly
underneath the pan settling free of particles. Although the pm versus l,~ curve may be
obtained with high precision, there is also some uncertainty in determining the tan-
gential intercept. Donoghue (41) has, however, pointed out that this error is not so
large as commonly supposed.
a H. Heywood, British Patent 560,037 (1948).
CENTRIFUGAL METHODS BASED ON THE CHANGE IN CONCENTRATION

AT A GIVEN LEVEL
As with gravitational sedimentation, the major problem is the precise determina-
tion of concentration as a function of time at a given level. To avoid errors caused by
repeated stopping and starting of the centrifuge, Kamack (16) has devised a sector-
shaped centrifuge tube with a built-in pipet capable of removing samples during
centrifugation. The apparatus has operated satisfactorily and is capable of extension
to a large number of tubes. The errors described under the Andreasen pipet method
are also applicable here.
In addition to designing special centrifuge cups, Kamack (16) has given an approxi-
mate solution of Eq 24 for the cumulative distribution
mation is based upon the replacement of the area under the curve of
f[~F(D)dD. (rn/S) 2 versus The approxi-
cn/co bythe area of a series of trapezoids (trapezoidal rule). For tm selected so that tl
< t2 < ta and, on the basis of Eq 19, D2 = ~ 1)1, and Da = 89D1, sequence
the first three equations are as shown in Eqs 36, 37, and 38.
D, F(D) dD -- 89 + (r/S)'l~]cl + 1 -- (r/S),12 + (r/S),/4 ] F(D) dD
+
[ ,.is + F(D) riD.. (36)
ki~fi-+--~-~/~ (~/s),/, + i _I fjo~
foD2F(D) dD= 89 + (r/S)l/'lc, + I1 1 - i;7~,:~j
r/s 1 [jo~'F(D)dD . . . . . . . . .
(37)
D3F(D) dD = ~ + 1 ] ca . . . . . . . . . . . . . . . . . . . . . . . . . (38)
The cm are determined experimentally at the times t,n. Solutions with m > 3 have
been given by Kamack whose notation of the Dm and cm is the reverse of that used
above, that is, tl > t2 > ta . . . .
CENTRIFUGAL METHODS BASED ON THE CUMULATIVE METHOD
Since it has not been possible to give an exact solution of the integral F(D)dD
in terms of centrifuge variables for the variable time method, approximate solutions
of Eq 29 have been used:
Jacobsen and Sullivan's Method (15):
There are two approximations used in this method. In the first it is assumed that
centrifugal sedimentation can be regarded as equivalent to gravitational sedimenta-
tion if the settling height is small compared to the distance from the center of rota-
R--S
tion to the bottom of the suspensions. Values of R - 0.047 or R/S = 1.05 were
used and the constant g in Eq 5 replaced by the average centrifugal acceleration
r giving
./ 18~(R - s)
D,,~ = , ~ , V i ~ Y ~ - / ; ~ ' ......................... (39)
110 SYMPOSIUM ON PARTICLE SIZE ~/[EASUREMENT
The second approximation involves the neglect of errors caused by replacing the
sector-shaped tubes with cylindrical tubes.
To determine the fraction sedimented, the supernatant suspension is separated
from the sedimented material and the concentration determined by evaporating an
aliquot to dryness. For this, Eq 10 is modified to
100 X P,~ ~ co -- ct~ X 100. . . . . . . . . . . . . . . . . . . . . . . . . . . (40)

Co
where ct.~ -- concentration at time tm, and the gravitational Eq 11 is used to calcu-
late the cumulative distribution. In this and other variable time centrifugal methods,
the time of acceleration and deceleration is allowed for by the method of Marshall
(36).
Robison and Martin's Method (37,38):

In this method an approximate solution of Eq 29 was derived by repeated differ-
entiation and an approximation to remove the integral signs, and reintegration of the
resulting linear differential equation. Although Robison and Martin have given higher
approximate solutions, they have found that the first approximate solution which is
based on the assumption that R/S ~ 1 is sufficiently accurate for most particle size
determinations. This solution is given by Eq 41
jl D'~F(D) dD= 1--[M(6--M)

d p P'~+
) TMD'~
8 ( ~ ~+M(M--2)(M--4)]-8D~_
fOo'~ pDM-i dD m = 1, 2, 3,.. (41)
4(R ~ _ s ~)
where: M = $2 In R2/S 2 is determined from the centrifuge constants.
In practice this equation is evaluated by considering Dm and pm to be functions of
the parameter t,,. The pm are determined experimentally and the Dm by calculation
from Eq 19. From a plot of pm versus Dm the quantity ~ is determined from the
m
pDu-ldD by using Simpson's rule for approximate inte-

slope and the integral
fo~176
gration.
Brown's Method (14):
This depends on the use of Eq 30 or 32 in which the p~ are determined experi-
mentally and the D~ calculated at the variable heights S~. Brown's method has been
confirmed both by Jacobsen and Sullivan (15), who compared results with those ob-
tained by their method of approximation, and by Robison and Martin (38), who like-
wise compared results with those obtained by their method. Although Brown's method
has the advantage of being based on an exact solution of the integral
f0 F(D)dD,
in practice it has been found to be inconvenient. This is largely due to the necessity
of varying the centrifuge angular velocity in order to determine the complete particle
size range encountered with most materials.
SULLIVAN AND JACOBSEN ON S E D I M E N T A T I O N 1PROCEDURES 111
A variation of Brown's method has recently been developed by Donoghue and Bos-
tock (39) in which the distance from the center of rotation to the bottom of the sus-
pension rather than to the top is varied. A special centrifuge head which is available
commerically has been constructed to facilitate the collection and removal of sedi-
mented samples.
TABLE III.--RESULTS OF CENTRIFU-

GAL SEDIMENTATION OF INCOM-
TABLE II.--RESULTS OF GRAVITA- PLETELY MILLED RUTILE PIGMENT.
TIONAL SEDIMENTATION OF INCOM-
PLETELY MILLED RUTILE PIGMENT. Concentration
Time, tm, min at Time, tra, g 100 X tJm a
per liter
Time, tm, min iW t -- gW t o ,a W , , gb 100 X Pro*
I 0 .............. 30.60 0
0 ......... 0 0 0 5.0 ............ 17.75 42.0
1.5 ....... 0.045 0.059 1.01 10 . . . . . . . . . . . . . . 11.88 61.3
2.0 ....... 0.060 0. 079 1.35 20 . . . . . . . . . . . . . . 5.11 83.3
2.5 ....... 0.075 0. 0 9 8 1.68 40 .............. 1.53 95.0
3.0 ....... 0.090 0.118 2.02 55 . . . . . . . . . . . . . . 1.07 96.5
4.0 ....... 0.110 0.144 2.47 75 . . . . . . . . . . . . . . 0.77 97.5
5.5 ....... 0.125 0.164 2.81 90 .............. 0.61 98.0
8.0 ....... 0.160 0.210 3.60
14 . . . . . . . . . 0.210 0. 275 4.71 a F r o m E q 4 0 w i t h co = 3 0 . 6 0 g p e r liter.
24 . . . . . . . . . 0.260 0.341 5.84
35 . . . . . . . . . 0.310 0.406 6.95
TABLE IV.--CUMULATIVE DISTRI-
60 . . . . . . . . . 0.403 0. 5 2 8 9.04
BUTION FROM GRAVITATIONAL DATA.
84 . . . . . . . . . 0.480 0. 629 10.8
127 . . . . . . . . . 0.610 0.800 13.7
159 . . . . . . . . . 0.702 0. 9 2 0 15.8 Diameter, T i m e , lm
Tangential 1 0 0 f Dm F ( D ) d D ,
Dm , tt min a Intercept,
226 . . . . . . . . . 0.880 1.154 19.8 per cent b per cent c
274 ......... 0.998 1. 308 22.4
327 . . . . . . . . . 1.110 1.455 24.9
18.0 ...... 3.16 0.5 99.5
384 . . . . . . . . . 1.240 1. 6 2 6 27.8
15.0 ...... 4.56 0.8 99.2
420 ......... i 1.320 1.731 29.6
I 10.0 ...... 10.3 2.0 98.0
7.0 ...... 20.9 2.5 97.5
a Wt = weight on the balance arm at time t 5.0 ...... 41.0 4.0 96.0
Wto = w e i g h t o n t h e b a l a n c e a r m a t t i m e to.
3.0 ...... 114 5.0 95.0
b F r o m E q 34 u s i n g ds = 0 . 9 9 7 g p e r c u c m 2.0 ...... 256 7.5 92.5
a n d dv = 4 . 2 0 g p e r c u cm, w e h a v e 1.5 ...... 456 10.5 89.5
1
W~ ( W t - Wto)
0.997 a F r o m E q 5 u s i n g v = 0 . 0 0 8 9 4 poise, h =
4.20 12.0 c m , dp = 4.20 g p e r c u c m , d~ = 0.997 g
p e r c u c m , t e m p = 25.0 C , w e h a v e :
= 1 . 3 1 1 ( W t -- W t o ) .
18 X 0.00894 X 12.0 6.152 X 1 ~ 4
* F r o m E q 10: W~ is c a l c u l a t e d f r o m E q 35 tm
a t a c o n c e n t r a t i o n of 3 0 . 6 0 g p e r liter a n d t h e (4.20 -- 0 . 9 9 7 ) 9 8 0 D m 2 D,n ~
d i m e n s i o n s of t h e a p p a r a t u s t o be: If tm is e x p r e s s e d in m i n u t e s a n d Dm in m i c r o n s ,
w. ooo 10.25 X 10 2
- 1000 X ~r - - X 12.0 = 5 . 8 4 0 g . t h e n tm
Dm 2
b F r o m F i g . 2.
c F r o m E q 33.
PRACTICAL EXAMPLE
TO illustrate the use of the above equations, a practical example, based on the
methods of the authors has been calculated in detail. The sedimentation balance and
the centrifuge as well as the technique of operation have been described in the original
articles (15,34).
Table II contains the gravitational sedimentation data and Table III the centrif-
ugal sedimentation data for an incompletely milled rutile pigment dispersed in wa-
ter by the addition of 0.3 per cent sodium hexametaphosphate (on the rutile basis) as
a dispersing agent.
The data of Tables II and III are plotted in Figs. 2 and 3 respectively and the
5.0
4,0
3.0
2.o.
1.0
I
0 #'
x
I I I I I I I I
o
o 0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0
~30.0
g~
E
3 25.o
20.0
15.0
10.0'
50;
I I I I I I I I
0 50 100 150 200 250 300 350 400 450
Time, tin, rain
Fro. 2,--Gravitational Sedimentation Curves of Incompletely Milled Rutile Pigment.
tangential intercepts shown as dotted lines. In practice these plots are made on a
large scale to minimize the error in determining the tangential intercepts.
The method of calculating the cumulative distribution is illustrated in Tables IV
and V and the results shown graphically in Fig. 4. It will be noted that both gravi-
tational and centrifugal sedimentation must be employed to determine the complete
size distribution of this sample. With regard to the precision of the methods replicate
data have shown that the coefficient of variation of p,, is about 0.5 per cent for each
method, and the coefficient of variation
f0 F(D)dDbetween 1.0 and 1.5 per cent.
100 j _ ~ I00
Ct~
90
0 GravitationalSedimentation
11 CentrifugalSedimentation
8o
80
"-~ 7O zo t~
x
o o_
o
60 8o 0
5o' i~- 50
0
r
C~
~, 4 0 4O
o
o- Q_
30 .E 30
2O 20
10 ~0 9
C]
P~
9 J I I I I I I I 0
0 0 I0 20 50 40 50 60 70 80 90 0 I 2 3 4 5 6 7 8 9 I0 II 12 13 14 15 16 17 18
Time, tin, rain Diameter, Dm,/~,
F r o . 3 . - - C e n t r i f u g a l S e d i m e n t a t i o n C u r v e of I n c o m p l e t e l y M i l l e d Fro. 4 . - - C u m u l a t i v e D~stribution of Incompletely Milled Ruffle Pig-

Rutile Pigment. ment.
oa
114 Sx~vOSltnr ON PARTICLE SIZE MEASUREMENT
TABLE V.--CUMULATIVE DISTRIBU- TABLE VI.--DISTRIBUTION FUNC-

TION FROM CENTRIFUGAL DATA. TION OF INCOMPLETELY MILLED RU-
TILE PIGMENT.
hngential D
Diameter, T~me, tm V F(D)dD,
[ntercept, 100join
Tangential 100 X
Dm , ,u __mina _ _ p ecent
r b per cent c Diameter, loofoDm F(D)dD, Intercept IF(Dm), per
D m , Iz per cent a per cent a cent per ~b
1.00 ...... 3.0 15.0 85.0
0.75 ...... 5.3 25.0 75.0 0.2 ..... 4.0 -1.0 25.0
0.50 ...... 12,0 37.0 63.0 0.4 ..... 35.0 0 87.5
0.40 ...... 18.8 53.5 46.5 0.6 ..... 68.0 4O.O 46.7
0.30 ...... 33.3 79.0 21.0 0.8 ..... 79.0 50.0 36.3
0.20 ...... 75.0 93.5 6.5 1.0 ..... 85.0 66.0 19.0
2.0 ..... 92.5 83.0 4.8
a F r o m E q 39 u s i n g ~ = 0.00894 poise, R - - 5.0 ..... 96.0 93.5 0.5
S = 1.00 c m , dp = 4.20 g p e r cu c m , d~ = 0.997 10.0 ..... 97.5 95.0 0.25
27F X 350 18.0 ..... 99.0 98.0 0.06
g p e r eu c m , w 6 ~ r a d i a n s p e r sec,
= 20.8 c m , t e m p e r a t u r e = 25.0 C w e h a v e : a F r o m F i g . 4.
b Calculated from
18 X 0.00894 X 1.00 D
tm
(4.20 -- 0.997)(3.663 X 10+1) 2 X 20.8Din 2 lOO d fo '~ F ( D ) d D
100 X F ( D m ) =
1.800 X 10 -6 dDm
D
D ,) lOOfo m F ( D ) d D - tangential intercept
I f t~ is e x p r e s s e d in m i n u t e s a n d D ~ in m i c r o n s , = D~
3.00
t h e n t~ = D , 3 "
b F r o m F i g . 3.
F r o m E q 33.
lOO [ -- -- '-
8O
~ 70
20
10
0
0 1 2 5 4. 5 6 7 8 9 IO 11 12 15 14 15 16 17 18
Diameter, Om,,~
FIG. L - - D i s t r i b u t i o n F u n c t i o n of I n c o m p l e t e l y M i l l e d R u f f l e P i g m e n t .
T h e distribution function F(D) m a y be calculated b y differentiating the cumulative

distribution curve graphically. T a b l e VI contains the numerical d a t a for this calcu-
ation, and Fig. 5 is a plot of the distribution function against the particle diameter.
Although a loss in precision has resulted from the graphical differentiation of the
cumulative distribution curve, the distribution curve, as given in Fig. 5, is often
valuable in enabling the nature of the distribution to be more readily visualized. F o r
example, Fig. 5 shows t h a t this sample of incompletely milled ruffle p i g m e n t has a
relatively narrow size distribution with a m a x i m u m a t a b o u t 0.4/z and substantially
zero weight fraction above 5 ~. This information is not so a p p a r e n t from Fig. 4.
T h e above example was based upon the modifications of gravitational and centrif-
ugal sedimentation developed b y the authors. M a n y of the other methods described
have been found satisfactory for determining particle size distribution within the
limits of precision desired, so t h a t the u l t i m a t e choice of m e t h o d will depend upon
the proper balance of precision, cost of a p p a r a t u s and convenience.
R~EFERENCES
(1) J. M. Dallavalle, "Micromeritics," Pitman (10) H. E. Schweyer and L. T. Work, "Methods

Publishing Corp., New York, N. Y., 2nd for Determining Particle Size Distribu-
Edition (1948). tion," Symposium on New Methods for
(2) G. Herdan, "Small Particle Statistics," Particle Size Determination in the Sub-
Elsevier Publishing Co., New York, N. Y. sieve Range, Am. Soc. Testing Mats., p. 1
(1953). (1941). (Issued as separate publication
(3) R. S. Cadle, "Particle Size Determina- ASTM STP No. 51.)
tion," Interscience Publishers, Inc., New (11) W. J. Kelly, "Determination of Distribu-
York, N. Y. (1955). tion of Particle Size," Industrial Engineer-
(4) H. Gessner, "Die Schl~mmanalyse," Aka- ing Chemistry, Vol. 16, p. 928 (1924).
demische Verlagsgesellschaft, Leipzig (Ger- (12) S. Od4n, "Eine neue Methode zur Bestim-
many) (1931). mung der KSrnerverteilung in Suspensio-
(5) F. V. yon Hahn, "Dispersoidanalyse," nen," Kolloid Zeltschrift, Vol. 18, p. 33
Theodor Steinkopff, Dresden (Germany) (1916).
(1928). (13) S. Od4n, "Sedimentation-Analysis and Its
(6) H. Lamb, "Hydrodynamics," Cambridge Application to the Physical Chemistry of
University Press (England), 6th Edition Clays and Precipitates," Alexander's "Col-
(1933). loid Chemistry," Vol. I, Chemical Cata-
(7) F. Eisner, "Das Widerstandsproblem," logue Co., New York, N. Y. (1926).
Proceedings, Third Int. Congress Applied (14) C. Brown, "Particle Size Distributions by
Mechanics, Stockholm, 1931 (in R. C. Centrifugal Sedimentation," Journal Physi-
Binder, "Fluid Mechanics,") Prentice- cal Chemistry, Vol. 48, p. 246 (1944).
Hall, Inc., New York, N. Y., p. 173, 2nd (15) A. E. Jacobsen and W. F. Sullivan, "Cen-
Edition (1949). trifugal Sedimentation Method for Par-
(8) S. Berg, "Bestimmung der Korngr6ssen- ticle Size Distribution," Industrial En-
verteilung von groben Produkten," Be- gineering Chemistry, Vol. 18, p. 360 (1946).
richte, Deutsche Keramische Gesellschaft, (16) H. J. Kamack, "Particle Size Determina-
Vol. 33 (7), p. 229 (1956). tion by Centrifngal Pipet Sedimentation,"
(9) S. W. Martin, "The Determination of Sub- Analytical Chemistry, Vol. 23, p. 844 (1951).
sieve Size Distributions by Sedimentation (17) W. Jost, "Diffusion in Solids, Liquids,
Methods," Symposium on New Methods Gases," Academic Press Inc., New York,
for Particle Size Determination in the Sub- N. Y. (1952).
sieve Range, Am. Soc. Testing Mats., p. 66 (18) G. Joos, "Lehrburch der theoretischen
(1941). (Issued as separate publication Physik," Akademische Verlagsgesellschaft,
ASTM STP No. 51.) Leipzig (Germany), 3rd Edition (1939).
116 S~wrOSltr~ ON PARTICLE SIZE MEASUREMENT
(19) J. Svedberg and J. B. Nichols, "Determi- (30) J. R. Musgrave and H. R. Harner, "Tur-
nation of Size and Distribution of Size of bimetric Particle Size Analysis," The Eagle-
Particles by Centrifugal Methods," Jour- Picher Research Laboratories, Joplin, Mo.
nal Am. Chemical Soc., Vol. 45, p. 2910 (1947).
(1923). (31) H. E. Rose, "The Measurement of Particle
(20) A. Romwalter and M. Vendl, "Die Ermitt- Size in Very Fine Powders," Constable,
lung der KSrnungskurve aus Schleuderver- London (1953).
suchen," Kolloid Zeitschrifl, Vol. 72, p. 1 (32) D. S. Skinner and S. Boas-Traube, "The
(1935). Light-Extinction Method of Particle Size
(21) A. H. M. Andreasen, "Uber die Feinheits- Estimation," Symposium on Particle Size
bestimmung und ihre Bedeutung fiir die Analysis, The Institution of Chemical En-
keramische Industrie," Berichte, Deutsche gineers, London, p. 44 (1947).
Keramische Gesellschaft, Vol. 11, p. 675 (33) S. Odin, "The Size Distribution of Par-
(1930). ticles in Soils and the Experimental Meth-
(22) A. H. M. Andreasen, "Sur la D~termina- ods of Obtaining Them," Soil Science, Vol.
tion de la Finesse de Matiere Pulverulentes 19, p. 1 (1925).
Industrielles par la M~thode de la Pipette,"
(34) A. E. Jacobsen and W. F. Sullivan,
Chimie & Industrie (Paris), Vol. 70, p. 863 "Method for Particle Size Distribution for
(1953). the Entire Subsieve Range," Analytical
(23) C. J. Stairmand, "Some Practical Aspects
Chemistry, Vol. 19, p. 855 (1947).
of Particle Size Analysis in Industry,"
Symposium on Particle Size Analysis, The (35) W. Bostock, "A Sedimentation Balance
Institution of Chemical Engineers, London, for Particle Size Analysis in the Sub-sieve
p. 58 (1947). Range," Journal Scientific Instruments, Vol.
(24) M. K/Shn, "Beitri/ge zur Theorie and Praxis 29, p. 209 (1952).
der mechanischen Bodenanalyse," Land- (36) C. E. Marshall, "A New Method of De-
wirschaflliches Jahrbuch, Vol. 67, p. 485 termining the Distributions Curve of Poly-
(1928). disperse Colloidal Systems," Proceedings,
(25) G. J. Bouyoucos, "The Hydrometer Royal Soc. (London), Vol. A126, p. 427
Method for Making a Very Detailed Me- (1930).
chanical Analysis of Soils," Soll Science, (37) H. E. Robison and S. W. Martin, "Beaker-
Vol. 26, p. 233 (1928). Type Centrifugal Sedimentation of Sub-
(26) B. A. Jarrett and H. Heywood, "A Com- sieve Solid-Liquid Dispersions," Journal
parison of Methods for Particle Size Analy- Physical Chemistry, Vol. 52, p. 854 (1948).
sis," British Journal Applied Physics, Sup- (38) H. E. Robison and S. W. Martin, "Beaker-
plement, Vol. 3, p. 21 (1954). Type Centrifugal Sedimentation of Sub-
(27) A. Klein, "An Improved Method for Use sieve Solid-Liquid Dispersions II," Journal
in Fineness Determinations," Symposium Physical Chemistry, Vol. 53, p. 860 (1949)
on New Methods for Particle Size Deter- (39) J. K. Donoghue and W. Bostock, "A New
mination in the Subsieve Range, Am. Soc. Technique for Particle Size Analysis by
Testing Mats., p. 52 (1941). (Issued as Centrifugal Sedimentation," The Institu-
separate publication A S T M STP No. 51.) tion of Chemical Engineers, London (1955).
(28) H. E. Schweyer, "Sedimentation Proce-
(40) J. G. Rabatin and R. H. Gale, "Determi-
dures for Determining Particle Size Dis-
nation of Particle Size With a Simple Re-
tribution," Bulletin Series No. 54, Florida
cording Sedimentation Balance," Analytical
University Engineering and Industrial
Chemistry, Vol. 28, p. 1314 (1956).
Experimental Station, June 1952.
(29) H. Heywood, "The Scope of Particle Size (41) J. K. Donoghue, "The Accuracy of Par-
Analysis and Standardization," Sympo- ticle Size Determination by Cumulative
sium on Particle Size Analysis, The Insti- Sedimentation Methods," British Journal
tution of Chemical Engineers, London, p. 1 Applied Physics, Supplement No. 5, Vol. 7,
(1947). p. 333 (1956).
STP234-EB/Aug. 1959
CENTRIFUGE SEDIMENTATION SIZE ANALYSIS OF SAMPLES OF

AIRBORNE DUSTS COLLECTED IN MEMBRANE FILTERS*
BY K. T. WttlTBu 1 A. B. ALGREN,2 AND J. C. ANNISa
SYNOPSIS
The application of the rapid general purpose centrifuge sedimentation
method developed at the University of Minnesota to the size analysis of fine
powders has been described in a previous publication (2)4
Through the development of special fine-bore capillary centrifuge tubes, this
method has been extended to the size analysis of fractional milligram quan-
tities of airborne dusts collected on 47-mm membrane filters. Evaluation 0f
this method against light and electron microscope data and its extensive use
in an airborne dust survey have shown that it is a practical and convenient
tool for the size analysis of airborne dusts. Application of this method to the
size analysis of airborne dusts and of very fine, dilute suspensions of particles
in a liquid is also described.
Sampling a n d size analysis of air- T h e practical limit of resolution of the

borne dust is required for m a n y purposes light microscope for size measurement
in air pollution a n d dust control work. is a b o u t 0.4 g. If the area or mass distri-
W i t h most practical sampling methods, bution is desired, elaborate and time-
only a few milligrams of dust are available, consuming multistage count proce-
so t h a t size analysis has usually been dures are required to obtain acceptable
done b y microscope count. However, accuracies a t the coarse end of the dis-
size analysis b y microscope has certain tribution. Though the electron micro-
severe limitations: scope has a low enough limit of resolu-
tion, experience has shown t h a t it is
extremely time consuming (40 to 60
* This paper is the result of research spon-
sored by the U. S. Public Health Service and the man-hours per analysis) and t h a t electron
Am. Soc. Heating and Air Conditioning Engrs., microscope d a t a m u s t be combined with
in cooperation with the Mechanical Engineering light microscope or sedimentation d a t a
Dept., Univ. Minnesota, Minneapolis, Minn.
1Assistant Professor of Mechanical Engineer- to avoid large errors in the estimates
ing, Mechanical Engineering Dept., Univ. of the particles over 1 g.
Minnesota, Minneapolis, Minn. Consideration of the above problems
Professor of Mechanical Engineering, Chief
Division of Heating, Air Conditioning and t{e- has led to a few a t t e m p t s to a p p l y
frigeration, Mechanical Engineering Dept., sedimentation methods to the size
Univ. Minnesota, Minneapolis, Minn. analysis of airborne dust samples. Burke
a P~eseareh Fellow, Mechanical Engineering (1)4 used a t u r b i d i m e t e r to measure
Dept., Univ. Minnesota, Minneapolis, Minn.
4 The boldface numbers in parentheses refer the size distribution of silica particles
to the list of references appended to this paper. released from a dissolved m e m b r a n e
117
filter. However, gravity sedimentation corresponds to about 45 divisions on

methods are time-consuming if particles the screen and the minimum useful
under 1 # are to be measured. total sediment height corresponds to
This paper describes the application about 0.2 mg of dust.
of a centrifuge sedimentation method To prevent the irreversible agglomera-
described in a previous publication (2) ation of certain natural airborne dusts
to the size analysis of samples of air- containing sticky particles, it has been
borne dusts collected on a membrane
filter. The techniques described here I I
~, o 2
I Scole-[n.
T22:::;.9 14ram - -
,
INIL
J /Motor, llOV-ac
J/
9000 rpm Connected
| to Varioc for Speed
Control.
Support Motor in a
.) Universal Clamp on
', o Ring Stond.
Ilmm
FILLING LINE" /
Ll~ 40 ml Centrifuge
CONTOUR AS SHOWN~.
III
125mm
0.5 mm CAPILLARY
-I
r i I '}'n?''2;72e;~
ill ~ Impeller Approxi-
3 ~ \~ mately a s shown
FIG. 1.--Special Centrifuge Tube and Feed-

ing Chamber. Sediment Height Is Read with I
Projector Type Viewer.
FIG. 2.--Special Stirrer for Dissolving Mem-
have been used extensively in a recent brane Filters and Dispersing Dust.
dust survey (3) and in research on air
cleaner performance. found necessary to keep the dust load
to less than 1 mg for 47-mm membrane
APPARATUS AND TEST PROCEDURES filters. Smaller diameter filters or greater
The centrifuge size analyzer is the dust loads per filter can be used with
same apparatus as that described in a dusts that do not contain sticky particles.
previous publication (2), with the ex-
ception of the centrifuge tube. Special
Sample Preparation:
centrifuge tubes having a capillary bore Solution of a dirty membrane filter is
of 0.5 mm (Fig. 1) have been developed accomplished by placing it in a 40-ml
in order to obtain sufficient image height cone tip centrifuge tube with about 35
on the projector screen when analyzing ml of acetone, and then stirring it
fractional milligram quantities of dust. vigorously for several minutes with
With the projector used, 1 mg of dust the stirrer illustrated in Fig. 2. This
WHITBY ET AL ON ANALYSIS O~ SAMPLES ON ]-\/~EMBRANEFILTERS 119
suspension is then centrifuged in an dropper or pouring to the feeding

ordinary centrifuge at 3000 to 3500 chamber (Fig. 1) and then to the centri-
rpm for 1 hr to precipitate all particles fuge tube where the suspension is left
above approximately 0.1 ~. The super- floating as a sharp layer on the surface
natant acetone solution of the membrane of the pure acetone or other sedimenta-
filter is then siphoned off and the sedi- tion liquid by means of techniques
ment resuspended without drying by described in a previous publication (2).
stirring for several minutes in about 1 Readings are then taken according to
ml of 15 per cent naphtha, 85 per cent a precalculated time schedule. Since
acetone feeding liquid. most airborne dusts normally contain
few particles above 20 ~, it is usually
TABLE I.--TYPICAL ALL-CENTRI- possible to use an all-centrifuge time
FUGE DATA SHEET FOR THE SIZE schedule similar to that illustrated in
ANALYSIS OF AIRBORNE DUSTS.
?imepk )rojec, Per Per 1.0
:entri Correc- tor Cent Cent
D~,~ fuge, tion, Read- Greater Less
rpm m i n : sec ings Than Than ==
"5
20 ...... 300 16 0.2 0.7 99.3 .9- 0.9
12 . . . . . 30O 28 0.6 2.0 98.0
6 ..... 300 2:09 1.7 5.7 94.3
3 ..... 600 2:15 5.4 18.1 81.9 =,.:
1.5... 1200 2:22 7.5 25.2 74.8
1 ..... 1200 3:47 10.4 34.9 65.1 " 0,8
o
0.7... 1800 3:16 15.6 52.4 47.6 o
0.5... 1800 5:54 20.0 57.1 32.9
0.35.. 1800 12:15 25.6 35.9 14.1
0.25... 1800 23:08 28.8 96.6 3.4
0.165.. 1800 1 hr 29.8 99.9-}- 0.1-- 0.7
60 70 80 90
T e m p e r o t u r e , deg Fohr
FIG. 3.--Viscosity-Temperature Relation of
For some dusts, it has been found One 47-ram Type AA Membrane Filter Dis-
desirable to make the sedimentation solved in 10 ml of Acetone.
analysis in liquids in which the membrane
filter is not soluble. Though it is theoreti- Table I. Elimination of the gravity
cally possible to dissolve the filter in readings permits two samples to be
acetone and then dry and resuspend run simultaneously.
the particles in another liquid, the time
and effort required makes this procedure Homogeneous Sedimentation Technique:
impractical. The layer sedimentation technique
For m a n y mineral dusts it has been described previously usually requires
found practical to wash the dust from precipitation and resuspension to elimi-
the filter by placing it with the dust nate the dissolved membrane filter
load inward in a 40-ml centrifuge tube and to concentrate the dust. Trouble
with the appropriate liquid and then m a y arise from two sources: (a) The
brushing the dust from the surface. precipitate m a y form aggregates which
If concentration and resuspension are difficult to disperse later, and (b)
are required, it is done as described the extra handling of the suspension
above, in the feeding chamber m a y cause
some loss. This small loss is undesirable
Layer Size Analysis Procedure:
if the amount of sediment in the centri-
The suspension of particles in the fuge tube is used as a measure of the
feeding liquid is transferred by eye- amount of dust on the filter.
To eliminate these difficulties, the this difference is of small importance in

following homogeneous sedimentation many applications.
technique may be employed. After
solution of the membrane filter in 10 DiA~culties Encountered in the Analysis
ml of acetone, the suspension is poured of Airborne Dusts:
directly into the special centrifuge tube Natural airborne dust samples usually
(Fig. 1) and the size analysis run, using contain some fibrous material such as
the usual reading procedure for the lint, plant fibers, etc. If more than a
layer method. few per cent of such fibers are present
9aa
99.9
I I
99 | Layer Method Z
A Homogeneous Method
09
g 95
-~ 8o
70
-~ 60
9o
/
>50
.o 40
Ee 3 0
o 2o
~- to!
5~"//~1 II I I I I I I I I I I I I I ] I II
0.5 1.0 I0 Ioo io 100
Op, /~ Dp,
a b
Fio. 4.--Comparison of Layer and HomogeneousMethods of Starting Centrifuge Size Analysis.
(a) Arizona Road Dust, (b) Glass Beads.
Since the dissolved membrane filter in the sediment, some compaction of the
increases the viscosity of the acetone sediment column during the final stages
sedimentation liquid, tables must be of centrifugation is inevitable. During
calculated using the viscosity values the American Society of Heating and Air
shown in Fig. 3. Conditioning Engineers (ASHAE) dust
Figure 4 compares analyses by the survey (3), this source of inaccuracy
layer method and the homogeneous was kept at a reasonable level by using
method on two different powders. It 170 wire stainless steel screens ahead
can be seen that the homogeneous of the samples or else by passing the
method tends to increase slightly the dust suspension through 325 wire screens
apparent size of the particles at the prior to analysis.
coarse end of the distribution. However, If more than 1 mg of natural airborne
WI-IITBY ET AL ON ANALYSIS OF SAMPLES ON I~EMBRANE FILTERS 121
99.99
99.9
99
95
9O
.~ 80
7O
P, 6O
~ 50
~' 40
~ 30
J
2O
; 5
0.1
0.01
0.01 0.1 I 10 20
Dp, /z
FiG. 5.--Combined Size Analyses of Fourth Sample of Airborne Dust Sampled in Particle Labora-
tory.
99.99
O Sedimentation
99.9 Electron Microscope ,,"
[] Light Microscope ~ I x~ I I
b5 99
g
~95
9O
~, 8o
* 70
~ 40
~, 30
x~ 20
~, 5
D_
I
;
0.1
o.o,i
O.02 0.1 I0 20
Dp, p.
FIG. 6.--Combined Size Analyses of 80 per cent Coal, 20 per cent Precipitated Carbon Test
Dust.
dust is collected on a membrane filter, After considerable study of this prob-

irreversible agglomeration may occur lem, a procedure was worked out in
and large aggregates will be seen in the which electron microscope data below
suspension. about 1 ~ was combined with the sedi-
The naphtha used in making up the mentation data above 1/~ to calculate a
feeding liquid should be a highly re- combined distribution which is pre-
fined grade. Some naphthas, when ex- sumably more accurate than either
posed to light and air for several months, method alone over the entire size range.
form gums that affect the dispersion. Further, the area distribution and the
For opaque dusts having more than optical density were then calculated
10 to 15 per cent by weight below 1 u, and compared with the measured optical
it may be difficult to see the line of density of the original membrane filters.
demarcation between the sediment As has been pointed out before (4),
column and the suspension above it. this comparison also serves as a useful
With the projector type viewer, a fine measure of the relationship between the
wire mounted in front of the tube capil- .degree of dispersion on the dry membrane
lary so that it can be aligned easily filter and in the sedimentation liquid.
with the sediment line is helpful. The
line of demarcation can usually be ob- TABLE II.--SEDIMENT COLUMN
P O R O S I T I E S F O R S E V E R A L DUSTS.
served under incident light striking Porosity, a
the capillary from the side at a 45-deg per cent
angle. The sediment height is then read Atmospheric d u s t - - p a r t i c l e labora-
tory . . . . . . . . . . . . . . . . . . . . . . . . . . 73.7
by noting the position of the wire image 80 per centcoal, 20 per cent K-1 car-
on the projector screen. Graduated b o n - - t e s t dust . . . . . . . . . . . . . . . . . 55.8
tubes or the detachable plastic scales Arizona road dust . . . . . . . . . . . . . . . . 45.6
supplied with the commercial version a The weight of dus t on the m e m b r a n e filter
of the instrument 5 may also be used. is determined accurately by sampling simul-
taneously w i t h a second filter a t a higher, accu-
EVALUATION r a t e l y known air flow using the a p p a r a t u s de-
scribed in reference (6).
Evaluation of the characteristics and
accuracy of a sedimentation method of Combined Size Analysis Procedure:
size analysis for particle sizes in the
submicron range is difficult because of Outlined below is the procedure used
the lack of methods having greater to obtain the combined size distributions
accuracy. About the only nonsedimenta- illustrated in Figs. 5 and 6.
tion method available is the electron 1. Two membrane filter samples were
microscope. However, the electron micro- taken, one having an optical density
scope, or any other count method, (2) of from 0.05 to 0.1 for electron micro-
measures the number distribution while scope and light microscope analysis
the centrifuge sedimentation method and one containing from 0.5 to 1 mg
measures the volume distribution. For of dust for sedimentation analysis.
broad distributions, the volume distribu- 2. Five electron photomicrographs
tion cannot be calculated from the were then prepared from a carbon film
number distribution with sufficient accu- replica, at several magnifications. I t has
racy to provide a useful check on the been found that counts at a magni-
sedimentation results. fication of 12,000 will yield accurate
data between 0.04 and 0.6 ~. If accurate
5 The commercial version of the centrifuge data at smaller and larger sizes is de-
size analyzer is available from the Mine Safety
Appliance Co., Pittsburgh, Pa. sired, counts at several magnifications
W H I T B Y ET AL ON A N A L Y S I S OF SAMPLES ON M E M B R A N E F I L T E R S 123
are required. The electron microscope arbitrarily joining this distribution to

data of Fig. 5, for example, was obtained the sedimentation data between 0.5
from photographs at 6000 and 30,000 and 1 ~. In Fig. 6, for example, this
magnification. junction is at 0.57 g. Note in Fig. 6 that
3. The sedimentation size analysis the electron microscope number analysis
was determined by the layer technique appears to be low above 0.57 g while
described earlier in this paper. The total the sedimentation analysis is low below
sediment column height in conjunction 0.57 ~.
with the measured sediment column 6. The combined number distributions
porosities, Table II, was used as a were computed similarly by arbitrarily
TABLE III.--COMPARISON OF MEASURED AND CALCULATED OPTICAL DENSITIES

FOR AN ATMOSPHERIC DUST SAMPLE AND FOR A COAL AND
PRECIPITATED CARBON TEST DUST.
ATMOSPhERiC DUST----LABORATORY SAMPLE NO. 3
Calculated
Measured K = 1 Ka for Diff. Theory

Distribution Optical
Density
Calculated Calculated OD Calculated Calculated OD
Optical Optical -
Density Measured OD Density Measured OD
L i g h t M i c r o s c o p e alone . . . . . . . . . . . 0.122 0.0115 0. 094 0.0187 0.15

E l e c t r o n M i c r o s c o p e alone . . . . . . . . 0.122 0.1128 0.93 0.1434 1.18
S e d i m e n t a t i o n alone . . . . . . . . . . . . . . 0.568 0.324 0.57 0.460 0.81
Combined ....................... 0.122 0.129 1.06 0.117 0.96
80 PER CENT COAI~, 20 PER CENT K-1-C/~RBo~ DUST b
Light Microscope alone ........... . 0.0480 0.0131 0.27 0.0205 0.43

E l e c t r o n M i c r o s c o p e alone . . . . . . . . ! 0.0480 0.0240 0.50 0.0222 0.46
Sedimentation alone .............. 0. 692 0. 210 0.30 0. 315 0.47
Combined ....................... 0. 0480 0.042 0.88 0.046 0.96
a T h e l i g h t s c a t t e r i n g coefficient K , Fig. 8, is t h a t s u g g e s t e d b y D a v i e s (4), for o p a q u e p a r t i c l e s

i n a t r a n s p a r e n t m e d i a . N o s a t i s f a c t o r y d a t a e x i s t s for o p a q u e p a r t i c l e s on a t r a n s l u c e n t filter media.
b T h e c o m p o s i t i o n , p u r p o s e a n d p r e p a r a t i o n of t h i s d u s t is described i n reference (6).
measure of the amount of dust on the joining the converted sedimentation

filter and to calculate the theoretical data to the electron microscope number
optical density. distribution at the chosen size.
4. Light microscope counts were made 7. The theoretical optical densities
using a Porton reticule in a 10 X eye- of the dust on the membrane filters are
piece, 97 X oil immersion objective, and a calculated by the procedure previously
blue filter under the substage condenser described (4). Measured and calculated
to reduce eyestrain. A total of about values are given in Table III. Due to
10,000 particles were counted by a uncertainty in the applicable light
multistage procedure. scattering coefficients, optical densities
5. The combined volume analyses have been calculated for K = 1 (area
shown in Figs. 5 and 6 were computed scattering) and for Davies diffraction
by converting the electron microscope theory scattering for a photocell semi-
number analysis to volume and then angle of acceptance of 20 deg, Fig. 8.
APPLICATION pended in motor oil and gasoline has

The centrifuge sedimentation method been measured in this way.
has been used extensivelyby the authors SUM~EARY AND CONCLUSIONS
for the analysis of natural airborne
dusts (4). During this survey about 1. Extensive use of this centrifuge
man-hour per sample was required. Total sedimentation method for the size
elapsed time, including initial centri- analysis of 0.2 mg or greater quantities
fugation, was 31 hr for two samples. of airborne dust collected on 47 mm
Since two samples were ordinarily run membrane filters has demonstrated that
simultaneously 4 to 6, samples per 8-hr it is a useful tool for measuring particle
day could be run to a lower size limit size from about 0.1 to 100 microns.
2. From four combined sedimentation
of about 0.16 u. It has been used to a
and electron microscope analyses that
99 e~Fume from Scarfing I,,~r O O
Operation ~ 2 Y ~ 3
o,o"1"2
8=Semiangle of Acceptance of
Mea,,,,ing P,atece,, L ~
95 Fine Dust f r a m e '
Pittsburgh r~L_/L.~9_~
c 90
&,Arizona Road I J //e ~i ~_ / ~ o ~ .
~ 8o -
~ 7o
3 60
Fraction
~~ /
~.o%%J .... . . .i . . . . . . ~o
Dp,
a 3o
N 2o F1G. 8.--Light Scattering Coefficient for
Opaque Particles in a Transparent Media. Data
.~ I0 above 0.48 t* is for Opaque Particles, that Be-
low 0.48 t* for Transparent Particles of 1.5 Re-
U fractive Index in Air.
- , , 1 1 ~, ' ~ ~ i i i till
0- 0.2 I
10 20
Dp, /.t have been made, three on natural air-
FIG. 7.--Centrifuge Sedimentation Size Anal- borne dust and one on the coal-carbon
yses of Three Airborne Dusts. test dust, it has been concluded that
the combined data provides a better
limited extent for obtaining the size estimate of both the number and volume
distribution of fine dusts passing through distributions than either alone. Note
high-performance air cleaners. that the measured and calculated optical
Size distributions obtained on three densities for the combined analyses
different dusts are shown in Fig. 7. agree quite well and are reasonably
The Pittsburgh dust sample was the independent of the K value used.
finest obtained in the ASHAE Airborne 3. From Figs. 5 and 6, it can be seen
Dust Survey (4). that the sedimentation analysis provides
The membrane filter technique has a low estimate of the volume of particles
also been used to measure the size dis- below about 0.4 •. This is especially
tribution of very dilute suspensions true of the coal-carbon test dust, Fig. 6.
of particles in a liquid. The suspension This is probably caused by the fact
of particles is filtered through a mem- that most of the submicron particles
brane filter of suitable pore size until are precipitated carbon which behaves
enough particles are collected. This differently than the larger coal particles.
method of concentration is much more The fact that calculated optical density
rapid than centrifugation for very dilute is lower than the measured value for the
suspensions. sedimentation analysis also indicates
The size distribution of particles sus- that the particles have essentially the
WHITBY ET AL ON ANALYSIS OF SAMPLES ON MEMBRANE FILTERS 125
same degree of dispersion in the sedi- microscope a t best can provide only a
m e n t a t i o n liquid as on the d r y membrane rather poor estimate of the size distribu-
filter. tion of airborne dusts. N o t e from Table
4. F o r comparison, the light micro- I I I , t h a t the light microscope accounts
scope size analyses are shown in Figs. 5 for the smallest fraction of the scat-
and 6. I t is readily seen t h a t the light tering area of a n y of the methods used.
REFERENCES
(1) W. C. Burke, Jr., "Size Determination of (4) K. T. Whitby, A. B. Algren, and R. C.
Silica Particles Collected on Membrane Jordan, "Size Distribution and Concentra-
Filters," Am. Industrial Hygiene Assn. tion of Airborne Dust," Transactions,
Quarterly, No. 14, pp. 299-302 (1953). Am. Soc. Heating and Air Conditioning
(2) K. T. Whitby, "A Rapid General Purpose Engrs., Vol. 61, pp. 463-482 (1955).
Centrifuge Sedimentation Method for (s) K. T. Whitby, A. B. Algren, and R. C.
Measurement of Size Distribution of Small Jordan, "The Dust Spot Method for Evaluat-
Particles, Part I.--Apparatus and Method; ing Air Cleaners," Transactions, Am. Soc.
Part II.--Procedures and Applications," Heating and Air Conditioning Engrs.,
Transactions, Am. Soc. Heating and Air
Conditioning Engrs., Vol. 61, pp. 33-50 Vol. 63, pp. 171-186 (1957).
and 449-462 (1955). (6) K. T. Whitby, A. B. Algren, R. C. Jordan,
(3) K. T. Whitby, A. B. Algren, R. C. Jordan, and J. C. Annis, "Evaluation of Air Cleaners
and J. C. Annis, "The ASHAE Air-Borne for Air Conditioning and Ventilation, Part
Dust Survey," Heating, Piping and Air I.--Apparatus," Heating, Piping and Air
Conditioning, Vol. 64, pp. 185-192 (1957). Conditioning, Vol. 30, pp. 171-178 (1958).
DISCUSSION
MR. K. T. Wm~BY (author).--Some occur and I would guess t h a t there are
time ago in discussing sedimentation perhaps 5 per cent of the materials
size analysis with someone experienced which we have analyzed in the labora-
in the field we ended our discussion b y tory in which we have had sufficient
concluding t h a t there are no new sedi- compaction to reduce the accuracy of the
m e n t a t i o n methods, only new investi- fine end of the distribution. If too much
gators with new compromises. So I would lint is not present, most organic materials
like to introduce the discussion with t h a t in the normal airborne dust, seem to be-
background because this is essentially a have all right. The repeatability of size
new set of compromises to a v e r y old distribution measurements b y this
technique, aimed a t a specific degree of method is at best a b o u t 4-1 or 2 per
accuracy and versatility. cent a t the fine end, and therefore, the
MR. E. S. PALI~:.I--Are a n y difficulties last point on the size distribution curve
experienced with sample compaction in which we ordinarily plot is the one at
the centrifuge sedimentation method of a b o u t 1 per cent. W e have found t h a t if
particle size measurement? the material will not compact, then it
MR. WHITBY.--This is one of the usually meets all the other dispersion
most sensitive measures of proper dis- criteria.
persion t h a t we know of. We consider a MR. WILLIAM A. BUERKEL3--Are the
dispersion satisfactory if this does not two liquids immiscible?
1 Chemist, General Electric Co., Cleveland, 2 Engineer, General Eleetrie Co., L. W. & P.
Ohio. Department, Cleveland, Ohio.
126 SYMl,OSltnvi ON PARTICLE SIZE MEASUREMENT
MR. WtIITgY.--They are miscible. fore obtain whatever degree of mechani-

MR. DONALD L. PASTER.a--The air cal dispersion we feel is necessary.
cleaner test dust that was mentioned in MR. CI~ARLES M. HUNT.~--In the
the paper--is that the same as the Air comparison of the electron microscope
Filter Institute test dust without the with sedimentation data shown is that
fibers? supposed to show there is a good com-
MR. WIIITBY.--No it is not. This is a parison or a poor comparison?
test dust which we have developed to Mm WHITBu 6 illustrates a
reproduce as many characteristics of poor comparison below about 0.4 # in
normal airborne dust on the average as is size.
possible, inchlding size distribution. I t MR. HUNT.--How do you make a valid
consists of anthracite coal which is ball comparison between a method which
milled to certain specifications after measures amount by bulk volume with a
which 20 per cent precipitated carbon is method which counts the individual par-
added and it is ball milled a further ticles?
period. After the dust is prepared, it is MR. W~IITBY.--It will be noted that
dried and kept in the presence of silica Figs. 5 and 6 were obtained by combining
gel until used. We have a complete set of size analyses obtained by electron micro-
specifications for this material. When dis- scope and by sedimentation. For ex-
persed by proper procedures and ap- ample, in Fig. 6 the solid line of the
paratus, it reproduces natural airborne weight distribution below 0.67 u was
dust. calculated from the electron microscope
The project in which this is being de- number distribution and the weight dis-
veloped is sponsored jointly by the tribution about 0.67 u is the sedimenta-
United States Public Health Service and tion analysis. The number microscope
the American Society of Heating, Air- can be used to calculate a valid weight
conditioning, and Refrigerating Engi- distribution only below about 1 ~ and
neers. the sedimentation analysis to calculate a
MR. PASTER.--Will the author please valid number distribution above about
comment on the micro stirrer that is lv.
used? MR. H. W. DAESCI-INER.5--I-Iave yOU
MR. WmTBu started out using tried ultrasonic energy for dispersion?
the Waring blender or a malted milk MR. WHITBu have not, but one
mixer. With combustible liquids these of the users of this equipment has. I t is
created a fire hazard. We then developed found that ultrasonic dispersion under
a small stirrer which could disperse the the proper conditions are capable of re-
particles directly in the feeding chamber. ducing primary particles. As I see it,
This was also abandoned because of the the problem of dispersion is not obtain-
fire hazard and the extremely high ing sufficient severity, but rather the
speeds made necessary by the small blade problem of picking the right level. One
sizes. We now use an air stirrer or an can generate the forces required to dis-
electric stirrer without brushes similar to perse particles by mechanical or by sonic
the one shown in this paper. With an air means or by use of air.
turbine we can operate this particular
one up to about 15,000 rpm and there- 4 Chemist, National Bureau of Standards,
Washington, D. C..
3 Chief, Applied Research, Fram Corp., Provi- 5 Chemist, Shell Development Co., Emery-
dence, R. I. ville, Calif.
S T P 2 3 4 - E B / A u g . 1959
A LIQUID S E D I M E N T A T I O N M E T H O D FOR
P A R T I C L E SIZE DISTRIBUTIONS
BY L. 1VI. CARTWRIGET1 AND R. Q. GREGG1
For the determination of particle size sample may be computed from formulae
distributions in the range from 0.5 to 100 based upon Stokes' law.
/~, a liquid sedimentation technique origi- The over-all application of the method
nally described by K. T. Whitby, and requires close technical supervision, par-
subsequently published by him, 2 has ticularly during the early stages of ap-
been found to be a rapid and repeatable plication to a new material. However,
means for obtaining distributions on a routine application may be carried
wide variety of materials, such as cata- through easily after very little training
lysts, dusts, pigments, filter aids, salts, and practice. The time required for a
metal powders, clays, sandstones, etc. complete analysis is about an hour for
A specially shaped tube, as shown in most routine samples.
Fig. 1, is nearly filled with a suitable
APPARATUS
sedimentation liquid. The sample is dis-
persed in a second liquid which is mis- The major items of the apparatus ~
cible with the sedimentation liquid but used in this method are shown in Fig. 2
of slightly lower density. A thin layer and include:
of this dispersion is then floated onto the 1. Specially designed sedimentation
surface of the sedimentation liquid, tubes having specifications as shown in
with minimum mixing, so that all of the Fig. 3.
particles start essentially at the top of 2. Two synchronous centrifuges; one
the sedimentation tube. Thus, as the 600 and 1200 rpm and one 1800 rpm,
sedimentation progresses, the particles specially designed to provide reproduc-
become classified according to size (see ible starting and stopping characteristics.
Fig. 1). After the larger particles have Also, the maximum acceleration during
settled to the bottom under gravity, the starting and stopping has been adjusted
sedimentation tube is centrifuged to re- to be not greater than 5 radians per sec
duce the time required for the smaller per sec, which is accomplished through
particles to reach the bottom. By meas- the utilization of an appropriate inertia
uring the volume of particles accumu- disk together with a series resistor in one
lated as a function of time, the equiva- of the motor windings. Each centrifuge
ent spherical size distribution of the is equipped with an appropriate electri-
cal timer which can be set to 1 sec for
1Phillips Petroleum Co., Bartlesville, Okla.periods up to 1 hr.
K. T. Whitby, "A Rapid General Purpose
Centrifuge Sedimentation Method for Measure- 3. A tube holder and tapper assembly
ment of Size Distribution of Small Particles," stand. This holds the sedimentation tube
Part I--Apparatus and Method, Heating,
Piping & Air Conditioning, Vol. 27, Jan., 1955, Purchased from Pillsbury Mills, Inc.; now
p. 231. Part II--Procedures and Applications, available from Mine Safety Appliance Com-
ibid., June, 1955, p. 139. pany.
127
128 SYMPOSIIN ON PARTICLE SIZE MEASUREMENT
during the gravity settling period and size distribution curve from the data on
while taking readings of the sediment the size-time table.
height in the tube capillary. The tapper
portion of the device applies light blows PROCEDURE
to the end of the tube about every two Choosing Sedimentation and Dispersing
seconds to assist the particles in moving Liquids:
down the sides of the tube.
4. Special chamber, shown in Fig. 3. In selecting the liquids to be used,
This is used to introduce the sample dis- several factors need to be considered.
persion onto the surface of the sedimen- Obviously, the liquids must be inert to
tation liquid. the material to be examined and must be
miscible with each other. Both must also
adequately disperse the sample during
, SAMPLE
DISPERSION sedimentation. For convenience, the vis-
LAYER cosity and density of the sedimentation
liquid should be such that the largest
particles present do not settle out sooner
than l0 sec after the start of the run,
since it is difficult to obtain the first
SEDIMENTATION reading before this time. Also, if very
LIQUID large particles are present, Stokes' law
does not accurately apply when these
exceed a critical diameter given by
[-21.6X l o ~ ] 1"
= L - p0)gJ
FIG. 1.--Sedimentation Tube Showing Clas- where:
sification of Particles as Sedimentation Pro-
gresses.
= viscosity of liquid,
p0 = density of liquid,
OUTLINE OF PROCEDURE p, = skeletal density of particle, and
The principal steps in this method are g = gravitational acceleration constant.
as follows: The density of the dispersing liquid
1. Select sedimentation and dispers- must be less than that of the sedimenta-
ing liquids and determine density of the tion liquid so that a stable layer of the
sample. sample dispersion may be floated onto
2. Calculate a particle size-settling the surface of the sedimentation liquid.
time table. Under certain conditions, particles may
3. Disperse the sample in dispersing tend to hesitate and accumulate at the
liquid. interface of the two liquids resulting in
4. Prepare the sedimentation tube and the formation of streamers which upset
initiate the run by introducing the sam- the proper performance of the sedimen-
ple dispersion. tation. It has been found that these ef-
5. Record the readings of the sedi- fects can be reduced by using a combina-
ment height in the capillary of the sedi- tion of liquids which have a small density
mentation tube at the times previously difference and for which the viscosity of
calculated for the various particle sizes. the dispersing liquid is about twice that
6. Calculate and plot the cumulative of the sedimentation liquid.
CARTWRIGHT AND GREGG ON LIQUID SEDIMENTATIONMETHOD 129
Several liquids can frequently be used iently determined with the use of a
as the sedimentation liquid for a particu- volumetric Cassia flask (100 ml) and a
lar sample; the one to be chosen is that controlled temperature water bath. The
which gives the most convenient size- empty flask is weighed, about 10 g of
time relationship. I t has been found that sample placed in the flask which is then
benzene or carbon tetrachloride is very weighed again. About 100 ml of the sedi-
suitable as a sedimentation liquid for a mentation liquid containing a dispersing
wide range of materials such as catalysts, agent are added to the flask containing
pigments, metal powders, salts, etc. the sample and the flask is again weighed.
Kerosine is an appropriate dispersing After taking care so that the sample is
liquid to use with either of these liquids. well dispersed and no air bubbles are
Fro. 2.--Pillsbury Apparatus for Sedimentation Particle Size Distributions.
When the exact density of the sample trapped in the sample, the flask is placed
is not known, an approximate value may in the water bath. The flask and its con-
be used to determine if a given sedimen- tents are allowed to attain a temperature
tation liquid will be satisfactory. Afte{ a (not much greater than ambient room
sedimentation liquid is chosen, the sam- temperature) at which the density of
ple density can be found, using this the sedimentation liquid is known to four
liquid, by the method given in the next decimal places. When this temperature
section. is reached, the volume of the total con-
tents of the flask is read from the cali-
Density Determination:
brated neck of the flask.
For many samples, the skeletal density The density is determined from:
value may be obtained from a handbook.
However, if the skeletal density of the W~-Wf
skeletal density = p~
sample is not known, it may be conven- V c - Vz
where: where:
Wf = weight of flask empty, n = viscosity of the medium,
W~ = weight of flask with sample, v = velocity of the sphere,
W, = weight of flask with sample and d = diameter of the sphere,
liquid, 08 = skeletal density of the sphere,
V~ = total volume of flask contents at po = density of the liquid, and
specified temperature, g = acceleration of gravity.
W~ W,
-
Thus,
Vz = = volume of liquid in
pl
~rda
flask at specified temperature, and 3~rnvd = ~ - (o, -- p0)g
m -=- density of liquid at specified tem-
perature. (p~ -- po)gd2
v . . . . . . . . . . . (1)
187
where v now represents the terminal
velocity.
SEDIM
The time for a sphere to settle a dis-
TUBE Q tance h is therefore:
13.5W- 18nh
mm t- (2)
(p~ - - po)gd ~ . . . . . . . . . . .
SAMPLE ~mrn
~TRODUCTION[~__~
CHAMBER --s Similarly, a sphere being centrifuged
40MESH
TRAI (BRASS) " ~ W l R E reaches a terminal velocity when the
SMC SCREEN
POS ~- viscous drag equals the net centrifugal
0.75O force:
7rd8
FIo. 3.--Sedimentation Tube and Sample net centrifugal force = ~ - (p. -- po)o~r
Introduction Chamber.
where:
Calculation of Particle Size-Settling Time
Table: r = angular velocity of the centrifuge,
and
To perform the necessary calculations r = radius of rotation at the position of
for this method, the equations governing the sphere.
the motion of a body through a liquid Therefore,
under the influence of gravity and of a rrd 3
centrifugal field must be understood. 3~nvd = y (o. - oo),o~r
When a solid sphere settles in a liquid
under gravity, it reaches a m a x i m u m (Ps -- Oo)co2rd ~
v ........ (3)
terminal velocity when the viscous drag 187
becomes equal to the net downward
where v is again the terminal velocity
force. The viscous drag on the sphere is
but is now a function of r. The time to
given by a form of Stokes' law:
settle a given distance must be deter-
v i s c o u s d r a g = 3~r~vd; mined by integration. Since
and the net downward force on the dr
sphere is:
~d 3 . dr (p8 - - po)oJ~d 2
net downward force = y (p~ - - po)g, dt
r 187
CARTWRIGHT AND GREGG ON LIQUID SEDIMENTATION METHOD 131
Integrating between limits, r~ and r2 at has settled below the surface of the
times 0 and t, sedimentation liquid during the
period of gravity settling.
f~r~dr
r- (p* --i ~ P~176 dt
During the gravity settling time, 6 , all
particles larger or equal in diameter to
187 r2 do settle a distance h to the bottom. All
t In . . . . . . . . (4)
(p~ - p0)o~*d2 rl particles of diameter d smaller than do
Wa a. d b ~ u :~= CONSTANT
\
k
\X\
lc ~ .... e
o tz %
TIME
FIG. 4.--Typical Acceleration Curves for Determining Centrifuge Start-Stop Correction Term.
This gives the time for a sphere to settle will have settled a lesser distance, hg.
from rl to r2 while being centrifuged. From Eq 2,
In this method, the sample particles h ho
become classified during the gravity to cc - - =
dos
--
d~
settling period, larger particles settling
more than smaller particles. This means and
that the value of rl in Eq 4 is different d%
for different diameter particles and must
do~
be determined by an equation of the
form: Thus,
rl = ro Jr ro d2h
rl = ro + ~do--:
where:
Substituting in Eq 4,
r0 = distance from the axis of rotation
to the surface of the sedimentation 187 r2
t (o. - po)o~'d' In [ d2h\...(5)
liquid, and
ro + rig-';/!
rg = distance a particle of particular size k
From this equation a table of desired area oabc. This requires that in Fig. 4 the
centrifuge times corresponding to vari- area enclosed by bb'c'c be equal to the
ous diameter particles to be sedimented difference between the areas enclosed by
could be calculated if the centrifuging oad and bec. The time correction, r~,
took place at constant speed. The cen- (t3 -- t2), is determined by dividing this
trifuge is actually started and stopped difference by the area equivalent of unit
between readings and the time value re- time at oJ2 = constant. Therefore, the
quired is that to which the timer must equation for the calculation of the cen-
be set. This value includes only the trifuge timer setting is
periods of starting and of constant speed
and is obtained by adding a correction, 18~ rs
r~, to the time determined from Eq 5. t = (o~ - p0),ou' t . / dsh\ + " . . . . (6)
The velocity of settling of a particle k ro + --!doS/
-a- Starting Curve
4 000 ~ -o- Stopping Curve
5 600 \ I Area Over Start Curve-Area Under Stop Curve 9 9 -
\ I T20~r = K
\ I
5 200 \ / K : l (in.-cm) x Unit "i'ime (in.-cm)
2800 \ ( 5 8 . 4 - 4 9 . 8 ) sq cm
\ x"z~ = (9.85x0.4) sq cm per sec
2 400 \ r 2 o . - _ 3.~-4--
8 . 6 _ 2.a sec
"oi ~
2 000 ~... l /
I 600 \ / I I
I 200 / " -...
800 /fi "o~ . . _ . ~ j J
400 /'" "/ ~" h--c-- --- --- . . . . .
00 I0 20 50 40 50 6~
Time,sec
FIG. 5 . - - A c c e l e r a t i o n C u r v e t o D e t e r m i n e S t a r t - S t o p C o r r e c t i o n T e r m f o r a 6 0 0 r p m C e n t r i f u g e
] ? l o t t e d p o i n t s d e t e r m i n e d w i t h u s e of a s t r o b o s c o p e .
at a given radius is proportional to the It is evident that there is a r~ to be

square of the angular velocity. A plot associated with each centrifuge speed
of w" against time yields a curve the area and that these must be determined for
under which is proportional to the dis- each particular centrifuge. An example
tance settled by a particle. Figure 4 of the determination of r20~ for one of
shows such a curve (odbe) for a typical the Pillsbury centrifuges is given in Fig. 5.
centrifuge run. In practice, Eq 6 gives directly only
By Eq 5, for a time period h , the the timer setting for the first centrifuge
distance a particle would settle is pro- run. Any succeeding times calculated
portional to the area enclosed by oabc. from this equation must be corrected to
However, the actual distance a particle account for previous centrifuging. Put-
would settle for a timer setting of t2 (in- ting Eq 6 in the form
dudes only starting and constant speed t = t ' + r~
periods) is proportional to the area en-
closed by odbe. A correction to make where:
these distances equal is arrived at by t,= 18, 1. ( dsq,
using a different timer setting, ta, such (o, - oo)~o2d~
ro + doS]
that the area odb'e' becomes equal to the
successive timer settings at the same The appropriate equations for calculat-
centrifuge speed m a y be computed from ing the settling times can then be sum-
the series marized as follows:
t,, = ~',, - t',-1 + ~. . . . . . . . . . (7) Gravity settling time:
where n = 1, 2, 3, etc., indicates the K
order of the centrifuge runs and t'0 = 0. d=
In Eq 7, the term t'~-i is the constant
speed time equivalent of previous cen- Centrifuge settling time:
trifuging.
If the speed of centrifuging is increased t' K~, In
between any two successive runs, the d2 d2h~
t'~_: term for the first run at the new ro + d~2]
speed must be changed. Since, from Eq
4, an interval h at speed o01 is equivalent centrifuge timer settings.
to an interval o0fl/~@ tl at speed ~o2,
/'n_l(COl/Oa2)2 gives the time equivalent at Successive constant speeds:
the new speed of the previous centrifug-
&= t%- t%-l+r~
ing. Thus, after the speed change, the
first time is computed from the expres- First time after changing speeds:
sion:
t __ . ..,
& = gin - - l u - 1 "t-"&o. (8)
r
where r~ is the appropriate value for the In the above equations,

new centrifuge speed. Successive runs at
the new speed are computed from Eq 7 d = Stokes equivalent particle diam-
as before. eter, ~,
In preparing the particle size-settling n = viscosity of sedimentation liquid,
time table, a series of particle diameters poise,
are chosen which will cover the size range h = total settling depth, cm,
of the sample. Then the corresponding p, = skeletal density of sample, g per
settling times for these diameters are cu cm,
computed. In these computations it is p0 = density of sedimentation liquid, g
convenient to express the particle diam- per cu cm,
eter, d, in #, thereby introducing a factor g = gravitational acceleration constant,
of 108 in the numerical factors of Eqs 2 cm per sec per sec,
and 4. Since these factors are constant co = angular velocity of centrifuge, ra-
during a given experiment it is conven- dians per sec,
ient to represent them by K and K ~ . r0 = distance from rotation axis to sur-
face of sedimentation liquid in
18 X 108hn tube, cm,
K-
(o, - po)g r2 = total distance from rotation axis a
18 X lOSn particle settles = r0 + h, cm,
do = diameter of last particle just sedi-
mented during gravity settling
and portion of run, **, and
K,~ = ! K % = centrifuge s t a r t - s t o p correction,
hw = sec.
134 Su ON PARTICLE SIZE MEASUREMENT
In application of these equations, it is trifuge settling is most conveniently

sufficient to take the total settling depth, made 5 to 10 min after the start of a run.
h, as an average settling distance for all The centrifuge timer settings should not
the particles, although the different be shorter than the starting times to
diameter particles do settle slightly dif- reach constant speed because of compli-
ferent total distances. Also, the thickness cations which would be introduced in
of the dispersion layer is neglected since making the centrifuge corrections. Cen-
it is thin compared to the total settling trifuge speed is increased at the oppor-
depth. For the Pillsbury apparatus, h tune times to reduce the total time to a
is 10 cm. minimum.
Ioo
90
80
03
70 43- First Run __
-b. Second Run
-- -0- T h i r d Run
60 - -
.E
u_ 50
o~
ID
40
rl
~= 30 r
20
,o F-
0 10 100 400
Sbkes . Equivolent DiomeIer, ~t
FIG. &--Sedimentation Analysis of Ammonium Nitrate.
It should be noted that K and K~ are Sample Dispersion:

indirectly functions of temperature since
One of the more important steps in
they contain the viscosity and density of
the procedure is to obtain a good disper-
the sedimentation liquid. However, the
sion of the sample. For many materials
K values do not change significantly un-
this is not an easy task. Often, during
less temperature changes greater than 4
the sedimentation process, the sample
F occur. Thus, the size-time table need
particles begin to flocculate, or stick to
not be recalculated between routine runs
the sides of the tube, or compact in the
of samples of the same material unless
sediment column after settling. These are
the room temperature varies more than
this amount. all symptoms of an unsatisfactory dis-
The size-time table is usually prepared persion and another trial at dispersing
as part of the data sheet as shown in the sample must be made.
Table II of the example given in Appen- The satisfactory dispersing of almost
dix I. The change from gravity to cen- all materials is greatly aided by the use
CARTWRIGHT AND GREGG ON LIQUID SEDIMENTATION ~/[ETHOD 135
of a surface-active agent in both the dis- tion liquid with dispersant to a level
persing and sedimentation liquids. In such that the sample introduction cham-
hydrocarbons, Twitchell Base 82404 has ber will not quite touch the surface
proved to be excellent for this purpose when inserted in the top of the tube. Air
at a concentration of about 0.1 to 0.3 bubbles entrapped in the tube capillary
per cent. are released with the aid of a steel clean-
The concentration of solids in the dis- ing wire. The vial containing the sample
persion should be about 1 per cent by dispersion is well shaken and about 0.8 ml
volume, this being about the amount of the dispersion transferred by means
required to obtain a satisfactory total of a straight pipet to the introduction
sediment height of 10 to 15 mm in the chamber which is held with the left in-
capillary of the sedimentation tube. Con- dex finger against the screen end. The
centrations much larger than this may right index finger is placed over the top
give rise to undesirable streaming effects. of the chamber which is then shaken.
No definite dispersion routine has been The chamber is righted, right finger
established because different materials raised momentarily to release pressure
often require different techniques. The and then replaced, the left finger re-
best over-all results in dispersing mate- moved, the chamber placed in the top
rials have been given by placing about of the tube, the right finger removed and
0.15 cu cm of dry sample on a glass plate, the chamber withdrawn with a twisting
adding several drops of dispersing liquid motion. With a little practice, this trans-
containing a dispersing agent, and rub- fer procedure can be performed rapidly
bing the thin mixture with a spatula. such that little mixing occurs and a sharp
Only agglomerates and not individual layer of the dispersion is left on the sur-
particles should be broken up with the face of the sedimentation liquid.
spatula. When the sample is dispersed, When the sample introduction cham-
the mixture is transferred to a small vial ber is removed, a stopwatch is started
containing about 15 ml of the dispersing and a cap placed over the top of the
liquid with dispersant. sedimentation tube. The purpose of the
A second technique, used with moder- cap is to eliminate convection currents
ate success, consisted of placing the sam- produced by evaporative cooling of the
ple and appropriate amount of dispersing liquid surface and to guard against pos-
liquid in a small vial with a few glass sible spillage when the tube is in the
beads and rolling with a bottle roller for centrifuge.
several hours. Such treatment also breaks
up agglomerates. Since the suspension is Calculations of the Size Distribution
relatively dilute, break-up of individual Curve."
particles apparently does not take place. The data obtained during an experi-
Use of a blender and an assortment of ment consist of a series of sediment col-
stirrers gave results judged to be inferior umn heights measured at the times given
to the above. by the size-time table. These heights are
read to the nearest 0.1 mm from a scale
Initiating the Run: on the sedimentation tube capillary.
In preparation for the start of a run, During the sedimentation, the par-
the sedimentation tube is carefully ticles are classified by diameter and those
cleaned and filled with the sedimenta- reaching the bottom at any one time
have the same equivalent diameter. As-
4 Emery Industries, Cincinnati, Ohio. suming no interaction among the par-
136 SYMPOSIIIN[ ON PARTICLE SIZE IV[EASUREMENT
tides, they wilt settle in dose-packed a v e r a g e d i a m e t e r of t h e s a m p l e m a y b e

configuration which will have a very computed as shown in the example in
nearly constant percentage of void-space A p p e n d i x I.
for the various diameter particles. Con-
EVALUATION OY RESULTS
sidering this, the volume of sample
sedimented is very nearly proportional As mentioned, the data obtained by
to the weight of the sample sedimented this method are expressed as cumulative
at any particular time. Thus, the ratio size distribution curves. Since the com-
of a given sediment height to the total putations assume Stokes' law for spheri-
sediment height at the end of a run gives cal particles, the plotted curves give the
the weight fraction of the sample greater d i s t r i b u t i o n of s p h e r i c a l p a r t i c l e s w h i c h
than the diameter corresponding to this w o u l d b e h a v e like t h e a c t u a l s a m p l e
TABLE I.--DATA FOR AMMONIUM NITRATE.
Sediment Height, mm Weight Finer than Size, per cent

Particle
Diameter,
1st Run 2nd Run 3rd Run 1st Run 2ndRun 3rdRun Mean
70 .......... 0.02 0.02 0.02 99.8 99.8 99,8 99.8

60 . . . . . . . . . . 0.1 0,1 98.9 98.8 98.8
50 . . . . . . . . . . 1.1 1".'0" 1.2 88.3 89.2 87.8 88.4
40 . . . . . . . . . . 2.6 2,5 2,8 72.3 73.1 71.4 72.3
35 . . . . . . . . . . 3.5 3.9 62.4 60.2 61.3
30 . . . . . . . . . . 5".'1 5.0 5,1 45.s 46.0 47.7 46.5
25 . . . . . . . . . . 6.2 6.1 6,3 34.0 34.4 35,7 34.7
20 . . . . . . . . . . 7.5 7.3 7.8 20.2 21.7 20.4 20.8
15 . . . . . . . . . . 8.4 8.2 8.9 10.6 11.6 9.5 10.6
10 . . . . . . . . . . 9.2 9.1 9.6 2.1 2.2 2.0 2.1
8 .......... 9.3 9.2 9.7 1.0 1.1 1.0 1.0
6 .......... 9.4 9.3 9.8 0 0 0 0
T h e above d a t a is represented by t h e curves on t h e graph in Fig. 6.
sediment height. By subtracting these with respect to this experiment. For this
values from one (or from 100 if expressed reason, the sizes on the distribution
as per cent) the weight fractions smaller curves are labeled as "Stokes Equivalent
than size may be obtained. These may Diameter." Because of the underlying
be conveniently exhibited in the form assumptions and the above interpreta-
of a graph by plotting on semitogarithmic tion of the results, it is clear that the
paper using the logarithmic scale for repeatability of this method has more
the particle diameters and the linear scale meaning than accuracy of comparison
for the corresponding weight fractions. A with results of other methods.
smooth curve representing the complete Data given in Table I for a ground
cumulative size distribution may be ammonium nitrate illustrate the degree
easily drawn through the plotted points. of repeatability possible with this tech-
In particular, the median diameter of nique. The maximum deviation from the
the sample can be read directly from the individual mean is 1.2 weight per cent
above curve. Data may also be obtained and the average deviation is 0.5 weight
from this curve such that the weight per cent.
APPENDIX I
ILLUSTRATION OF METHOD OF COMPUTATION
T o illustrate the details of the m e t h o d a typical r u n to d e t e r m i n e the size d i s t r i b u t i o n of

a s a m p l e of g r o u n d s o d i u m chloride will be given.
P r e v i o u s experience s h o w e d benzene to be a good s e d i m e n t a t i o n liquid for use w i t h
materials in the s a m e d e n s i t y r a n g e as s o d i u m chloride (p, = 2.16 g p e r cu cm, a h a n d b o o k
value). T h e critical d i a m e t e r in benzene w a s c o m p u t e d as a p p r o x i m a t e l y 90 /z, a n d the
g r a v i t y settling time for a 9 0 / z particle w a s calculated as 10.5 sec. T h e s e values a p p e a r e d
s a t i s f a c t o r y for this s a m p l e since a r o u g h screen analysis h a d indicated a m a x i m u m d i a m e t e r
b e t w e e n 75 a n d 100 #.
TABLE I I . - - D A T A SHEET.
Sample: NaC1
Density: 2.16 g per cu cm
Dispersion: 0.15 cu cm sample in 15 ml kerosine with 0.1 per cent Twitchell Base No. 8240
Sedimentation Liquid: Benzene with 0.1 per cent Twitchell Base No. 8240
Tube Capillary Bore: ~ mm Tube zero correction: q- 0.1 mm
K = 8.54 X 104 T = 77 F.
Observed Corrected Weight Weight Finer

Diameter, # Settling Time, mln-sec Sediment Sediment Greater than than Size,
Height, mm Height, mm Size, p e r c e n t per cent
80 .............. 13.3 0 0.1 0.8 99,2

60 . . . . . . . . . . . . . . 23.7 0.2 0.3 2.3 97,7
40 ............... 53.4 1.0 1.1 8.3 91,7
30 . . . . . . . . . . . . . . . 1:35 2.1 2.2 16.7 83.3
25 . . . . . . . . . . . . . . . 2:17 3.1 3.2 24.2 75.8
20 . . . . . . . . . . . . . . . 3:33 5.3 5.4 40.9 59,1
16 . . . . . . . . . . . . . . . 5:34 7.5 7.6 57.6 42.4
13 . . . . . . . . . . . . . . . 8:25 9.2 9.3 70.5 29.5
8 ............... 23.0 at 600 rpm 12.0 12.1 91.6 8,4
6 ............... 34.4 at 600 rpm 12,8 12.9 97.7 2.3
4 ............... 1:41 at 600 rpm 13.1 13.2 100 0
3 ............... 44.3 at 1200 rpm
2 ............... 1:52 at 1200 rpm
1.5 . . . . . . . . . . . . . . . 1 : 26 at 1800 r p m
1.0 . . . . . . . . . . . . . . . 3:27 at 1800 rpm
T h e s a m p l e was dispersed in kerosine using the glass p l a t e - s p a t u l a m e t h o d p r e v i o u s l y

described. Twitchell Base 8240 was used as the d i s p e r s a n t in b o t h liquids a t a c o n c e n t r a t i o n
of 0.1 p e r cent.
T h e size-time table was p r e p a r e d using the following c o n s t a n t s in t h e e q u a t i o n s given
previously:
n = 0.60 X 10 .2 poise, r0 = 3.3cm,
h = 10 cm, r2 = 13.3 cm,
p~ = 2 . 1 6 g p e r c u c m , dg = 1 3 # ,
P0 = 0.87 g p e r cu cm, r~0~ = 2.2 sec,
g = 980 c m p e r sec p e r sec, r40, = 8.7 sec, a n d
co = 207r, 407r, or 607r r a d i a n s p e r sec. rs0, = 22 sec.
T h e K values c o m p u t e d f r o m these values are:
K = 8.54 • 104
K20~ = 0.0248K = 2120
K,o~ = 0.0062K = 530
K~0~ = 0.00276K = 235
T h e complete size-time table for this e x a m p l e is given on the d a t a sheet in T a b l e I I .
138 SYM]?OSIUI~ ON PARTICLE SIZE MEASUREMENT
The calculations of the gravity settling times are straight-forward and will not be given.
However, the centrifuge timer settings are more involved and will be given in detail.
At 600 rpm
For 8/z particles:
K20~- u
tt = t'j -- t'o + r~o~ = d -T ln [ d2h ~ 0+ 2.2
k ro + --Idos/
2120 13.3
tt = T I n / , "82 X 10~ + 2.2 = 20.8 + 2.2 = 23.0 sec
k3 3 +
For 6 # particles:
2120 13.3
12 = t'2 -- t'l + T20~ = In ....... 20.8 + 2.2
6~ 62 X 10~
3.3 + 132 ]
t2 = 53.0 - 20.8 + 2.2 = 34.4 see
For 4 # particles:
2120 In 13.3 _
t3 = t'3-- t'2+r2o~ = 43 ( 3 . 3 + 4 ~X13310"~]- 5 3 . 0 + 2 2
t8 = 152 -- 5 3 + 2 . 2 = 101 sec
At 1200 rpm
For 3 # particles:
(20~ 2 K,0 ~ r2 1
t, = t', -- t'3 \ ~ - ~ / + r,o. ~ d2 ln(ro+d21~ / - ~ t'3 + 8.7
53O 13.3 1
t4 = - - In ( 3 . 3 + 3 ~7X l3O '"i - 46X - 3 8 1+5 2 8+ 8 " 7 7= = 4 4 3 s e c ~ ]
9
For 2 ~particles:
530 13.3
t5 = t'~-- t'4+r40~ = - - l n -- 73.6 + 8.7
2~ 2~ X l0 b
3.3 + 13~ ]
t6 ---- 177 -- 74 + 8.7 = 112 sec

A t 1800 rpm
For 1.5/~ particles:
Kso ~r r~ 4
t6 = t', - t'~ k~/ + ~,o~ =
e,
In
( ro + eda*, q] 9'
-"
+ 22
236
-(
t = 1.5= In
13.3
1.52 X 10
3.3 + 13------7 -
)
4
-- - X
9
177 + 2 2 = 1 4 3 - 7 9 + 22 = 8 6 s e c
For 1/z particles:

236 13.3
t, = t'7 - t'~ + .~ = T in / 1' x lO\ - 143 + 22
k3.3 + 1 - i 7 - 1~
t7 = 328 -- 143 + 22 = 207 sec
The observed heights of the sediment column were recorded on the data sheet as shown
(Table II), In this example, a zero correction of +0.1 mm was added to the observed heights
~oo
90
80
c
70
~= 6 0
4o
3o
2o
Io
02 - 1o Ioo 400
Stokes Equivolenf Diometer,~,
FIG. 7.--Sedimentation Analysis of Ground Sodium Chloride, d~,o= 21.2~.
because the scale zero did not coincide with the bottom of the tube capillary. As it turned
out, this particular sample contained no particles smaller than 4/~ so that the run was
actually terminated at this point. However, the centrifuge timer settings for sizes smaller
than this were included in the table so that their calculation could be illustrated.
The weight per cent fractions were calculated from the corrected sediment height data
and recorded on the data sheet. The size distribution curve was plotted on semilogarithmic
graph paper as shown in Fig. 7.
The weight average diameter of a sample is given by dw = 1/100 Is (weight per cent in
range N midpoint diameter of range). This may be calculated from data taken from Table
II as follows:
Size Range, tt Weight in Range, per Midpoint Diameter, t~ Product Terms

cent
1OO t o 80 . . . . . . . . . . . . . . . . . . . . . . . 0.8 90 72
8 0 t o 60 . . . . . . . . . . . . . . . . . . . . . . . 1.5 70 105
60 t o 4 0 . . . . . . . . . . . . . . . . . . . . . . . 6.0 50 300
4 0 t o 30 . . . . . . . . . . . . . . . . . . . . . . . 8.4 35 294
30 t o 25 . . . . . . . . . . . . . . . . . . . . . . . 7.5 27.5 206
25 t o 20 . . . . . . . . . . . . . . . . . . . . . . . 16.7 22.5 376
20 t o 16 . . . . . . . . . . . . . . . . . . . . . . . 16.7 18 301
16 t o 13 . . . . . . . . . . . . . . . . . . . . . . . 12.9 14.5 187
13 t o 8 . . . . . . . . . . . . . . . . . . . . . . . 21.1 10.5 222
81o 6 ....................... 6.1 7 43
61o4 ....................... 2.3 5 12
2118
2118
dw = : 21.2~.
100
DISCUSSION
MR. R. A. STEPHENS.I--It is men- that the Layer method compares well
tioned that the data obtained by this with the microscope.
method had been compared with other In another paper 3 which we had pub-
methods for the determination of par- lished on the method we have a com-
ticle size. In this paper it is assumed that parison of particle size analyses on
the void space is constant and that ac- Arizona road dust by centrifuge sedimen-
tually a volume is being measured and tation made with benzene and carbon-
converted to a weight basis. Do the tetrachloride as sedimentation liquid, the
authors have any idea of how close that Andreasen pipet with benzene, and the
agreement was with other methods? given analysis. The difference in the me-
MR. K. T. WHITBY (for the author).2-- dian is approximately 2.5 u between these
The paper we are presenting at this time analyses, the difference between the An-
shows one comparison on glass beads. dreasen and the centrifuge method being
Figure 4 contains not only the compari- about 0.3 u at the 8 ~ size.
son of the Layer and homogenous method MR. STEPttENs.--Of course, 8 # is a
but a microscope count on glass beads. relatively large size when you are deal-
This microscope count is the average of ing with some of the things such as lead
three determinations done by projection oxides which Mr. Musgrave was talking
with an estimated variation in the me- about3 I can see where you obtained
dian of about 0.75 per cent. So we feel fairly good correlation between the mi-
the microscope analysis there is very cron size of the fraction of a material
good. I t will be noted from this figure
a K . T. W h i t b y , " A R a p i d G e n e r a l - P u r p o s e
1 T e c h n i c a l C o o r d i n a t o r , C. K . W i l l i a m s & C e n t r i f u g e S e d i m e n t a t i o n M e t h o d for M e a s u r e -
Co., E a s t o n , P a . m e n t of Size D i s t r i b u t i o n of S m a l l P a r t i c l e s , "
2 Assistant Professor, Mechanical Engineering Heating, Piping and Air Conditioning, Vol. 27,
D e p a r t m e n t , U n i v e r s i t y of M i n n e s o t a , M i n - pp. 2 3 1 - 2 3 7 , J a n . , 1955.
neapolis, Minn. 4 See p. 172.
DISCUSSION ON LIQUID SEDIMENTATION METHOD 141
retained on a sieve and the micron size MR. KENNETH A. KANDER.S~With

of the sub-sieve fraction where you have regard to filter analysis, has anybody
relatively coarse sizes. But when you ever attempted to use a sedimentation
get down to the very fine micron sizes, method in analyzing the efficiency of fil-
say below 5 #, then the volume relation- ters used in hydraulic systems where we
ship does not seem to hold. have a condition of varying densities of
MR. WHITBY.--We know that there contaminant? We have everything from
are porosity variations in the sediment lint to steel. This applies not only to this
column. We have made several attempts paper but practically to all these papers
at measuring this. I know of one other discussing sedimentation. Does any-
company that is using this equipment body have any comment on the applica-
that made an extensive investigation on bility of such a method to the analyzing
one particular material. We found for of non-uniform contaminants?
airborne dust that there is about a 40 Mir WHITB'A--We have made several
per cent variation in porosity from 0.16 analyses of particulates in gasoline where
size to the 3 #. In most of the applica- one of the additives formed crystals. We
tions of particle size analysis, for a given concentrated the particulate by using
material, even at quite widely varying one of the finer grades of membrane
sizes, the porosity rating is generally filters and then used this technique for
quite similar. Our experience has been, size analysis. We also centrifuged a suffi-
in general, that the uncertainties in cient volume to collect the sample. The
dispersion are more serious than the membrane filter technique is to be pre-
uncertainties caused by porosity varia- ferred because it is more convenient.
tions. There are specific applications un- We have also had measured particu-
doubtedly where greater precision is lates in lubricating oil, such as lead de-
required and which could not be met by posits, and general dirt.
a method such as this. In the paper on This method, because it uses a column
sieving 4 which I presented where a fun- of sediment, will be sensitive to any-
damental study was being made, a sedi- thing that will affect the porosity of the
mentation method of any type would sediment column. Therefore in the case
not have been satisfactory for most of of airborne dust, which usually contains
the size analysis work due to the preci- fibers, the fibers must be removed if
sion required. there is more than about 37 per cent by
MR. B. J. HEINRICtI.5--Before we went volume. In the dust surveys referred to
over to this method, our people did com- here, we routinely wet-screened all the
pare it with electron microscopes and samples through No. 325 sieves and then
other microscopic methods. As pointed analyzed the less than 325 fraction. Or-
out in the paper, we were primarily in- dinarily the normal range of particle
terested in repeatability as against re- shapes and crystals will not cause any
producibility. Maybe it is not clear particular difficulty.
what is meant by repeatability and re- MR. L. T. WORK/--I am going to go
producibility. We consider reproducibil- back to Mr. Whitby's reconciliation of
ity data obtained by two or more lab- microscope and electron microscope.
oratories. We are more concerned in our
I gathered that this is a percentage of
research program in following the trend
in a process.
BResearch Engineer, Boeing Airplane Co.,
s Section Manager, Research Division, Seattle, Wash.
Phillips Petroleum Co., Bartlesvitle, Okla. 7 Consulting Engineer, New York, N. Y
frequencies of numbers of particles that croscope count is to obtain a proper

you were accumulating. Is that right? compromise between accuracy and time
MR. WlilTBY.--These were annula- required. These were all equivalent of
tive size distributions and they are pre- about 10,000 particles and this requires
sented there by a number area, weighted a considerable period of time.
by number area in weight. The upper MR. WogK.--I wanted to bring up the
curve is by number. The microscope is point on the grounds that the larger par-
by number. ticles are likely to be lost in both of the
MR. Wol~K.--The microscope and the counts. The electron microscope will lose
electron microscope in Fig. 5 I believe smaller particles on the large end more
could converge purely because the elec- than the optical microscope will. But it
tron microscope misses some particles did seem to me that those values might
about shall we say 2 t~. Is that correct be capable of reconciliation.
that you had already accounted for 100 Now if I may move over to one other
per cent of the particles in the electron aspect just by way of a little light com-
microscope at less than 2 t~? mentary, I think the question was asked
MR. WmTBY.--Undoubtedly they about using this equipment for some of
should converge, and if one were to the slimes from oil filters, etc. I had an
elaborate the staging of the count indefi- analogous question as to whether these
nitely, undoubtedly they would con- airborne dusts could contain the oil par-
verge. The problem in making the mi- ticles of automobile exhaust.
STP234-EB/Aug. 1959
DETERMINATION OF PARTICLE SIZE DISTRIBUTION BY EXAMIN-

ING GRAVITATIONAL AND CENTRIFUGAL SEDIMENTATION AC-
CORDING TO THE PIPET METHOD AND WITH DIVERS
BY SgPmN B ~ O
SYNOPSIS
The aim of the fineness analysis is to determine the particle-size distribution.
Methods by which only a numerical value is found for a quality of the product
depending on the fineness are of slight value except in cases where the particle-
size distribution is already known with the exception of a constant.
With the pipet apparatus for examining coarse products, the sampling from
the sedimenting suspension is effected from a horizontal tube in the side wall
of the sedimentation vessel by means of an automatic pipet. With ethylene
glycol as suspending medium the particle-size distribution can be determined
from a particle size of about 500/z when calculating the particle size by Stokes'
law. With water as suspending medium the particle-size distribution can be
determined from a particle size of about 150 #, when calculating the particle-
size by Allen's formula.
A correction is introduced for the retarding influence of the walls of the con-
tainer on the sedimentation, and it is shown that the time which elapses until
the particle has obtained the constant sedimenting velocity may be neglected
even for the largest particles examined.
When the particle size is below about 20 #, measurements can, in addition
to the pipet method, be effected by means of divers. With the diver method
the distribution of concentration in the suspension is determined by measuring
the depth below the surface at which a body of known specific gravity, a so-
called diver, completely submerged below the surface of the suspension during
the measurements, comes to a floating equilibrium.
When a diver is in equilibrium in a sedimenting suspension it will move
downward with the same speed as the largest particles found on the level of
its geometrical center of gravity, and thus the depositing of particles which
occurs in the hydrometer method is avoided or subsidiarily minimized. By
using globular divers having a diameter of about 7 mm only, measurements
can be effected at a slight distance below the surface of the fluid and very fine
products can thus be examined.
By numerical calculations it is shown that the influence of diffusion may
often be neglected for heterodisperse products down to a particle size of 0.035 #,
but that the influence is pronounced in the examination of monodisperse
products when the particle size is less than 0.2/z.
The range of measurements is 20/~ to 0.2 # even for monodisperse products.
For the examination of centrifugal sedimentation a beaker centrifuge is
used with conoidal sedimentation vessels and the centrifuge housing is ar-
ranged as a thermostat.
The measuring of the distributions of concentration can be effected by the
1 Civil Engineer, Lyngby (Copenhagen), Denmark.
143
pipet method with an automatic pipet and also by means of globular divers
of a diameter of 7 mm only.
It is shown that the influence of diffusion by centrifugal sedimentation,
even for monodisperse products, will first become noticeable at a particle size
of 0.005 ~.
Further it is pointed out that when new materials are to be examined pep-
tizing experiments compose the major part of the fineness analysis, both by
gravitational and by centrifugal sedimentation.
The chief problem of fineness analysis is to determine the particle-size distribution,

which presupposes the establishing of a definition of particle size which is independ-
ent of the shape of the particle.
Methods which determine only a numerical value for a quality of the product
depending on the fineness are of slight value except in cases where the particle-size
distribution is already known with the exception of a constant determined by the
measurement.
The particle size may be defined as the edge k of a cube (1),2 or the radius r of a
sphere, having the same volume as the particle considered. The particle size may thus
be determined by counting and weighing monodisperse fractions (1).
The particle-size distribution V ( k ) is defined by the equation
dC(k)
V(k) = . .................................. (:)
dk
where C(k), the so-called characteristic, is the relation between the sum of the weights
of those particles which have a particle-size smaller than k and the total weight of
all the particles.
The characteristic and thereby the particle-size distribution may be determined
on the basis of a study of the process of sedimentation in an originally homogeneous
suspension, and it can be carried out in three distinct ways, namely, by determining,
after different sedimentation periods, either
(a) The total amount of dispersed material which is present above a certain
horizontal plane across the container (2), or
(b) The amount of material which has sedimented out upon a horizontal plane at
a certain depth below the surface, usually the bottom of the container (3), or
(c) The corresponding values of depth and concentration of the dispersoid (4).
While methods (a) and ( b ) , as closer consideration will show, (S, p. 22), (6, p. 166),
involve relatively complicated calculations to obtain the characteristic and the
particle-size distribution of the material from the experimental data, the quantity
observed in method (c) is the characteristic itself. One simply plots as ordinate the
percentage of the original concentration of the material which remains at a given
level against the largest particle size calculated for that level.
If the concentration at the depth h after the sedimentation period t is Ch.t and the
original uniform concentration was c. ,0 one has
Ch,t
c(k) = --. .................................. (2)
~:.,0
The boldface numbers in parentheses refer to the list of references appended to this paper.
BERG ON GRAVITATIONAL AND CENTRIFUGAL SEDIMENTATION 145
where k is given by Stokes' law or Allen's formula depending on the particle size,
and provided they are valid for nonspherical particles (7-10).
ch., can be determined by the pipet method which was invented by Robinson (4),
while the pipet apparatus which is mostly used was constructed by Andreasen (11).
8 0 cm 20 cm
T--~---~ Nm::==~
FIo. 1.--Sedimentation Vessel with Horizon-

tal Sampling Tube. Fie. 2.~oose Pipet with Angular Tip.
ch.t may also be determined by means of a hydrometer (12--14) which indicates the
specific gravity directly, and thus the concentration at the level of the center of
gravity of the suspension displaced. A more accurate method consists in determin-
ing the specific gravity by means of so-called divers, which will be dealt with subse-
quently.
According to the methods described in this article it is possible to determine the
particle-size distribution of products within the particle-size range, 500 ~ to 0.005
when the density of the product is about 2.5.
Each method covers the following particle-size ranges even for monodisperse prod-
ucts:
The pipet apparatus (gravitational sedimentation) 500 ~ to 0.5
The diver method (gravitational sedimentation) 20 ~ to 0.2
The centrifugal method 0.5 ~ to 0.005
THE PIPET APPARATUS
(GravitationalSedimentation)
The apparatus comprises a sedimentation vessel, 90 cm high having an inside
diameter of 3 cm, with a mark 13 cm from the top, corresponding to a volume of
about 500 cu cm, and a horizontal sampling tube which is fitted in through the side
of the vessel, as shown on Fig. 1.
I00
f
0. 7 5
o //s J
= 50
E
O3
o
25
/ rEthylene glycol
Pipet Metl~od jWater according to Stokes' Low 9
.t= ~Woler according to Allen's Formula 9
, Sieving : Particle-size boundory o
O 50 I00 150 200 2,50 500

Particle Size,k,u.
FIG. 3.--Characteristic. Crushed Hard-Paste Porcelain.
Samples are taken by means of a loose pipet, Fig. 2, the upper part of which can
be closed by means of a two-way stopcock. The lower part ends in the short tip of
the pipet and forms an angle of 90 deg with the pipet tube. When the tip of the pipet
is connected to a rubber tube fitted to the sampling tube, the pressure inside the
vessel will make the suspension rise into the pipet beyond the two-way stopcock,
which is then switched, and the pipet is released from the rubber hose, which is
closed by a glass rod serving as a stopper.
The suspension above the stopcock is then blown out through the side tube of the
stopcock, and the pipet is emptied into a weighed vessel which is evaporated and
weighed.
The volume of the pipet, including the bore, is 10 cu cm. The volume is measured
automatically and extremely accurately, in accordance with the principle known
from the Knudsen pipet, that the pipet is checked by means of a stopcock.
For suspensions in viscous fluids a wider sampling tube is used and a pipet having
a wider intake aperture than for aqueous suspensions so that the pipet can be filled
in about 3 sec in this case too. The error due to the fact that the pipet is momentarily
not filled will remain a slight one.
By means of this apparatus, measurements can be effected in aqueous suspensions

over the whole of the area in which one must use a viscous fluid as a suspending me-
dium when employing Andreasen's apparatus.
For particles substantially greater than 100 ~, Stokes' law will not hold as regards
aqueous suspensions, but the particle size can be calculated by Allen's formula
(15,9,10). Stokes' law on the other hand, will hold for suspensions in viscous fluids,
the particle size which is critical for Stokes' law being proportional to the friction
coefficient of the fluid in the power of 3. Thus for ethylene glycol, for instance, it is
7.5 times as great as for water (9,10,16).
This is seen in Fig. 3 which shows the characteristic of crushed hard-paste porcelain
examined by the pipet method with ethylene glycol and water as suspending medium,
the particle size being calculated according to Stokes' law and Allen's formula. Points
determined by sieving and the particle-size boundary (17) determined by counting
and weighing are also shown. These determinations agree with Allen's formula when
k > 100 ~.
In the examination of coarse products the influence of the wall of the container
on sedimentation becomes marked and the accelerated movement of the particles
might also be of importance.
Influence of the Wall of the Container:
Lorentz (18) has given the following formula for the frictional force exerted on a
spherical particle with radius r, whose center is situated in a liquid with viscosity 7,
at a distance x from a plane wall, and which has a movement, with velocity v, paral-
lel to this wall:
z = 6~rrnv 1 -l- ............................... (3)
If one supposes that this formula is also valid for sedimentation in cylindrical
vessels, one has (9,10)
h~ 2(ok -- pf)gr ~
7) x -- __
where v~ is the velocity and h~ is the distance covered, within the time t, by a par-
ticle which initially was on the surface in a distance x from the wall (ok and p / a r e
densities of the particle and the liquid respectively).
For the particles which are not delayed by the influence of the wall one has
h 2
v -- (Ok - - p y ) g r 2
t 9n
and consequently
h~ 1
h 9r
14--
16x
On the interface B G E (Fig. 4) concentration and density are constant, and the
displacements of the individual particles of fluid have a tendency to make the inter-
face horizontal. If one supposes that these displacements occur without any flow
between the spaces B C D E G and A B G E F , and if the distance between the produced
horizontal interface and the surface of the fluid is h t, and the radius of the sedimen-
tation vessel is R, then one has:
~rh'R ~ =
f/ 2~r(R -- x)h~ dx
If Ak is the correction of the particle size, one has:

RR--X
R 2 - - 2 Jo f 9r dx
ak h-h' o 1+~ x
k 2h 2R~
(on the assumption that Stokes' law is valid).
By integration one finds :3
k i6-R l-- 1-k-l~ In 9r
and as 16 R >> 9 r one obtains with sufficient accuracy:
Ak~= --9 rl~ ( l + l n 91~R)
and therefore
=- ~ log~-0.024 )
3By substituting ~ = c the following equation is obtained:
2
/o R
1 + 16~
-- x dx = 2
f/ Rx__-- X ~ d x = 2R
// xdx 2
fo x ~dx
= 2R foR ~X +d ex -- 2R fo '~ xc+ -dxc 2 fo ~ ~~ -d ~x -- 2 foR x~ +dxe
= 2R ~ -- 2Rc[ln (x -{- c)]~ -- 2 // ( x - - c) d x - - 2c~[In (x + c)[~
= 2R 2 -- 2RclnR +_.. c _ R2 + 2 R c - - 2c 2InR-}-- c

C c
Or
( 9r) 9~ ( 9r) 1-}- 16~
= R~ I + ~ ---- I-}- 1 ~ In 9----7-
16R
~D
, 2R~
FIG. 4.--Sedimentation of Particles Delayed by the Wall of the Vessel.
k
W h e n ~ < 0.05 one may, with sufficient accuracy, substitute
k k
log _~ = 20 ~ - 2.2
from which it follows by substitution that:
hk k (1.8 16k) ~, 1,8 k . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

k R R
This equation is valid within the sphere of application of Stokes' law. On the as-
sumption that the expression:
h. 1
h 9r
1 + 16"--~
remains valid also in the sphere of application of Allen's formula one gets:
3.6k
. . . . . . . . . . . . . . . . . . . . . . . . . . (5)
k R R
T A B L E I . - - C O R R E C T I O N S FOR T H E I N F L U E N C E OF T H E WALL OF T H E
C O N T A I N E R W H E N STOKES' LAW IS VALID.
100 ~ = 100~? (1.8 -- 1 6 ~ )
Radius, cm i000 800 600 .u 400 ,u _ _ 2 0 0 ,u 100p
3 ...........
2 ...........
~ 3.7
4.6
3.0
4.0
2.1 1.1 0.6 0.3
0.4
1 ........... 4.6 1.6 0.9
The correction is seen to be negligible when k < 100 #.

150 SY~POSlU~ ON PARTICLE SIZE MEASUREMENT
T h e Accelerated M o v e m e n t s o f _Particles:
In the fineness analysis it is generally supposed that the time elapsing before the
particles have obtained a constant velocity need not be taken into consideration.
In the present case, however, we are dealing with larger particles and then the
assumption is less certain.
If the velocity at the time t after the beginning of the sedimentation is v,, and
the constant velocity is v, one has:
4 dv~ 4
61rr~v, + ~ ~rr~pk - ~ = ~ ~rr3(m -- Pl)g . . . . . . . . . . . . . . . . . . . . . . . (6)
By simplification and introduction of

2r~ (p~ -- p~)g
v = 9-~
one gets:
2r2.pk dv,
Vt -~- - - V
97 dt
from which it follows by integration that

2r~'pk
t-- b- ~ln(v--v,)
The integration constant b is here determined by the condition vt = 0 when t = 0

which gives:
t = 2r~'Pk In ~ ................................ (7)

9~1 vt
V
If v , = v, o n e h a s t = oo
This means that the particles first attain their constant velocity after an infinite
time. However, by introduction of vt = 0.99 v one gets:
P k 9 ~,2
t~9% = 1.02. - -
From this it can be deduced that quartz grains of particle-sizes k = 107 ~ and
k = 800 ~, which according to Stokes' law are critical for water and ethylene glycol
respectively, attain 99 per cent of their constant velocities after T-~-~and ~ sec respec-
tively.
The error is therefore insignificant.
THE DIVER METHOD
(Gravitational Sedimentation)
Divers (5,6,19) are hollow glass bodies adjusted to fixed specific gravities of values
between the specific gravity of the suspending fluid and that of the homogeneous
suspension.
The specific gravity of the diver being known, it is sufficient to measure the depth
under the surface of the suspension where the diver comes to a floating equilibrium
and note the time, in order to have a set of corresponding values of Ch.t and t. The
8crn
(b}
(o1
FIG. 5.--Divers.
(a) Oblong. (b) Globular.
divers contain a flat horizontal plate of soft iron, so that they can be drawn out
against the wall of the vessel by means of a magnet and be observed there, and, after
measurements are obtained, they can be brought up to the surface of the suspension.
The great accuracy of the diver method is, among other things due to the fact that
a diver, in floating equilibrium in a sedimenting suspension, will move downwards
with a velocity equal to the sedimentation velocity of the coarsest particles present
at the level of its center of gravity.
The diver will, therefore, not be overtaken by settling particles, and one avoids,
or subsidiarily minimizes the depositing, as it occurs in the hydrometer method, when
particles weigh down the hydrometer, thus causing misleading determinations of the
specific gravity.
For measurements divers like those shown in Figs. 5(a) and 5(b) are used. The ob-
long-shaped one (Fig. 5(a)) is used for the examination of products within the par-
ticle-size range 4 to 20 u; 1 ~ = 0.001 mm).
The plate, M, which is made of soft iron, marks the center of the diver, it is sup-
ported by the rod, S, which is fixed to the bottom of the diver by shellac. O is a
ballast of mercury. The specific gravity of the diver at 20 C, as compared to that of
water at 20 C, is ordinarily 1.00000, so that the diver can float in water at 20 C.
The diver can be given the following specific gravities: 1.0010, 1.0020, 1.0030,
.......... 1.0100 by loading it with one or more of 4 ring-shaped platinum weights,
adjusted to fit around its top, whose weights have approximately the following rela-
tive values: 1 : 2: 2: 5.
Platinum weights cannot be used for the globular diver shown in Fig. 5(b). Its
small size would be prohibitive to convenient handling of such small pieces. It is
thus necessary to have a globular diver corresponding to every one of the specific
gravities of the loaded divers.
The globular divers carry in them an iron wire as magnetizable material.
For measurements by means of the larger oblong-shaped divers, the cylinder glass
shown on Fig. 1 can be used. One may also take out samples according to the pipet
method (9,10), this being essential when examining products comprising a fraction of
particles greater than about 20 u, in which case it is advantageous to make measure-
ments according to the pipet method as well.
For measurements by means of globular divers, one can carry out measurements
at a distance of only 1 to 3 cm from the surface of the fluid. The accuracy is still
satisfactory since the relative error in particle size k is only half as great as the rela-
tive error in the determination of the diver's distance from the surface of the fluid.
Even for such measurements, a sedimentation period of about 15 days is required
for the determination of the distribution down to a particle size of 0.1 u. This long
sedimentation time incurs the further difficulty that diffusion becomes marked
(15,5,6,19).
Influence of Diffusion:
The influence of diffusion on the analytical result is pronounced when the par-
ticles are of uniform size. The change of concentration of the suspension during sedi-
mentation will occur as if the sedimenting particles were influenced, not only by
gravity and frictional resistance, but also by a force of diffusion amounting to
RT ~ In ch,t
N ~h
where R is the gas constant, T the absolute temperature, and N is Avogadro's con-
stant. The equilibrium condition becomes:
47rr 3 . RT ~ In ch,t . . . . . . . . . . . . . . . . . . . . . . . (8)
61r~'71V = ----3-- (Pk -- Pf)g 1u ~-
BERG ON GRAVITATIONALAND CENTRIFUGAL SEDIMENTATION 153
Solving Eq 8 for v, one gets

2r2(Pk -- Ps)g RT 8ch,t
v = 9~ -- 6~rr~Nch.-~-~" 6h
where:
RT m
~--~D
6rcrnN 6rrknN k
m being a constant and D the diffusion constant. If one sets:

2rZ(pk -- Py)g 2k~(pk -- Pf)g
(1~2)x/3 = i(~ - pf)k2 = jk2 = B
9n 9n --
where i, j, and B are constants, then one obtains:
~ch,t = D ~26h, t -- B ~Ch, t

6t -~ -~ .............................. (9)
and
vch,, = Bch,, -- D ~ch'---!
6h
Mason and Weaver (20) give the following solution when the sedimentation vessel
can be considered as extending downward without limit:
ch,, BV/~ (B*-h) z 1 [ [ B t -- h'~'~
-.,~ = c(~, h, ~) = _ _ y _ ~ 4~ + -~ t . ' - ~ k ~ ) )
+~1~- 1+ (.,+h) 1 - . k v - - ~ ) ) (1o)
where q~ \ ~ ] and ~ ~ % / ~ ] signify probability integrals whose arguments
Bt -- h Bt + h
are, respectively, ~r and %/----~
Equation 10 holds for sedimentation in vessels of limited depth as long as the con-
centration in one part of the vessel remains equal to the original concentration and is
thus constant. These conditions may easily be realized by gravitational sedimenta-
tion of suspensions of fine products.
Equation 10 reduces to Eq 11 when the first and third terms on the right-hand
side cancel each other. In this case
%-2 = U ( k ' h ' t ) = 2l -, \~]]{Bt -- h~'~ = 1(2 1 - ~2 1I/'u ,-~

3 ' ~0y /'l = ~ ( ~ - ~ ( y ) ) . . ( m
z ~ and z = h t -- h
where y - 2Dt/2tll
154 SYMposiuM ON PARTICLE SIZE ~/IEASUREMENT
and thus
( 3~Nnr~ i,2
Y= ~ \ 2RTt / ................................ (12)
Here h' signifies the distance through which the particles would have sedimented
if no diffusion occurred.
The probability integral
q~(y) = ~ e -y~ d y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (13)
is given in tables (for example Czuber (21)).

I00 f
t k=G2 F
o5O
0
#
0
0 0.1 0.2 0.3 0.4 0.5
k,/~ "~'~"
I00
t k=O.I F
/
o 50
0
0.05 0.1 0,15 0.2. 0.2.5
I lO0
o 50
!
0
0 0.025 0.05 0,075 0.1 0.125
k,p-
100 c~,t
FIG. 6.-- - t;.,0
- as a Function of k = 11.6 ( Stokes' Law).
B E R G ON GRAVITATIONALAND CENTRIFUGAL SEDIMENTATION 155
Introducing into Eq 12, T = 293, k = -- r = 1.612 r, and the values of the

various constants, one gets, when z is given in cm, k in #, and t in min:
y = 1 llOzkl/=t -II2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (14)
Svedberg and Rinde (22) used Eq 11 for the case of sedimentation in the centrifuge,
in calculating the concentration. I t is valid when the concentration in the upper part
of the vessel is zero.
The assumption that one can calculate points of the characteristic of a material
from the concentration ct~,, determined by the pipet or diver methods amounts to the
assumption that the equation
(where kh,, is the particle size calculated from Stokes' law, u = pk - pf and b is a
constant) holds with such accuracy that the ordinary experimental error, about 2 to
5 per cent of c..0, is not exceeded.
In Fig. 6 the characteristics are shown which, according to Eq 11 would be found
for three monodisperse products of density 2.5 and particle size 0.2, 0.1 and, 0.05 it,
by measuring the distribution of concentration after such sedimentation periods in
which the particles would in each case have been able to sediment 2 cm, if no diffu-
sion occurred (h' = 2 cm).
As the three characteristics are perpendicular to the axis of the abscissae it is seen
that the influence of the diffusion is of the same order of magnitude as the experi-
mental error for k = 0.2 g, but not negligible for the two products with smaller par-
ticles.
On the other hand, uniform size will very rarely occur in practical work, and when
the material is distributed over a fairly wide range of particle sizes the influence of
diffusion on the distribution of concentration will often be less than the ordinary ex-
perimental error even for materials whose particles belong to particle-size ranges for
which diffusion is pronounced. We therefore now turn to considering suspensions of
particles of unequal size.
One has:
Ch,~t
= [km~x G(k, h, t)V(k) dk . . . . . . . . . . . . . . . . . . . . . . . . . . (15)
C.,O fdO
if C ( b ~ / / ~ ) - ch'--t is s y m b ~ b y z ~ C ( k h ' t ) ' it f ~ 1 7 6
If the characteristic of the material under consideration satisfies the equation:

(C(k)); = ak
then,
n(C(k)) ~-~ dC(k) = a dk
and
dC(k) 1 1 1-,~
V(k) - - .a~.k ~
dk n
156 SYMPOSIUM ON PARTICLE SIZE I~[EASUREMENT
TABLE I I . - - AC (kh.~) CORRESPONDING TO n = 1/2, n = 1, AND n = 2.

Sedimentation period, t, rain . . . . . . . . . . 12017 27038 55180 108153 220720 432610
/r ~ ............................. 0.1500 O. 1000 0.0700 0.0500 0.0350 0.0250
AC(/~h,~) per cent for:
0.2 0.2 0.1 --0.18 [--0.36
n ~ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.4 0.8 1.0 0.4 I--0.5
n ~ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.3 0.8 1.5 1.1 --0.1
In this case, therefore

1
~C(k~,,) = ~ ~ h ~ _ Jo a(k, h, t).k ~ dk
I n Table I I are recorded the sedimentation time t (in rain), b ~ / / ~ = kh,, (in #),
and AC(kh,,) (in per cent) corresponding to n = 89 n = 1 and n = 2 for a -- 5.
By the use of calculated curves for G(k,h,t) ((S), p. 55 and (6) p. 201), shown graph-
1.0
I
~'o.s
7,
0
0 0.05 0.I0 0.15 0.20
k,/z 9
FIG. 7.--Calculated Curves for G(k,h,t).
ically in Fig. 7, ch'--Ais determined by numerical integration fop n = 89 n = 1, and

C.,0
n = 2, and a = 5, that is for cases where the characteristic is a parabola whose C ( k )
axis is the axis of symmetry and whose maximum lies in the origin, a straight line
through the origin, or a parabola whose axis of symmetry is the k axis and whose
maximum lies at the origin, respectively.
These forms of the characteristic are chosen because a straight line through the
origin can be considered as a simplification of a frequently occurring case and the two
parabolas are both simplifications of extreme cases of the form of the characteristic
corresponding to finer materials.
I n Fig. 8 are plotted the characteristics:
(C(k)) t/~ = 5k, C(k) = 5k, and (C(k)) 2 = 5k
4 I n the ealeulations, quadrature formulas of Cotes' type were used, especially Simpsou's and
Weddle's formulas (see reference (23)).
~BERG ON GRAVITATIONAL AND CENTRIFUGAL SEDIM~ENTATION 157
Furthermore, points are plotted corresponding to calculated values of

1 ~kma x 1--n
Ch,t 5~ I a(k, h, t)k ~ - dk . . . . . . . . . . . . . . . . . . . . . . . . . (16)
~ = ~-e0
f o r n = 89 n = 1 a n d n = 2.
T h e numerical integrations were carried out, assuming h = 2 cm a n d pk -- pl =
u = 1.5. If the depth at which measurements are made is hi and the difference be-
-~ 75
m 50
la.,.
.~ 25
,/" ,,,,,,,,
' o
,oo
ii ! i
9
a
0 0.05 0,10 0.15 0.20 0,25
Portiele Size,/Gp.
FIG. 8.--Characteristics: (C(k)) 112 = 5 k, C(k) = .5 k, (C(k)) 2 = .5 k and Plotted Points of the
Function.
tween the density of the particles and the medium is u l , then it holds t h a t (S, p. 57)
and (6, p. 202):
a(h, k, t) = a ( k , , h,, t,)
when
tl = t -- and kl = k
v,1/ \~,/ \ ~ /
T h e table and the figure have therefore a more general significance (5, p. 64) and
(6, p. 208) than might be considered.
Table I I and Fig. 8 show t h a t the characteristic of heterodisperse products can
v a r y greatly in form without the systematic errors from diffusion exceeding the or-
dinary experimental errors of the pipet method (S,6,24).
I t is therefore possible in a great number of cases to carry out the observation b y
examining gravitational sedimentation as if no diffusion occurred down to a particle
size of 0.035 ~. This is of great value for the fineness analysis as the examination by
gravitational sedimentation is much easier to perform than by centrifuging. The
method is particularly convenient for preliminary peptizing experiments by which a
small systematic error is unimportant.
Influence of Electrical Charges:

The electrical charges can exert an observable influence upon the course of sedi-
mentation, for as a result of the movements of the particles the charges cause elec-
trical potential differences to arise which oppose sedimentation.
Even by examination of very fine particles with the ultracentrifuge the effect of
charges may be eliminated by applying a sufficiently high concentration of soluble
salts ((25) pp. 12, 21, 49). Further the author of the present paper has shown by cal-
culation that one can neglect the effect of electric charges when the particle size is
greater than about 0.015~ and besides the concentration of peptizing agent is greater
FIG. 9.--Conoidal Vessel.
than about 0.001 mole per liter even if no other soluble salts than the peptizing
agent are present ((5) pp. 65 to 68 and (6) pp. 209 to 212).
THE CENTI~IFUCAL MET~IOI~
When using centrifugal sedimentation it becomes possible to investigate much
finer materials, than the finest which can be studied by gravitational sedimentation.
Svedberg (25,22,26) has constructed the well-known ultra-centrifuge by which the
concentration in sectoriaI vessels is measured photographically when the centrifuge
is running. It is, however, much less complicated to use a beaker centrifuge and meas-
ure the concentration when the centrifuge has been brought to a stop.
This has been done by Romwalter and Vendl (27), Brown (28), and Robison and
Martin (29,3o), according to Od6n's principle by the use of cylindrical or sector-
shaped vessels, and by Norton and Spell (31) using the hydrometer method in a cen-
trifuge in which the sedimentation vessels are located at such a great distance from
the axis of the centrifuge that the variation in the centrifugal field is relatively small.
Schlesinger (32) has developed a method by which vibration and convection currents
in the sedimentation vessels is tolerated and further Kamack has published an in-
teresting contribution (33). In a sectorial vessel which is free to swing out to horizontal
position he takes out samples while the centrifuge is in motion. He derives an equa-
tion (Eq 23) based on measurements by the "variable height" method which he
develops to permit an approximate calculation of the characteristic based on meas-
urements by the "variable time" method. His Eq 23 is identical with Eq 49 of the
author's 1940 dissertation (S, p. 103) and is the same as Eq 21.
In the centrifugal method developed by the author (8,6,19) round-edged conoidal
vessels (Fig. 9) have been used. Such vessels are easy to blow from glass, and from a
theoretical point of view they are as good as sectorial vessels and may be used in an
ordinary beaker centrifuge just as well as cylindrical vessels. The sector shape is a
special case of a right conoid only.
h .B A
C E
E
F 6
(a) (b)
FIG. lO.--Schematical Diagram of Apparatus Used for the Centrifugal Method.
A--Stroboscope E--Centrifuge cups
B--Tachometer F--Heating element
C--Centrifuge housing G--Cooling tube
D--Contact thermometer H--Motor
The glass vessels containing the suspensions are placed in the centrifuge cups. In
order to guarantee that particles can move along the sidewall of the vessel under the
influence of the centrifugal force, that wall must have the form of a right conoid
having, at a horizontal position of the beaker, the axis of the centrifuge as a directrix.
For centrifuging, the beaker centrifuge shown in Figs. 10(a) and (b) has been used.
The stroboscope A consists of a 12-holed plate. If this is observed in the light of a
neon glow-lamp, driven by an alternating current of a frequency of 50 cps from a
transformer having a core of " M u " metal, then the plate will seem to stand still
when the speed is a multiple of 500 rpm.
B is a liquid tachometer which can be used to read the order of magnitude of the
speed.
D is a contact thermometer through which the heating current of the electrical
heater placed inside the housing of the centrifuge is regulated by a relay.
G is a copper coil connected to a hydrant.
The centrifuge glasses are about 6 cm high, and their largest diameter is about 4
cm. The distance between the rotation axis and the surface of the liquid is 12 cm.
The space between the centrifuge glasses and the cups is filled with water to avoid
160 SYMPOSlIJ~t ON PARTICLE SIZE MEASUREMENT
the glasses being exposed to a too-heavy unilateral pressure; the cups are counter-
balanced in pairs to insure the same weight for two corresponding cups to avoid vibra-
tion when the centrifuge is operated.
The cups with the centrifuge glasses containing the suspension are placed in a
thermostat regulating at 20 C. The centrifuge also set at 20 C is first run without the
cups in it then stopped during the short interval required for placing the cups and
restarting the thermoregulator, without the temperature changing to any great ex-
tent.
Once the centrifuge is started it is brought to the desired speed in 1 rain.
To stop the centrifuge it is slowed down smoothly in the course of 2 rain to a speed
of about 100 rpm, and then brought slowly to a stand still in a further 4 min. If
these conditions are observed approximately in starting and stopping the centrifuge
the time of centrifugation can be set equal to the time during which a constant speed
is maintained + 1 min. This procedure is the result of a mathematical consideration,
see (S, p. 92) and (6, p. 236).
It is now possible to make concentration measurements in the suspension by means
of methods explained below.
In order to avoid losses by evaporation during centrifuging, the cups are closed
with rubber stoppers with beads resting on the upper edge of the cup Figs. 10(a)
and (b).
The surface of the suspension is situated at the distance a from the rotation axis.
A particle at the distance a + y from the rotation axis will be subjected to a force
equal to
4
- ~r~(pk - ps),o~(a + y)
3
Introducing Stokes' law we get:
4_ ~rr~(ok - ps)o~2(a -t- y) = 6~rrn d(a -t- Y) . . . . . . . . . . . . . . . . . . . . . (17)

3 dt
and
d(a + y) 2#(ok -- pl)r t
(a -t- Y) 97
Integrating between the limits a and a -t- y, one has:
In a + y 2r2(ok -- Pl)~~ t
a 97
and
/ a + y \1+~
(9nln a )
r = \2(o--2- ~St/ ............................. (18)
When N is the number of rpm and k is expressed in tt and r in min, one has:
k = 64000 (7 log a : yl 1/~

x \SE - V / " .......................... (19>
If one now considers an originally homogeneous suspension of particles of unequal

sizes, and if the concentrations in the distances y and y + Ay from the surface after
a centrifugation period of t sec are cy,t and cy,t + Acv,~, respectively, and the par-
ticle radii are r and r + Ar, then the increase in concentration Acy,t will have arisen
from particles within the particle-size interval r to r + Ar. If the original concentra-
tion of such particles is called Acv,o, then one has
2xcy,o (a + y)2
lim - - -
Aye0 ACy,~ a2
~Cy,O
*y (a + y)~
-- - - . ................................ (20)
~Cy, ~ a~
~y
The concentration cy,0 of all particles having a smaller radius than r is obtained by
integration
Cv,o = fo y (a +a 2 y)2 ~cv,~

6y dy
If the particle size corresponding to t is k, then one has

c~,~
C(k) =cv,o f~ (a + y)2 c.,oQdy

C.,o do aS ~Y
Pz
k
c (7 )-----4
I
0 i
Qy ~.
(a + y)~
FIG. 11.-- a~ as a Function of Q(y).
162 SYMPOSIUM ON PARTICLE SIZE I~/[EASUREMENT
If Ov stands for c~,,

C.,0
then we have:
C(k) =
fo Qy (a +a 2 y)2 . dP.y . . . . . . . . . . . . . . . . . . . . . . . . . . . . (21)
After having determined a number of corresponding values of ()y and y, one can
(a + y)2
plot a curve, (Fig. 11) showing aS as a function of Oy, and C ( k ) can then be
determined by measuring the area between the curve and the axis of abscissae, see
(5, p. 109) and (o, p. 253).
This method is to be applied when the product is monodisperse or nearly mondis-
perse and is the most accurate method.
If the product is heterodisperse, it can, however, be shown that approximately
(5, pp. 105-110; 6, pp. 250-254).
C(k) = Qv-]-~(SQy.=4C(~)) ........................ (22)
if y < about ~ a, and that

[ 2y'~
C(k) =Qy~l+~a ) .............................. (23)
if at the same time Qy < about 0.15.

Equation 23 is used for the computation of that value of C ( k ) which corresponds
to the smallest value of Qy, and Eq 22 provides the other value of C ( k ) . Since
/Tk
C(k) = Owhenk = O, inorder to estimate t h e v a l u e s f o r C ( 2 ) onewilldrawthe

characteristic linearly from the point corresponding to the smallest measured value
of k and to the origin.
This method is applicable for heterodisperse products which comprise the majority
of products encountered in practice.
The object of measuring the concentrations in centrifuged suspensions must be,
as can be seen from Eqs 21, 22 and 23, to determine corresponding values of ()~ and
y after each centrifuging.
Measuring of concentrations can be made by the pipet or diver methods.
For measurements by the pipet method one can use a pipet having two opposite
throttles 1 to 4 cm from the end of the pipet, functioning according to the well-known
Knudsen principle, as shown in Fig. 2, but without the angular tip.
Afterwards each centrifuging measurement is made with 2 or 3 pipets with throttles,
for example, in the distances of 1, 3 and 4 cm from the tip of the pipet.
During the sampling, the end of the pipet is touching the bottom of the centrifuge
glass, and the suspension is sucked up above the two-way stopcock. The stopcock
once closed, the surplus suspension is blown out through the side tube of the stop-
cock. The contents of the pipet are then emptied into a weighed cup, and the con-
tents of suspended material are determined by evaporation and weighing. As the
centrifuge glasses cannot be very big, the volume of the pipet should not exceed 1 to
100
. /
75
j At-rl
-6 5O
E
09
0
/
"~ 25
E Divers-Gravitational sedimentation, before centrifuging
Divers-Gravitational sedimentation, after centrifuging
Divers-Centrtfugot sedimentation
Divers-Centrifugal sedimentation
o
o o.I '
0.2 0 I3 I
0.4 01.5 0.6
Particle Size,k,/~
FIG. 12.--Characteristic. Czechoslovakian Bail Clay (Wildsteiner Clay).
I00
"E J
75
~, 50
g
o
g_ 25
/0 Divers-Gravitational sedimentation, before centrifuging
Divers-Gravitational sedimentation, after centrifuging
o Divers-Centrifugal sedimentatioJ'
Divers-Centrifugal sedimentation
0 i I I
0 0.1 0,2 0,3 0.4 0.5

Particle S i z e , k , / x
FIG. 13.--Characteristic. English Ball Clay (A-Clay from Hexter and Budge, Ltd.).
2 cu cm, and it will usually be necessary to employ a micro or a semimicro balance for
weighing.
If divers are preferred to effect measurements of concentrations, globular divers
having a diameter of 6 to 8 mm are very suitable. Measurements are made with 2 or
3 consecutive divers, if the difference in specific gravity in the centrifuged suspension
permits it, that is, if the product is not too monodisperse. The centrifuge cups must
be carefully taken out of the centrifuge and put into the thermostat. The centrifuge
glasses are then taken out from the centrifuge cups and placed in the thermostat,
where the measurements can be made by means of divers.
Because of the short sedimentation period, the diffusion will make itself felt much
less at the centrifuging of the same product than where investigations are made in a
gravitational field. This is clear from the following consideration.
A monodisperse suspension of particle size k and density 2.5 is centrifuged with
such a speed and for so long a" time, that a particle originally situated at the surface
of the suspension would have sedimented 2 cm, if no diffusion occurred.
The characteristic of the product is then determined, in the ordinary way for
monodisperse products, by measuring the distribution of concentration in the suspen-
sion. Applying Eq 11 to the centrifuged suspension, it may be seen that the influence
of diffusion on the result is the same as shown on Fig. 6 for a monodisperse product
with particle size 0.2 ~ examined by gravitational sedimentation if, according to Eq
14,
kll2.t-ll~ = 0.21/2.t1-1/2
and if no experimental error occurs. Here t is the time elapsed from the beginning of
the centrifuging till the measuring of concentration has been finished and h is the
time in which grains of particle size 0.2 ~ may sediment 2 cm under the influence of
gravity, if no diffusion occurs.
When using a sufficiently high speed of the centrifuge, t may for instance be 150
rain--the measurements take less than 30 rain--and h may be calculated, from Stokes'
law, to 6760 rain.
We then have:
kll2.t-ll~ = 0.21/2.6760-1/2
k = 0.0045~
Even for monodisperse products, diffusion will not disturb by centrifuging down
to a particle size of about 0.005 ~ and when the particles are of unequal size still finer
products may be examined than by centrifugal sedimentation.
Figures 12 and 13 show the characteristics of a Czechoslovakian and an English
ball clay examined by centrifugal sedimentation according to the method for hetero-
disperse products and by gravitational sedimentation before and after centrifuging.
This procedure has been followed to make sure there is no coagulation during the
measurements.
In the author's dissertation (5, pp. 112-154) a series of similar measurements are
further given which show the same good agreement between centrifugal and gravita-
tional sedimentation as shown in Figs. 12 and 13.
This agreement was to be expected according to the theoretical considerations on
the influence of diffusion by gravitational sedimentation.
:BERG ON GRAVITATIONAL AND CENTRIFUGAL SEDIMENTATION 165
IO0
75
g
J
~ 5o
t/'
/
g.
"~ 25
._~
dreosen Apparatus-Gravitational sedimentationlbefore centrifuging
]~l 9 Divers-Gravitational sedimentation ,before cenlrifuging
_,~3" n Divers-Gravitational sedimentation,after centrifuging
IDivers-Centrifugal sedimentation, separate runs
a Dwers-Centrifugal sedimentation, series centrifugation
0 ' ' = =
0 0.1 0.2 0.3 0.4 0.5
Particle Size, k, F
FIG. 14.--Characteristic. Barytes Pulverized 72 hr with Steel Balls 7.94 mm in Diameter.
I00
-
I=
~-~75 /~~
~o
g
-~
g.
,S
i
"~ o Andreosen Apporotus-Gro'~itotionol sedimentation,before centrifuging

._o, 9 Divers-Gravitational sedimentation ,before centrifuging
:~ ~ a Divers-Gravitational sedimentation ,after centrifuging
9 Divers-Centrifugal sedimentation t separate runs
a Divers-Centrifugal sedimentation , series centrifugotion
O0 0.0: 03'0 0.15 0.20 0.25 0.30

Particle Size, k,F
FIG. 15.--Characteristic. Barytes Pulverized 72 hr with Steel Balls 3.93 m m in Diameter.
166 SYMPOSIUM ON PARTICLE SIZE MEASIFRE~IENT
I00
$ 75
/
O.
50
E
tO
O-
2S
o
Y:
vers - Gravitational sedimentation,beforecentrifuging
,,/o 9 Divers- Gravitational sedimentation,afler centrifuging
a Divers- Centrifugal sedimentation
0 I I I I
0 0.05 0.10 0.15 0.20 0.25
Particle Size,k,,u.
FIC. 16.--Characteristic. Barytes Pulverized 216 hr with Steel Balls 7.94 m m in Diameter.
I00
75
t3 9Q C
E
r 50
"c
#_
"6
.T= 25
._~
! !!i!i~!i IIs!i! !!!i!ii!inn "ba~~:~I c::~l~irfiufg~g g
0
0 0.025 0.050 0.075 0.100 0.125
Particle Size,k,p.
Fie. 17.--Characteristic, Barytes Pulverized 216 hr with Steel Balls 3.93 m m in Diameter,
B E R G ON G R A V I T A T I O N A L AND C E N T R I F U G A L S E D I M E N T A T I O N 167
It was desirable to obtain a measure of the effect of the disturbances caused by

starting and stopping the centrifuge and by the other necessary manipulations. In
the author's dissertation (5, pp. 112-121) centrifugations were therefore carried out,
partly with separate runs, for each of which a fresh suspension was used, and partly
by repeatedly centrifuging the same sample (so-called series centrifugation) in its
vessel and determining its density after each stage, but not homogenizing it before
centrifuging it again. In the second and later stages the centrifuge was started slowly.
Figures 14 and 15 show the characteristics of barytes pulverized 72 hr with steel
balls, 7.94 mm and 3.93 mm in diameter respectively, determined both by separate
runs and by series centrifugation. Contamination with iron resulting from milling
IOO
.----rr" ~ / . . . . . e
/l FY
$Q. 7 5
g
"5
50
DYers
idlienaton
i
25
.c
t~ Treatment No. 8
A Treatment No. 9
x Treatment NQ I0
0.05 0.10 0.15 0.20 0.25 0.50

Particle Size , k,/~
FIG. 18.--Characteristics. Barytes Pulverized 216 hr with Steel Bails 3.93 mm in Diameter.
Different Treatments.
was removed by treatment with acid. The agreement between gravitational and cen-
trifugal sedimentation is in this case also as good as could be desired.
This shows that the disturbances are of little or no importance and that sampling,
when the centrifuge is running, as was done by Kamack (33), is not necessary under
the experimental conditions applied. Sampling may, however, be desirable, when
examining diluted suspensions or, when the specific gravity of the product differs but
little from the specific gravity of the suspending medium, as the stability against dis-
turbances, under these circumstances, is reduced. In this case however it is very im-
portant to keep the temperature constant. In sedimenting suspensions with small
density differences even slight changes in temperature give rise to local systems of
convection currents (stratification) (5, pp. 186-216) and (6, 332-374).
The characteristics of baryte ground 216 hr with the same steel balls are shown on
Figs. 16 and 17 to illustrate how well the increase of fineness by grinding is measured
by these methods. The examination is carried out by gravitational and centrifugal
sedimentation (separate runs).
168 SYMVOSlUM ON PARTICLE SIZE MEASUREMENT
Figure 18 shows how many experiments with different treatments it was necessary
to carry out to obtain a good peptization. "Characteristics" were determined with
divers, by gravitational sedimentation corresponding to the different treatments.
Treatment No. 8 shows the greatest fineness and therefore was selected for the main
experiments, the results of which are shown on Figs. 16 and 17.
By gravitational experiments the sedimentation time is long, but the work accom-
plished is very limited. By centrifugal experiments, on the contrary, the sedimentation
time is limited, but the work performed is considerable.
When a new material is investigated, it may be convenient to begin with a centrifu-
gation in order to ascertain whether or not the material is so heterodisperse that the
examination by gravitational sedimentation can be performed down to a particle
size smaller than 0.2 u, eventually down to 0.035 ~.
As heterodisperse products are more common than monodisperse substances, the
gravitational method may often be applied, thus measurements are highly facilitated.
Peptization and Coagulation
In the fineness analysis it is necessary first that the material to be investigated be
divided, by a preliminary treatment, into individual particles. Shaking, boiling and
washing with a peptizing agent may be done and the particle-size analysis may then
be carried out as mentioned in (S, pp. 19 and 122-140), or (6, pp. 162 and 267-286).
Even if a complete dispersion into individual particles has been obtained by a
preliminary treatment, a perikinetic or orthokinetic coagulation may appear during
the sedimentation. The theory of coagulation has been worked out by Smoluchowski
(34), Miiller (35), and Tuorila (36). Among the peptizing agents found so far, for
aqueous suspensions, possibly the best is sodium pyrophosphate, which has been
proposed by Chwala (37). Particle-size analysis can be carried out with different pep-
tizing agents as shown by Andreasen, Berg, and Kjaer (38), and by Andreasen and
Berg (39).
According to Tuorila (36), one can determine whether orthokinetic coagulation
occurs during the sedimentation process by making two fineness analyses differing
either in concentration of the dispersion or in sedimentation height. As the diver
method is very easy to operate, especially by gravitational sedimentation, and as
the random error is extremely small, the method is very convenient for peptizing
experiments. Such experiments make up the major part of the fineness analysis since
no absolute criterion is known to determine whether the material analyzed is present
as single particles or not.
This is the case both when examining gravitational and centrifugal sedimentation
in research work.
GENERAL CONCLUSIONS
Several symposia on particle-size analysis have been held: ASTM 1941 (4o), Insti-
tution of Chemical Engineers (41) and Institute of Physics (42), and so many methods
have been worked out that the literature describing them has assumed considerable
proportions, Hahn (43), Gessner (44), Herdan (45), Sharratt (46), Rose (47), and
Broughton (48).
On the other hand, the development in the last 30 years has had the consequence
that in fineness analysis sieving methods and methods based on an examination of
the change in the concentration (or in the extinction (49)), which takes place within a
certain distance from the surface of the suspension, by gravitational and centrifugal
sedimentation, m a y be preferred except in special cases.
Actually it is possible, with water as suspending medium, to determine the particle-
size distribution by the sedimentation methods up to a particle size where sieving,
with determination of particle-size boundary by counting and weighing (I,17), is
reliable and easy to practice. This is of great importance because the peptizing condi-
tions in aqueous suspensions are far better known than those in viscous fluids.
Even elutriation methods m a y now advantageously be replaced by the sedimenta-
tion methods, because the elutriation process is difficult to govern by low velocities,
due among other things to the fact that the equilibrium in the suspension is instable
because the pure medium, which has a lower specific gravity than the suspension,
enters in the bottom of the apparatus.
The situation is therefore more advantageous when the sedimentation method is
used rather than the elutriation method. A sedimenting suspension of heterodisperse
particles is always in equilibrium because the specific gravity of the suspension in-
creases with the distance from the surface, both in gravitational and centrifugal sedi-
mentation.
Acknowledgment:
Acknowledgment is due to A. Hald, Professor in Statistics at the University of
Copenhagen for having carried out the numerical calculations of the functions
U(k,h,t) and G(k,h,t) and the numerical integrations of the expression
ch,t _ n5~ fo km~x G(k, h, t). k 1-~

c.,o ~ - dk
which was necessary for the plotting of the characteristic in Fig. 8.
REFERENCES
(1) A. H. M. Andreasen, "Zur Kenntnis des (7) A. H. M. Andreasen, "tSber die Gtiltigkeit
Mahlgutes; theoretische und experimen- des Stokes'schen Gesetzes ffir nicht kugel-
telle Untersuchungen fiber die Verteilung f/Srmige Teilchen," Kolloid-Zeitschrift, Vol.
der Stoffmenge auf die verschiedenen 48, p. 175 (1929).
Korngr/Sssen in zerkleinerten Produkten," (8) A. H. M. Andreasen and J. J. V. Lundberg,
(Dissertation) Kolloid-Beihefte, Vol. 27, p. "t3ber Schl~mmgeschwindigkeit und Korn-
349 (1928). gr6sse," Kolloid-Zeitschrift, Vol. 49, p. 48
(2) G. A. Wiegr~er, "tSber eine neue Methode (1929).
der Schl~mmanalyse," Landwirtschaftlichen (9) S. Berg, "D~termination de la R~partition
Versuchs-Statlonen, Vol. 91, p. 41 (1918). Suivant leur Grosseur des Particules de
(3) S. Od6n, "Eine neue Methode zur mecha- Dimensions Notables," Atti del I V Con-
nischen Bodenanalyse," Internationale Mit- gresso Internazionale della Ceramica, Firenze
teilungen far Bodenkunde, Vol. 5, p. 257 (1954).
(1915). (10) S. Berg, "Bestimmung der Korngr~ssen-
(4) G. W. Robinson, "A New Method for the verteilung yon groben Produkten," Be-
Mechanical Analysis of Soils and Other richte der deutschen keramischen Gesellschaft,
Dispersions," Journal Agricultural Sciences, Vol. 33, p. 229 (1956).
Vol. 12, p. 306 (1922). (11) A. H. M. Andreasen and J. J. V. Lundberg,
(5) S. Berg, "Studies on Particle-Size Distribu- "Ein Apparat zur Feinheitsbestimmung
tion," (Dissertation) Ingeni~rvidenskabelige nach der Pipettemethode mit besonderem
Skrifter, Vol. 2, Copenhagen (1940). Hinblick auf Betriebsuntersuchungen,"
(6) S. Berg, "Untersuchungen tiber Korn- Berichte der deutschen keramischen Gesell-
grSssenverteilung," Kolloid-Bdhefte, Vol. s6haft, Vol. 11, p. 249 (1930).
53, p. 149 (1941). (12) G. J. Bouyoucos, "The Hydrometer as a
170 Su162 ON PARTICLE SIZE MEASUREMENT
New and Rapid Method for Determining (28) J. Callaway Brown, "Particle-Size Distri-
the Colloidal Content of Soils," Soil Science, bution by Centrifugal Sedimentation,"
Vol. 23, p. 319 (1927). Journal Physical Chemistry, Vol. 48, p.
(13) G. J. Bouyoucos, "The Hydrometer 246 (1944).
Method for Studying Soils," Soil Science, (29) H. E. Robison and S. W. Martin, "Beaker-
Vol. 25, p. 365 (1928). Type Centrifugal Sedimentation of Sub-
(14) A. Casagrande, "Die Ar~ometer-Methode sieve Solid-Liquid Dispersions--I," Jour-
zur Bestimmung der Kornverteilung yon nal Physical Colloid Chemistry, Vol. 52, p.
B6den und anderen Materialien," Springer 854 (1948).
Verlag, Berlin (1934). (30) H. E. Robison and S. W. Martin, "Beaker-
(15) H. S. Allen, "On the Motion of a Sphere Type Centrifugal Sedimentation of Sub-
in a Viscous Fluid," Philosophical Maga- sieve Solid-Liquid Dispersions--II," Jour-
zine, Series 5, Vol. 50, p. 323 (1900). nal Physical Colloid Chemistry, Vol. 53, p.
(16) H. Lamb, Lehrbuch der Hydrodynamik, 860 (1949).
Teubner, Leipzig.and Berlin, p. 682 (1907). (31) F. H. Norton and S. Spell, "The Measure-
(17) J. Andersen, "Uber Maschenweiten und ment of Particle Sizes in Clays," Journal
Korngr6ssen," Zement, Vol. 20, p. 224 American Ceramic Soc., Vol. 21, p. 89
(1931). (1938).
(18) H. A. Lorentz, "Ein allgemeiner Satz, die (32) M. Schlesinger, "Die Verwendung einfacher
Bewegung einer reibenden Flfissigkeit bet- Becherzentrifugen zur Bestimmung der
reffend, nebst einigen Anwendungen des- Teilchengr6sse in kolloiden L6sungen,"
selben," Abhandlungen tiber theoretische Kolloid-Zeitsehrift, Vol. 67, p. 135 (1934).
Physik, Vol. 1, p. 23, Teubner, Leipzig (33) H. J. Kamack, "Particle Size Determina-
and Berlin (1906). tion by Centrifugal Pipet Sedimentation,"
(19) S. Berg, "Die Tauchwaagenmethode zur Analytical Chemistry, Vol. 23, p. 844 (1951).
Bestimmung der Korngr6ssenverteilung," (34) M. v. Smoluchowski, "Drei Vortr~Lge fiber
Berichte der deutschen keramisehen Gesell- Diffusion, Brownsche Molekularbewegung
scha[t, Vol. 23, p. 271 (1942). und Koagulation von Kolloidteilchen,"
(20) M. Mason and W. Weaver, "The Settling Physikalische Zeitschr![t, Vol. 17, p. 557
of Small Particles in a Fluid," Physical (1916).
Review, Vol. 23, p. 412 (1924). (35) H. Mfiller, "Die Theorie der Koagulation
(21) E. Czuber, "Wahrscheinlichkeitsrech- polydisperser Systeme," Kollold-Zeltschrift,
nung," Vol. 1-2, Teubner, Leipzig and Vol. 38, p. 1 (1926).
Berlin (1914). (36) P. Tuorila, "t3ber orthokinetlsche und
(22) Th. Svedberg and H. Rinde, "The Ultra- perikinetische Koagulation," Kolloid-Bel-
Centrifuge, a New Instrument for the hefte, Vol. 24, p. 1 (1927).
Determination of Size and Distribution of (37) A. Chwala, "Zerkleinerungs-Chemie," Kol-
Size of Particle in Amicroscopic Colloids," lold-Beihefte, Vol. 31, p. 222 (1930).
Journal American Chemical Soc., Vol. 46, (38) A. H. M. Andreasen, S. Berg and E. Kjaer,
p. 2677 (1924). "Einige Kolloidmahlversuche mit einer Ku-
(23) J. F. Steffensen, "Interpolationslaere," gelmfible," Kollold-Zeitschrift, Vol. 82, p.
Gad, Copenhagen, Chapter 16 (1925). 37 (1938).
(24) S. Berg, "The Diver Method for Deter- (39) A.H.M. Andreasen and S. Berg, "Beispiele
mination of Particle-Size Distribution," der Verwendung der Pipettemethode bei
Transactions, International Ceramic Con- der Feinheitsanalyse unter besonderer Be-
gress, Maestricht (1948). riicksichtigung der Feinheitsuntersuchun-
(25) Th. Svedberg and K. O. Pedersen, "Die gen von Mineralfarben," Beihefte zur Ve-
Ultrazentrifuge," Steinkopff, Dresden and reins deutscher Chemiker, No. 14 (1935).
Leipzig (1940). (40) Symposium on New Methods for Particle
(26) Th. Svedberg and J. B. Nichols, "Determi- Size Determination in Sub-Sieve Range,
nation of Size and Distribution of Size of Am. Soc. Testing Mats. (1941). (Issued as
Particle by Centrifugal Methods," Journal separate technical publication A S T M STP
American Chemical Soc., Vol. 45, p. 2910 No. 51.)
(1923). (41) Symposium on Particle Size Analysis, Sup-
(27) A. Romwalter and M. Vendl, "Die Ermitt- plement to Transactions, Inst. Chemical
lung der K6rnungskurve aus Schleuderver- Engrs., Vol. 25 (1947).
suchen," Kolloid-Zeitschrift, Vol. 72, p. 1 (42) "The Physics of Particle Size Analysis,"
(1935). Conference arranged by The Institute of
Physics on the Measurement of Particle Size Grading," Transactions, British Ce-

Size, particularly in the Sub-Sieve Range, ramic Soc., Vol. 47, p. 22 (1948).
British Journal Applied Physics, Supple- (47) M. E. Rose, "Measurements of Particle
ment No. 3, London (1954). Size in Very Fine Powders," Constable,
(43) F. V. v. Hahn, "Dispersoidanalyse," Stein- London (1953).
kopff, Dresden and Leipzig (1928). (48) G. Broughton, "Colloidal and Surface
(44) I-I. Gessner, "Die Schl~Lmmanalyse," Aka- Phenomena," Industrial and Engineering
demische Verlagsgesellschaft, Leipzig Chemistry, Vol. 46, p. 898 (1954).
(1931). (49) L. A. Wagner, "A Rapid Method for the
(45) G. Herdan, "Small Particle Statistics," Determination of the Specific Surface of
Elsevier Publishing Co., Amsterdam, Hous- Portland Cement," Proceedings, Am. Soc.
ton, Tex., New York, N. Y., Paris (1953). "resting Mats., Vol. 33, Part II, p. 553
(46) E. Sharratt, "The Industrial Control of (1933).
A P H O T O E L E C T R I C S E D I M E N T A T I O N M E T H O D F O R P A R T I C L E SIZE
DETERMINATION IN THE SUBSIEVE RANGE
BY H. R. HARNER1 AND J. R. MUSGRAVE2
SYNOPSIS
The method consists essentially of measuring the light absorbed by a sus-

pension of the particles in a liquid medium; increments of light absorption are
measured as the particles settle in the medium. A photoelectric cell is used to
measure the light absorption.
The apparatus is simple and comprises a stable light system, a cell (for con-
taining the suspension), a photoelectric cell, and a microammeter.
Calculations are based on Stokes' law, with modifications to compensate
for variations with very fine particles. Comparison with other methods shows
good agreement.
While not absolute, the method is reasonably accurate and reproducible; it
has the distinct advantage of speed and simplicity and gives a complete size
distribution. The elapsed time required for a determination is approximately
1 hr.
A wide variety of materials has been successfully analyzed by this method.
Most of the important methods of suspension, the change in light trans-

determining particle size and distribution mission is measured. From these d a t a - -
are discussed in detail in the Symposium time versus light t r a n s m i t t e d - - t h e par-
on New Methods for Particle Size De- ticle size and distribution of the material
termination in the Subsieve Range is calculated.
(I941)? Outlined therein are the develop- For the types of material to be ana-
ment of sedimentation and turbidimetric lyzed in this laboratory, a simple, rapid,
methods. In some of the procedures, the and accurate method was desired. A
material is suspended in a liquid medium survey of methods indicated that photo-
and a beam of light is passed through the electric sedimentation offered the great-
suspension, the light transmitted through est possibility; however, it was felt that
the suspension being measured by a an improved apparatus and simpler
photocell. As the particles fall in the calculations could be developed. No new
1 Research Manager, The Eagle-Picher Co., principles are involved in the method
Chemical Division, Joplin, Mo. described in this paper.
2Research Department, The Eagle-Picher
Co., Chemical Division, Joplin, Mo. APPARATUS
3 Symposium on New Methods for Particle
Size Determination in Sub-sieve Range, Am. Figure 1 presents a schematic diagram
Soe. Testing Mats. (1941). (Issued as separate
publication A S T M S T P No. 51.) of the apparatus, which comprises a
172
HARNER AND MUSGRAVE ON PHOTOELECTRIC SEDIMENTATIONMETHOD 173
stable light source, a sedimentation cell, Light Slot (9).--Cut in cell housing for
and a photocell and microammeter. passage of light beam.
Secondary Condensing Lens System (10).-
Spotlight Bulb (1).--A standard 6-v 15 Similar to first system (see above (3)) ; set to
candle power automobile headlight bulb. focus on photocell.
Power source is a 100 amp-hr lead-acid stor- Barrier-Layer Photocell (//).--Dry disk
age battery kept well charged.4 type of barrier-layer photocell; approxi-
Parabolic Reflector (2).--A 3-in. reflector, mately 3/~amp per foot-candle.
such as used on a carbide lamp. Microammeter (12).--Standard type, 50
Condensing Lens System (3).--Two 3-in. //amp full scale; an arbitrary 0 to 150 (equal
condensing lenses set to focus on sedimenta- division) scale is used.
tion cell.
Heat Filter Glass (4).--Standard (dark The light source and the means for
green) glass, 3 in. diameter, approximately measuring the transmitted light are self-
-~ in. thick. explanatory. The cell level adjustment
--l]-]1~ -. . . . . .
7
Fro, 1.--Schematic Diagram of Apparatus Showing the Important Elements of its Construction,
1. 6-v spotlight bulb. 7. Cell level adjustment.
2. Parabolic reflector. 8. Sedimentation cell.
3. Condensing lens system. 9. Light slot.
4. Heat filter glass. 10. Secondary condensing lens system.
5. Adjustable iris diaphragm. 11. Barrier-layer type photocell.
6. Cell housing. 12. Microammeter.
Adjustable Iris Diaphragm (5).--Standard allows raising or lowering of the sedi-

photographic diaphragm--2 in. maximum mentation cell to obtain the desired
opening. height of fall from the liquid level to the
Cell Housing (6).--Sheet metal box of ap- light beam slot. The iris diaphragm al-
propriate size to contain sedimentation cell;
lows adjustment of the light intensity;
open at top and bottom; has 1 by l-in. slot
on right side and 89by -~-in. slot on left side; this has been found to be more satis-
slots centered on light beam. factory than varying the current to the
Cell Level Adjustment (7).--A 1-in. diame- light bulb.
ter screw, 14 threads per in., with plate
fastened on top; plate fits inside of cell hous- DISPERSION
ing. Proper dispersion is probably the most
Sedimentation Cell (8).--Pyrex cell with important and most critical step in con-
polished plane surfaces. Inside dimensions
ducting a particle size analysis. Some
3.25 by 6.7 cm, 8.8 cm, depth, 3.5 mm wall
thickness. (Sold as water cell for some photo- investigators have commented that
micrographic apparatus.) proper dispersion is more important than
the method, equipment, and technique
4 An electronically stabilized power source has used in conducting the analysis.
also been developed and is being successfully
used. Certainly one should not expect repre-
sentative data from a poorly dispersed heavy, coarse material, a liquid of high
sample. In the development of techniques viscosity and a greater height of fall are
for the wide variety of materials which used. For finer, light materials, the media
have been analyzed by this method, it should have a low viscosity and the
was frequently necessary to spend much height of fall should be reduced.
time and effort in securing a satisfactory In the apparatus described, the height
dispersion. When adequate dispersion of fall from the liquid level to the light
was achieved, the analysis of the ma- beam Call be varied from 1.25 to 5.00
terial was usually accomplished with cm. For the more common liquids in-
little difficulty. vestigated, xylene has a viscosity of 0.006
Each material poses its own dispersion poises and kerosine of 0.018 poises. If
problem. The liquid medium to be used, higher viscosities are desired, mixtures
the dispersing agents, and the means of of white mineral oil and xylene have been
dispersion must all be considered. Care- found satisfactory. To avoid changes in
ful study of each dispersion problem is viscosity, all size analyses are made at
mandatory; it will certainly be reward- 27•
ing. For convenience, the volume of sus-
pension is varied for different height of
PROCEDURE falls. If a 1.25-cm height of fall is used,
Stokes' law allows calculation of the the volume is 100 ml; for 2.50-cm height
time of fall of particles through a fluid of fall, 120 ml is the appropriate volume.
medium. It shows that the time of fall is In sedimentation methods, one of the
directly proportional to (1) height of fall postulates is unhindered settling or "free
of the particles and (2) viscosity of the fall"; this is achieved by varying the
fluid medium; the time of fall is inversely amount of the material being analyzed.
proportional to (1) the difference in Practical experience with the method
density between the particles and the indicates that the best results are ob-
fluid medium and (2) the square of the tained when the suspension initially al-
radius of the particles. This law assumes lows 20 to 40 per cent of the light to be
that the particles are spheres; further, transmitted, as compared to 100 per cent
it becomes inapplicable when colloidal transmitted through the clear liquid
forces interfere with free fall. medium. Accordingly, the amount of the
Liquids used as media must of neces- material is adjusted to give a suspension
sity be nonreactive with the particulate which will fulfill these conditions. It is
material being analyzed. For this reason, permissible to extend these limits slightly
organic liquids have been used in most when, for example, direct comparison is
of the analyses in this laboratory; they desired of several samples of the same
have proved to be quite satisfactory in material and for this reason the same
the majority of cases. Xylene and weight is used for all samples.
kerosine have been the most widely used; In the actual analysis, the sedimenta-
both have a density of about 0.85. tion cell is filled with the clear liquid
For any specific material, the factors medium and the light intensity adjusted,
in Stokes' law which can be conveniently by means of the iris diaphragm, to obtain
varied are (1) height of fall and (2) a reading of 100 on the microammeter
viscosity of medium. (Most media have (using the arbitrary 0 to 150 scale). The
a density of 0.8 to 1.0. This is too small dispersed material is suspended in the
a variation to change the differential appropriate volume of medium and the
density appreciably.) Therefore, for a suspension is p~ured into the empty
HARNER AND ~VfUSGRAVE ON PHOTOELECTRIC SEDIMENTATION METHOD 175
sedimentation cell through a short un- CALCULATIONS

constricted funnel. Taking "zero time"
The basic data recorded are time v e r s u s
as the moment when all of the sus-
pension has entered the sedimentation per cent light transmission. For con-
cell, readings of the light transmission venience, light transmission is changed
are taken at 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, to per cent light a b s o r p t i o n by subtracting
and 2 min and each minute thereafter to each light transmission figure from 100.
a maximum of 20 min. Coarse materials The time v e r s u s light absorption curve is
may require a shorter reading time. plotted on 4-phase semilog paper, using
Since there will be turbulence in the the logarithmic scale for time (from 0.01
85
80
.- 60
g
o
/
/
._~
d 40
50
Material -PbO
See Appendix of Paper
for Calculations
2O
t0
0
0.125 0.25 0.5 0.75 1.0 2 3 4 5 6 7 8
Radius, b~
FIG. 2.--Plotting and Extrapolation of Data.
suspension for a few seconds when it is to 100 min) and the arithmetic scale for
poured into the sedimentation cell, no per cent light absorption. By this
reading at zero time is attempted; the method, it is possible to extrapolate the
numerous readings taken during the first curve to 0.01 min and also to 100 min.
minute allow extrapolation to zero time From Stokes' law can be calculated the
in the calculations. time of fall for particles of appropriate
In most analyses, good curves are ob- radius down to 0.5 ~; when these times
tained up to 20 min; after this time are marked off on the curve, the per cent
deviations are sometimes encountered. light absorption for any size interval can
The reasons for such deviations are not be determined.
fully understood; they are not necessar- "Zero time" is taken as 0.01 min. To
ily peculiar to this method, since other estimate the smallest particles, a second
sedimentation methods have shown curve is plotted on special paper (see Fig.
similar variations. 2) of radius in microns v e r s u s light
176 SYMPOSltrM ON PARTICLE SIZE MEASUREMENT
/ I00
Equivalent Hiding Factors

/ 50
/ 20
//
/ 10 ~
5
g
>
hJ
I -me of :.olioilS
7 Y:
Experlme~ 2
(2a
"~
I _9o
x~
0.5
0.2
0,1
005 0 I 0.2 05 2 5 10 20
Particle Radius,H.
FIO. 3 . - - G r a p h of Theoretical and Experimental Hiding Factors.
TABLE I.--EQUIVALENT H I D I N G FACTORS (RELATIVE W E I G H T S FOR

EQUIVALENT HIDING).
Mathematical FineParticle CoarseParticle
Micron Interval Average Radius Relationship Factors Factors
) to 0.125. 0.0625 0.16 1.35

). 125 to 0.25, 0,1875 0.50 1.55 1.70
).25 to 0.5. 0. 375 1.00 1.90
D.5 to 1. 0.75 2.00 2.40 2.40
1 to 2. 1.5 4.00 4.00 4.00
2 to 3. 2.5 6.67 6.67 6.67
3 to 4 3.5 9.3 9.3 9.3
to 5 4.5 12.0 12.0 12.0
5 to 6 5.5 14.7 14.7 14.7
6 to 8 7 18.7 18.7 18.7
8 to 10. 9 23.8 23.8 23.8
10 to 15. 12.5 33.3 33.3 33.3
15 to 20. 17.5 46.7 46.7
20 to 30. 25 66.7 66.7
30 to 50. 37,5 100. 100.
HARNER AND MUSGRAVE ON PHOTOELECTRIC SEDIMENTATION METHOD 177
absorption. Since at 0 u (size) there will tion concerning the sample. (A sample
be zero light absorption, the curve is calculation is presented in the appendix.)
extrapolated to this zero point. (A stand-
ard French curve gives the best results.) DISCUSSION OF I~/[ETHOD
The light absorption for these fractions The method has been applied to
of small size can be taken from the material with densities as low as 2.3; it
graph. should be noted that these materials had
The validity of such extrapolation has a median radius of 1 ~ or larger. For
been checked by microscopic observa- finer materials in this density range, there
tion (both light and electron) and, as far will be greater difficulty.
as possible, by other methods. It appears When the density of a material is less
to be reasonably accurate, although not than 2.0, and the difference in densities
absolute. The incremental light absorp- between the material and the media be-
tion for appropriate size fractions can be comes rather small, it is not usually
determined from the curves and tabu- possible to obtain a good size analysis by
lated. this method.
Stokes' law assumes spheres; it also For materials of greater density but of
postulates unhindered settling. Under quite fine size, such as paint pigments,
these circumstances, the light absorbed good analyses can be obtained in the
by the particles should be proportional majority of cases. Some highly colored
to the great circle area of the particles; and finely divided materials present
thus, the relation of light absorption to difficulties. The accuracy of analysis for
weight of the particles for any given size platelike materials is extremely doubtful.
fraction can be calculated. Careful study If the material has no particles larger
indicated that, for particles 2-~ radius or than 0.5 ~ radius, there will be no "free
larger, this relation held true. Below this fall" and the curve of micron size v e r -
size, the relation was not valid; evalua- s u s light absorption will be a straight
tion of the conditions in this range by horizontal line. No extrapolation of such
other measurements finally led to the a line is possible and the method cannot
adoption of revised factors in the fine be used.
range. Figure 3 depicts the mathematical Within the range of the method, a
relation and Table I gives the actual wide variety of materials has been suc-
factors used for calculation of "equiv- cessfully analyzed. Since a complete
alent hiding." analysis can be made, including calcula-
When the incremental light absorption tions, in an hour, the method can be and
for each size fraction is multiplied by the is used as a routine control for both plant
appropriate factor, the values so ob- and research studies.
tained will give the relative weight of
Often, a complete size distribution
each fraction in comparison to the others.
analysis is a major advantage. If specific
The values are translated to a percentage
basis by dividing the individual values surface is required, a simple calculation
by the sum of all the values. will provide it.
Finally, the weight distribution data The present method is the result of
are plotted on log-probability paper. This development over a period of years.
type of curve, with a little experience in Other industries besides that with which
evaluating it, gives, besides the size- the authors are connected have found it
distribution curve, other helpful informa- to be useful.
178 SYMPOSIUlVI ON PARTICLE SIZE MEASUREMENT
APPENDIX
SAMPLE CALCULATION
Material ................................ Lead oxide (PbO)
Density ................................. 9.5
Weight of sample ......................... i0 mg
Dispersion ............................... 1 drop alkyd solution and sample rubbed up on slide
(microscope technique) ; suspended in 100 ml me-
dium.
Medium ................................. Xylene, 0.006 poises
H e i g h t of fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.25 cm
No~E.--Original data plotted as described in text. Figure 2 shows plot of micron size v e r s u s l i ght
absorption. Factors used in calculation of e q u i v a l e n t hiding are fine particle factors see Ta bl e I).
Radius Interval, ~ Incremental Equivalent WeighL, Cumulative

Absorption Hiding per cent weight, per cent
0 to 0.125 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36.0 48.6 36.1 36.1

0.125 to 0.25 . . . . . . . . . . . . . . . . . . . . . . . . . 16.0 24.8 18.4 54.5
0. 25 to 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . 14.0 26.6 19.7 74.2
0.5 to I ........................... 9.0 21.6 16.0 90.2
1 to 2 ........................... 2.5 10.0 7.4 97.6
2 to 3 ........................... 0.5 3.3 2.4 100.0
3 to 4 ...........................
4 to 5 . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 to 6 ...........................
6 to 8 ...........................
T o t a l .............................. 134.9 100.0
The cumu lative figures (last column) are plotted on log-probability paper.
M e t h o d of reporting can be varied as desired.
DISCUSSION
MR. L. T. WORK)--The discrepancy for some ten years. For certain par-
that was shown in the line curve leads ticulates it gives results which agree
me to recall some work by Stutz and closely with other methods of testing.
Pfund where they found short light We consider this procedure one of the
waves getting past particles which were most valuable in our laboratory.
below about 0.5 to 0.75 /~ in size. I MR. THOMAS Y. BUTLER.~I would
wonder if the authors have done any like to ask the authors whether it is
work with blue light in order to minimize possible to measure transparent or semi-
that effect. transparent particles with this instru-
MR. J. R. ~V~USGRAVE (author).--We ment or do the particles have to be
have done very little work with other opaque and homogeneous in this respect.
than white light. This is one of the Unfortunately many particle com-
variables that we would like to study posites to be analyzed for size distribu-
when time permits. tion are extremely heterogeneous as to
M R . ALAN R . L U K E N a . L F i l t e r s which color and clarity.
give a blue light, we believe, have given MR. MUSGRAVE.--When the particles
more exact results. are semi-transparent in the liquid me-
We have used the authors' test method dium, increasing the amount of sample
used will often give sufficient light ab-
i Consulting Engineer, New York, N. Y.
2 President, Lukens Laboratories, Inc., New- 3 Chemist, Research Cottrell Corp., Bound
ton, Mass. Brook, N. J.
DlSClISSlON ON PI~OTOELXCTI~ICSEDIMENTATIONMETHOD 179
sorption for a satisfactory determination. MR. V. D. FRECItETTEfi---Can the

Where this fails, we have sometimes been authors tell us in what respect their
able to use a different medium in which method differs from the Wagner Turbi-
the particles gave more hiding. dimeter which is standard in the particle
MR. R. P. LOV~LAND.~--I am won- size determination of portland cement.
dering why the suggestion made by T o y MR. MUSGRAVE.--We patterned our
and Davies of London, 5 was not pursued. apparatus on the Wagner Turbidimeter
By getting the undeviated light, which but made some changes that we con-
means a subtraction of the light measured sidered desirable. Also, we devised a
at a very small angle from the axis from different method of calculation which
that which goes straight along the axis, gave us size distribution while the Wag-
which can be done either by a double ner calculation gave only surface area.
measurement or continuously through We feel that the changes have meas-
closely adjacent slits, you then get light urably increased the utility of the
unaffected by scattering, color, or a lot method.
: of other properties. Just that light which MR. F•ECHETTE.--I wonder if anyone
is blocked out by the particles is used, has given consideration to the use of
and they showed, I think, that it is most radioactive isotopes to provide a type of
simply related to size. radiation which would not be so subject
MR. MUSGRAVE.--We were not aware to the scattering that is the difficulty
of this study. with these optical methods.
MR. MUSGRAVE.--We do not have a
4 Eastman Kodak Co., Research Laboratories, hot laboratory yet. I have seen some
Rochester, N. Y.
5 F. C. Toy, E. R. Davies, B. H. Crawford, comments on radioactive materials, but
and B. Farrow, "Report on Turbidity, with Spe- we have done no work on it.
cial Reference to Its Application to the Photo-
graphic Industry," Proceedings, Seventh Inter- 6 Professor of Ceramic Technology, State Uni-
national Congress of Photography, pp. 53-87 versity New York College of Ceramics, Alfred
(1929). University, Alfred~ N. Y.
STP234-EB/Aug. 1959
L I G H T S C A T T E R I N G I N S T R U M E N T A T I O N F O R P A R T I C L E SIZE
DISTRIBUTION MEASUREMENTS*
BY C. T. O'KONSKI,1 M. D. BITRON,I' 2 AND W. I. HIGUCItI1' 3
SYNOPSIS
An improved instrument is described for the characterization of particles

suspended in gases by means of light scattering. It consists of (1) a sensitive
right-angle optical system with a photomultiplier detector, (2) a coaxial flow
system which facilitates variation of the particle concentration range, (3) a
photometer which continuously records the average light scattering signal, and
(4) a pulse analyzer for size discrimination of individual particles. The particle
analyzer was calibrated with uniform polystyrene spheres from a 0.33 to 1.17 #
in diameter, employing air as a scattering standard. The scattering intensity
was found to be approximately proportional to the square of the diameter.
Resolving power was determined as a function of particle size, and the instru-
ment was critically evaluated. A brief review of particle detectors is given. A
versatile pulse height selector system is described. Some variations of the in-
strument are proposed.
Experimental studies of aerosols, production of an electrical pulse by some

9 9 J 9 9
which are commonly heterodisperse, have type of pickup devlce, and classification
been severely limited by the lack of rapid of the signals by electronic means.
and accurate methods for the determi- The detecting devices include: (a) the
nation of particle size distribution. Since scattered light optical system and photo-
1944, various types of automatic count- detector, already described in various
ing and sizing techniques have been informs (1-7) 3, 4 and discussed below; (b)
troduced. Those which possess the the electrostatic detector (8), energized
advantage that particles can be charac- by the electric charge transferred when
terized without prior removal from the a particle impinges upon a conductor,
gas are briefly considered here. I n gen- and (c) the hot filament detector (o),
eral, the automatic methods involve the which responds to the local change of
temperature produced when a volatile or
* Based upon Technical Report No. 3, Office combustible particle impinges upon and
of Naval Research, Contract No. ONR 222-12,
Project No. NR 051-302, Sept. 1, 1956.
1 Department of Chemistry, University of 3 The boldface numbers in parentheses refer
California, Berkeley, Calif. to the list of references appended to this paper.
2Present address: Weizmann Institute of 4 Reference (7) was based upon Technical
Science, Rehovoth, Israel. Report No. 1, Office of Naval Research, Contract
a Present address: California Research Corp., No. ONR 222-12, Project NR 051-302, June 16,
Richmond, Calif. 1954.
180
O ' K O N S K I ET AL ON PARTICLE SIZE DISTRIBUTION 181
is vaporized or oxidized at a hot metallic flow system in conjunction with appro-

surface. priate optics. 5 This is important for high
The electrostatic detector has the resolving power, that is, for discriminat-
characteristic that the response may ing between particles of nearly equal sizes.
vary widely with the physical and chemi- Judicious optical design permits reduc-
cal properties of the particles since con- tion of stray light to such a low level
tact electrification depends upon the that the light scattered from air mole-
detailed state of the surface (10AD. While cules is the major source of background
this may be an advantage for some ana- illumination. As a result, it has become
lytical applications, it is a disadvantage possible to combine the counter with a
generally, as the results may be variable photometer within one instrument, and
and difficult or impossible to interpret. to arrange the circuitry so that the light
From a consideration of the experimen- scattered by individual particles can
tal results and the theory of operation be compared to the highly reproducible
(12,13), it was concluded that this detec- molecular scattering from gases. Since
tor probably could not be made sensitive the combination comprises a common
enough for particles around 1 ~ in diam- phototube and optical system, an im-
eter or smaller. portant advantage is that, once the pulse
Vonnegut and Neubauer (0) showed amplitude v e r s u s particle size curve is
that the signal from a hot wire detector established, the instrument can easily be
depends not only upon the particle size recalibrated by reference to photometric
but also upon the vaporization and com- measurements on gases, irrespective of
bustion properties of the particles, the variations in light source intensity and
temperature of the detecting element, phototube sensitivity. Size analysis and
and the velocity of the air stream. For continuous photometric recording of
uniform particles, the spread of signals scattered light may be carried out con-
was accordingly rather large. The indi- currently.
,cation was that, under very favorable
PREVIOUS AND P R E S E N T
conditions, the limit of sensitivity would
CONTRIBUTIONS
correspond to particles around 2 ~ in
diameter. The general features of the first aerosol
The scattered light detection system particle counter 6 have been included in
has the advantage that particles can be all succeeding instruments, so a brief
measured with a minimum of disturb- description is appropriate. To achieve
ance of the aerosol, whereas the other high illumination intensity, a continuous
two methods require impingement, the source and relatively fast condensing
efficiency of which depends upon the lenses are employed. Particles are carried
particle size. The present lower limit of in a gas stream through a small sensing
size is 0.3 /~ in diameter, and this may volume7 bisected by the image plane of
be decreased further. Light scattering the source. In transit, they scatter light,
can be calculated, at least for spherical
U. S. P a t e n t No. 2,732,753, C. T. O'Konski,
isotropic particles (14,15), by application Jan. 31, 1956. See also references (1) and (2).
of the Mie theory (16). Recently (17) cal- 6 Reference (1) was based upon an N D R C
culations have been made for fast illu- Report, "A Particle Counting Smoke Penetrom-
eter," Contract 10-212 OEMer-B82, Northwest-
minating and collection systems. Experi- ern University, Aug. 31, 1945. T h e first working
ments reported here show that highly model was tested in Dec., 1944.
Defined in reference (7), p. 695. T h e nota-
uniform illumination and light collection tion ~hroughout ~his paper is t h a t employed in
have been achieved by use of the coaxial reference (7) unless otherwise specified.
some of which is collected by another nal small-angle counter by refining the

fast lens system and directed to a photo- optics and employed a totalizing counter
detector. The resulting voltage pulses are and a commercial single channel pulse-
amplified and characterized electroni- height analyzer. They determined the
cally. curve of signal v e r s u s particle size with
In the original counting instrument DOP (dioctyl phthalate) aerosols from
(1)6, the lens system collected light scat- 0.5 to 1.2 ~ in diameter. The sensing
tered between about 5 and 30 deg, after volumd was about 0.002 cu cm. The
the method of Zeiss8 and LaMer and scattering volume ~ in this type of instru-
Sinclair (18,19). Thallous sulfide photo- ment is relatively large because a long
conductive cells and multiplier photo- region along the optical axis is both il-
tubes were used. All pulses above a pre- luminated and viewed. The ratio of stray
determined level were counted. The light to air scattering was not reported.
lower limit of sensitivity corresponded The lower limit of sensitivity was esti-
to 0.6 u diameter droplets of n (refrac- mated to be 0.34 ~ diameter. Standard
tive index) = 1.5. The sensing volume deviations of pulse amplitudes obtained
was about 0.03 cu cm. Illumination was with DOP aerosols produced by an im-
not uniform and no study was made of proved Sinclair-LaMer generator were
the relationship between signal ampli- between 9 and 17 per cent for particle
tude and particle size. diameters ranging from 0.64 to 0.96 ~.
The second instrument (2) employed From their published results the devia-
a double condensing lens system with tions can be shown to correspond to 6 to
achromatic lenses to reduce stray light 10 per cent of the particle diameters.
and improve the uniformity of response. Thomas (3) modified the optical sys-
Light scattered in the vicinity of 90 deg tem so that light scattered through an-
was collected and directed to a multiplier gles around 45 deg was collected. Pulses
phototube (employed exclusively in all were fed to a differential discriminator,
succeeding instruments). It was shown motor-driven to scan the spectrum, and
that this optical system could be used to the output was sent to a count-rate meter
measure light scattering from gases, thus and a recorder. The response v e r s u s size
providing a convenient means for evalu- curve was measured with DOP aerosols,
ating background illumination or stray in the range from 0.55 to 1.85 # diameter.
light. This was reduced to about one Fisher, Alexander, and co-workers (S,6)
third of the scattering from air within employed a right-angle optical system,
the total scattering volume, 7 which was similar to the earlier design (2), in con-
0.016 cu cm. ~ Various light sources were junction with a multichannel pulse-
tested. An electronic pulse-height ana- height analyzer. Their instrument was
lyzer, consisting of two independently designed for the size range 1 to 60
adjustable discriminators, an anticoinci- diameter. Pulse amplitude distributions
dence circuit, and a pulse counter or rate were correlated with particle size distri-
meter was introduced. butions in heterodisperse systems. The
Three succeeding models of the count- instrument became insensitive around
ers were described between 1952-1955. 0.8 ~ diameter. Resolving power was not
Gucker and Rose (4) improved the origi- specified.
O'Konski and Doyle (7) have de-
8 German Patent No. 675,911 (1939). scribed a combination instrument which
0 See reference (7), p. 685. Henceforth "scat-
tering volume" will be considered synonymous incorporated both a counter and a scat-
with "total scattering volume." tered light photometer. By refinement of
O'KoNSKI ET AL ON PARTICLE SIZE DISTRIBUTION 183
the right-angle optics, the background measurements of signal amplitude versus

illumination was reduced and spherical particle size have been made with addi-
particles down to 0.3 ~ diameter could tional uniform latex aerosols. These con-
be counted. The sensing volume was firm the approximately square-law de-
about 0.002 cu cm. The resolving power pendence of the right-angle instrument
and response of the instrument were (7) from 0.365 to around 1/~ in diameter
evaluated with uniform aerosols pro- and indicate a significant deviation at
duced from the essentially monodisperse 1.2 ~ diameter.
hydrosols of polystyrene latex. 1~ For the
0.33, 0.5, and 1.0 ~ diameter particles DESCRIPTION OF THE INSTRUMENT AND
available at the time, the pulse ampli- DESIGN CONSIDERATIONS
tudes were found to be proportional
Optics:
within a few per cent to the square of
the diameter. Statistical evaluation of The right-angle optical system was
the pulse amplitude distributions re- chosen in preference to the small-angle
vealed that the typical standard devia- arrangement for a number of reasons.
tions for all three sizes were 6 to 8 per First, in the forward-angle system, the
cent of the diameter. The intrinsic re- optical efficiency is substantially reduced
solving power of the instrument was because only the outer portion of the
somewhat better than that, since stand- illumination lens can be utilized and the
ard deviations of the latex particles were aperture of the light collecting lens must
about 2 per cent of the diameter, and be confined to the shadow angle of the
some additional heterodispersity was central stop which is required to produce
probably introduced when these par- the dark field. Considering, for example,
ticles were dispersed as aerosols. The the case of a given illuminating lens and
photometer circuitry was employed to equal solid angles of illumination and
measure the relative scattering intensi- collection, a fourfold greater efficiency is
ties from several gases and to standardize obtained with the right-angle system
the response of the instrument by refer- since it permits the use of the full aper-
ence to the intensities measured with air ture of the illuminating lens and an
and helium in the scattering volume. Two equal aperture for the collecting lens.
discriminators and counters were em- Second, the stray light arising from dust
ployed to determine the count rate particles, bubbles, scratches on the
curves, from which the pulse amplitude lenses, and from diffraction, reflection,
distributions were obtained. and diffusion from edges and surfaces is
In this research, the optical arrange- much smaller at larger angles and, there-
ment is that employed previously (7),4 fore, as shown previously (2), could be
but the flow and electronic systems have reduced to a very low level in the right-
been improved. A novel and versatile angle system. The result is a decrease of
pulse analyzing system, suitable for a background noise at the multiplier pho-
multichannel pulse analyzer, is described. totube sufficient to overcome, in combi-
Complete descriptions of the optics and nation with the first factor, the lower
the electronics are given. The important scattering intensity at the larger angles.
factors influencing the resolving power Thus, the limit of sensitivity of the
are evaluated and discussed. Further right-angle counter was 0.3 ~ diameter
(7), and that of an improved small-angle
10 Kindly supplied by J. W. Vanderhoff,
Physical Research Laboratory, The Dow Chem- instrument, 0.34 ~ diameter (4).
ical Co., Midland, Mich. A third advantage of the right-angle
G
L.S / Sheath Air-In
$I
BP
Exhaust Aerosol-in
U~
L~,~7"~ Block Velvet
-6
9
H1 $3 o~
$9 / 9
PA
~V
~q
V2
o0
FIG. 1.--Scale Drawing of Optical System.

LS = tungsten filament lamp H1 = e n t r a n c e s l i t h o l d e r
L1-L6 = lenses H2 = exit slit holder
$2 -- e n t r a n c e s t o p s F = flushing manifold
$11 = e x i t s l i t P = phototube
$1, $10 = a p e r t u r e s l o t s PA = preamplifier box
$3-$9 = g l a r e s t o p s G = gaskets
T = background light trap BP = baekplate
C = s c a t t e r i n g cell VP = p r e a m p l i f i e r t u b e
system is that the background light level formed at the center of the scattering
is less sensitive to small displacements cell. The direct light was then absorbed
of optical components, such as are in a light trap consisting of a truncated
caused, for example, by vibrations. This cone $5 inserted in the cell which was
decreases sensitivity to shock. The curve closed off by the velvet-covered back
of pulse amplitude versus particle size is plate BP. The dimensions of $5 were:
less steep in the right-angle system than height 28.7 ram, diameters 9.00 mm and
in a small-angle instrument. In the case 27.5 mm at truncation and base respec-
of multichannel instruments, in which it tively.
is often desirable to cover a tenfold or The achromatic lens pair L5 and L6--
greater range of particle sizes, this pro- each a coated cemented doublet 34 mm
vides a fourth advantage by reducing the in diameter and of 65 mm focal length--
range of signals which must be accommo- collected the light scattered by the aer-
dated by the pulse analyzer. osol particles. The tubular spacer be-
Construction Details.--A scale drawing tween the lenses, $10, 31.6 ram, in inside
of the optical system is shown in Fig. 1 diameter, and 10 m m high, determined
which includes a cross-section of the the aperture of the collecting system,
coaxial flow system in the scattering cell which corresponded to a 14.0 4- 0.5 deg
C. All components were rigidly supported half-angle of convergence, n The exit slit
on a flat base plate. S l l , which was the field stop, was con-
Details of the optical system will be jugate to the cell center. $11 is a rec-
specified so an instrument of identical tangular knife-edged slit with its larger
response characteristics may be con- dimension placed parallel to the axis of
structed. I t is hoped that ultimately a the illuminating system. In this study
standard optical design will be adopted three exit slits were employed, the di-
so calibration data of various laborato- mentions being 1.2 by 2.2 ram, 2.3 by
ries can be compared. 3.8 mm, and 1.1 by 1.9 mm (see further
The light source LS was a tungsten under Experimental Results). After pass-
ribbon filament lamp operated at rated ing through $11 the scattered rays pro-
values, 2870 deg Kelvin. By means of the ceed to the photocathode of the photo-
auxiliary achromatic condensing lens multiplier tube P.
pair L1 and L2--each a coated cemented In order to minimize stray light, sev-
doublet 49 m m in diameter and of 75 mm eral light traps and stops were incorpo-
focal length--an4mage of the light source rated. Light trap T consisted of a trun-
was formed in the plane of the entrance cated cone on a short tube which was
slit $2, covering it completely. $2 was a backed with black velvet. The dimen-
rectangular knife-edged slit, 2.4 by 1.1 sions of the truncated cone were: height
ram, which is the field stop, and discrim- 4.0 ram, diameter 22.0 mm at the base,
inated strongly against all light not origi- and diameter 14.0 m m at the truncation.
nating directly at the source. The circular The diameter at the truncation was kept
aperture stop $1 of the illumination sys- as small as possible to provide a dark
tem, 33.3 m m in diameter was inserted background for the collecting system,
between L1 and L2 in order to reduce yet it was sufficiently large so that dif-
stray light from the lens edges. The re- fracted rays from its edges entering the
sulting half-angle of convergence was collecting lens barrel did not strike L5
12.5 4- 0.5 deg. With the aid of the main directly.
condensing lens pair L3 and L4, identi-
11The previously quoted value (7) was in
cal with L1 and L2, an image of $2 was error.
The conical stop $6, 6.2 mm high, 18.3 the illumination zone is an improved
and 5.9 mm diameter at the base and version of the one described earlier (1,2).5
truncation respectively, was part of the This type of flow system has the follow-
lens barrel of the collecting system and ing advantages: (a) I t facilitates contin-
intercepted most of the stray light which uous circulation of the aerosol stream in
otherwise would reach LS. Its diameter a spatially well-defined manner, without
at the truncation was made as small as the necessity for a solid transparent con-
possible consistent with the condition fining tube. If introduced, a tube would
that it would not intercept any ray which refract, reflect, and scatter the illuminat-
passed from the scattering volume to the ing rays, thus increasing stray light and
pupil of the collecting system. disturbing the uniformity of the field
The circular glare stop $3, 35.2 mm through which the particles pass. Fur-
in diameter, intercepted light scattered thermore, particles near the wall of a
out of the main beam by the preceding confining solid tube would move much
elements. The glare stop $4, a truncated more slowly than those near the center,
cone 20.1 mm high, 4.7 and 23.8 mm in with the result that pulses would vary
diameter at the truncation and base widely in length. In the coaxial system,
respectively, reduced the stray light flux at velocities below turbulent flow, the
in the background trap T and in the viscous transport of momentum between
collecting system. the central and sheath fluid streams in
Glare stops $7 (diameter 10.0 mm), the space beyond the inner end of the
$8 (diameter 16.5 mm), and $9 (diam- aerosol tube causes a smoothing of the
eter 22.0 mm) were held in position by flow pattern to approximately the para-
split retaining rings. They intercepted bolic distribution characterizing the flow
rays which entered $6 at grazing inci- in a long tube of diameter equal to the
dence to the barrel walls to prevent inner diameter of the sheath air and ex-
them from being reflected into L5. haust tubes. The aerosol tube is termi-
Experiments with aperture stops of nated well within the sheath air tube to
various diameters between the collect- permit this smoothing before the illumi-
ing lenses L5 and L6 showed that opti- nation zone is reached. Thus, there is
mum signal-to-noise ratio was achieved the advantage (b) that the linear flow
at the maximum feasible aperture, lim- vectors are essentially parallel and equal
ited by the spacer between the lenses. across the cross-section of the aerosol
(See Appendix I for an analysis of the stream within the illumination zone. In
signal-to-noise problem.) addition, (c), deposition of particles on
By the use of good-quality achromatic optical surfaces is avoided, and (d), rapid
lenses, the appropriate placing of the replacement of the contents of the sens-
additional stops and light-traps, and the ing volume is facilitated.
careful painting of all the interior sur- With the previous flow system (1,2),5
faces with optically black lacquer, the the aerosol flow rate was obtained as the
stray light was decreased to 30 per cent difference between the metered rates of
of the light scattered by filtered air in a the exhaust and sheath air streams. This
scattering volume of 0.0058 cu cm. 12 procedure had been adopted to obviate
the necessity for direct metering of the
Aerosol Flow System: aerosol stream, thus minimizing deposi-
The coaxial flow system for circulat- tion and fractionation of the particles.
ing the particle-carrying stream through However, when measuring by difference,
metering errors are greatly magnified if
12 This value for the total scattering volume
supersedes the previous (7) approximate value. the difference is small relative to the
O ' K o N s K I ET AL ON PARTICLE SIZE DISTRIBUTION 187
metered flow rates. This severely limited means of pump 1. The entire remainder
the concentration range which was prac- of the exhaust stream is recirculated as
ticable. Accordingly the flow system il- sheath air by means of pump 2. Since
lustrated in Fig. 2 was devised. the only flow entry to the system is the
aerosol tube connected to the sample
Sample space, and the only flow exit is through
k/ flowmeter 1, it follows that the sampling
rate is equal to the pump 1 exhaust rate
Straightener
U (F I)
,-
Sheath F1, and the total flow rate through the
cell is F1 + F2. The filter, flowmeter 2,
and pump 2 are dry units. Thus the
FZ) aerosol particles are removed but the
Image o vapor in the stream is recirculated
Entrance Jill I=I Flow
Slit
~.
'
IIIII
III [ ] Meter through the sheath air tube. After an
equilibration period determined partly
by the volume within the recirculation
loop and partly by the ratio F2:F1, the
"111" ""mPb sheath air stream approaches equilibrium
Iil "r with the aerosol vapor. This minimizes

particle size changes due to evaporation
of volatile constituents. Whereas the
continuous sampling feature of the earlier
system is preserved, and the use of a
Filter flow meter in the aerosol stream is
avoided, the aerosol flow rate is now
Flow-Meter 1 determined more accurately because it
Fro. 2.--Improved Flow System. is equal to the flow rate measured di-
rectly by flowmeter 1. This makes it pos-
Multiplier
Phototube -• Channel3
Gated Clamp
r
Anti-
sible to reduce the flow rate F1 to the
very small fraction of F2. When this is
done, the sensing volume decreases
I CoincidenceI because the aerosol stream is drawn out
l
Preamplifier I
and Recording
-~ Channel2 J--
G~m p
to a very small diameter within the
sheath stream. Accordingly (see Appen-
dix II) the concentration range of the
Photometer
Clamp }_ instrument is moved upward.
Driver There is one caution in the use of this
t system. When aerosol material is depos-
--~ Preset Scale I ited on the filter, it will act as a source
Pulse -~t ChannelI
Amplifier Gated Clamp of 10,0001 of vapor. This is generally desirable in
achieving equilibrium, but when a new
t Gate I aerosol system is placed under test, the
Fro. 3.--Block Diagram of Electronics. filter should be changed to avoid con-
tamination by the vapor of the previous
In this improv~ed arrangement, the en- system. Otherwise, undesirable reactions
tire exhaust stream from the cell is fil- or growth of the aerosol by solution of
tered and sent to the junction J. At that the vapor from the previous aerosol may
point a small and variable fraction is Occur.
withdrawn through flowmeter 1 by Operation.--Pumps 1 and 2 were vari-
able speed rubber tubing pumps. 13 Flow- decade steps was provided by the switch,
smoothing reservoirs of 2.5-liter capacity SW1, which permitted selection of four
were inserted at J, between V2 and different anode load resistors, Rll-R14.
pump 2, and between V1 and pump 1. The stray capacitance across R14, meas-
The system performed satisfactorily at ured dynamically with an impedance
flow rates (F1) from 100 down to 3 cu cm bridge, was 22 ~ f , so the input time
per min, which was the lowest rate at- constant, which determined the over-all
tempted in this work. bandwidth, was 220 microseconds. In this
Vl
1P21
K K'
P5
Pl
Hi~ ifier Box
NO.I
K'
P5
Preamplifier
Plug
R1 r.
5C ~.~-22.5V
+4 5 V ~ : ~
-6V ~ ~ "+6V
P6
Bottery Power
Pock
FIG. 4.--Preamplifier and Photometer.

Resistance values in kilohms unless otherwise specified.
Capacitor values in vf unless otherwise specified.
Electronics: application, it was maintained constant in

The Photometer and Preamplifier.- the other ranges by the capacitors Ca,
The photomultiplier, preamplifier, and CB, and Co. R14 was commonly used
photometer circuits are shown in Fig. 4. and the resulting low multiplier current
(10.9 amp) made the multiplier drift (21)
The photomultiplier was a selected RCA
1P21. The high voltage supply was the negligible. The anode signal was passed,
variable unit described by Higinbotham by direct coupling through the blocking
(2o), which facilitates a wide sensitivity resistor R15, to one grid of a differential
range. Additional sensitivity control in cathode-follower preamplifier (22,23),
which was designed for two functions:
13Manufactured by Schaar and Co., Chicago,
(1) to serve as an impedance trans-
Ill. former from the anode circuit of the
multiplier to the input of a Brown poten- One of these is that particles following
tiometer-type recorder, which had a 2.5- different flow lines may give signals of
mv span and was equipped with a high- different lengths, partly as a result of
gain amplifier, and (2) to act as a some dependence of linear flow rate upon
conventional cathode-follower with peak- position within the cross-section of the
clipping of negative pulses at about 2 v stream and partly because the light rays
to prevent blocking of subsequent cir- converge toward and diverge from the
cuits. image planes of both the entrance and
The preamplifier operated differen- exit slits. The flow rate effect is kept
tially only for the first function, for small by use of the specially designed
which the time constant was about 0.2 flow system discussed above. An analysis
sec. A helical potentiometer R24, the of the optics involving ray tracing re-
selector switch SW2, and resistors R21- vealed that the second effect apparently
R23, enabled control of the photometer cannot be avoided in any optical system
sensitivity independently of the multi- employing a large solid angle of illumi-
plier. The network R26-R33, excepting nation (to insure high sensitivity) and a
R32, which is for potentiometric meas- small total scattering volume (to decrease
urements of multiplier photocurrent, was stray light and random noise). Therefore,
for adjustment of the zero on the re- integrating action in the electronic cir-
corder. By appropriate tests and adjust- cuits is likely to cause a decrease in the
ments of R25, the recorder zero could be resolving power of the instrument. Con-
made relatively insensitive to variations sequently the time constant of the inte-
in the +45 v plate supply for V2. Never- grating RC combination at the input to
theless, because of the extreme stability the amplifier was kept short compared
desired, batteries were employed for this to pulse duration T~, in contrast with
circuit. Stability in this research was well previous practice (2,3,4). By this means,
within the figures already quoted (7). the amplitude of a pulse at the discrimi-
General Features of the Pulse Analyzer. nator is essentially independent of the
Electronic pulse analyzing systems for encountered variations in scattered light
nuclear applications have been described flux. As a result of the condition that
by a number of investigators (24-41). RC < Tp, noise fluctuations may pro-
These are generally designed for short duce a double or multiple peak upon the
pulses and are not capable of being easily pulse, so that special precautions should
adjusted to handle long pulses or a great be taken to eliminate multiple counts.
change of pulse duration from one ex- The latter were avoided by use of time
periment to the next. In some systems, delays incorporated in the anticoinci-
operation depends critically upon pulse dence circuits by means of univibrators
shape or rise time, which may depend (see Anticoincidence Circuit, below).
here upon details of the optical adjust- In accord with the recommended pro-
ment. Accordingly, it was desired to ar- cedure (21), the bandwidth of the ampli-
rive at a noncritical electronic system fier was made much wider than that of
and one sufficiently versatile to permit the input circuit, so the time constant
large changes in flow rate and optical of the latter determined the over-all
dimensions for various counting applica- bandwidth. Photomultiplier gain was ad-
tions, with a minimum number of elec- justed to such a level that the amplified
tronic adjustments. Moreover, certain random shot noise in the background
problems arise in this application which photocurrent exceeded all other sources
do not arise in nuclear instrumentation. of spurious signals. The background
190 SYMPOSIUM ON P A R T I C L E S I Z E M E A S U R E M E N T
photocurrent was considerably greater pulses within a given band of the pulse
than the dark current, so cooling the spectrum could be presented directly
multiplier to reduce the dark current upon completion of a preset number of
would not have improved significantly total counts, for example, 1000. Other
the signal-to-noise ratio. investigators (25,31) have already dis-
Because the particulate concentrations cussed the statistical advantages of this
of aerosol systems are often subject to type of pulse analyzer.
wide fluctuations, some type of conven- The amplifier, discriminators, and the
ient normalization procedure is desirable anticoincidence and counting systems
in the determination of pulse amplitude were designed for a range of operating
spectra. The scanning system with a conditions. Although the pulses were of
+300 Reg.
V---5,, ~-~X
R44 I . " 390
R37: R38 R43:
C9 100 : 100 ,33 75 i~?b~--]R48A
t
0 ,I 0C0503
V5
GL 5654 ~(" 6LV6454
C4 R34 ~----, k R34A ~ .
(From P2) I K K' RSS :~ 80 K K'
/ R35
4.7M
' :i
:R?6' '
27
~--
.
42: R45:
.
--
r
--*----~)
,,oT,miootor,
P8
I R 47,100 Output
Monitor
l, At" l c7, ,,
1.oo
(Shielded)
PS Power Plug C8, 5-35)a,uf
Power~ + 300 V
supply--,~7' % \
GND /~'~ O (~Y'-Heeter
Y-Heater ~ ' ~ ~ ~ - 1" 6 . 3 v ac
63v0c ~ -150V
Cable
Shield
FIG. 5.--Pulse Amplifier.
IZesistaneevalues in kilohmsunless otherwise speeified.
Capacitor values in/~f unless otherwise specified.
rate-meter and recorder employed by 1 millisecond duration in this research,

Thomas (3) is subject to errors produced it is estimated that pulses down to about
by concentration changes occurring dur- l0 microseconds could be handled. With
ing the course of a run. In the digital the shorter pulses, the dead time of the
system chosen for this work, pulses of system could be reduced by decreasing
amplitudes between predetermined ad- the delay time of the univibrators.
justable limits were counted during the The Pulse Amplifier.--The simple two-
interval required for a preset number of stage (V3, V4) negative feedback ampli-
pulses having amplitudes above another fier shown in Fig. 5 was found to be
predetermined and independently ad- adequate for this application. To prevent
justable limit. This eliminates the errors pulse distortion, the feedback network
caused by concentration variations. By was compensated (42) for both high and
incorporating decade preset units into low frequencies by means of R41 and C&
appropriate circuitry, the fraction of The amplifier was direct-coupled to the
O'KONSKI ET AL ON PARTICLE SIZE DISTRIBUTION 191
gated cathode-follower output stage V5. were employed (Vg-Vg, V14-V15, V19-
The gate signal was a > 200 v positive V20). These were modified (R52-R54,
step from the preset scaler which ren- etc.) to permit convenient adjustment
dered the stage V5 insensitive to the of the hysteresis to 0.5 to 1.0 v. The grid
amplified negative signals from V4. bias levels were each set in the range
Faithful reproduction of 1-v negative 125 to 175 v by means of the helical
square pulses of 1 millisecond duration potentiometers R7d-RT8. The 50-v range
was preserved ~4up to a 150-fold amplifi- was accurately adjusted by means of
cation. The over-all voltage gain from R74 and RSO, and the Schmitt trigger-
the grid of the preamplifier, V2, to the ing levels by means of R59, R90, and
output of V5 was adjusted to exactly 100 Rl18. Negative pulses were fed from
under normal operating conditions by the gated cathode follower amplifier V5
+300
[ Rf.3;c,2~o ~%7 (3iP12
Rg3~. "~ R62 Test Point"*~ ~: ,a~'f-
C11 ~ 2M (Uol) ~.~-~ .~-R.-6_8---r(2~='PlO
Test Point R~:~ : ,oo.,.I I ~ 1J32,~ ~ 1 Mole
(I) Pll (1~ VS 3 ~ :
Mo,e GL?22E_--t~__ ,so~ ! I -~-", I I f• II ~-'x cPSl
Test Point
Rs7 #&27 R61 1/2 V6 R65 ' ] ? Vl I
i k,~ R71 @P"

~ /RSOA--L~
• II 1/2 VlO
~/R73
~//[ "
I
§
-150
(21Pll
(Mole) -88 , o
112 V6 Test Point / GND Y'
12AX7 RTO (SB1)
(Male)]~esfPoint
721 P12
100 O0 1 GroundBus
(CD) - (1) P12
FIG. 6.--Totalizer Circuit (Channel 1).
Resistance values in kiiohms unless otherwise specified.
Capacitor values in/zf unless otherwise specified.
means of a precision 100:1 attenuator to the Schmitt control grids by means of

which permitted oscillographic compari- RC networks of 0.05-sec time constant.
son of the output signal with the input A rectangular positive pulse is generated
signal before attenuation. This was nec- at the plate of the first tube of each dis-
essary to establish correspondence be- criminator (for example, 1/8) for the
tween photometer sensitivity, also ac- period when the grid voltage was kept
curately determined, and the pulse below 125 v by the negative pulse. By
analyzer gain. means of the differentiating and bias
Pulse Analyzer.--The amplified pulses network, R60-R62, and Cll, and the
were classified by means of two electric diode (89 of V6, Fig. 6), triggering of the
counters consisting of the totalizer (Fig. univibrator, Vll, was withheld (pri-
6), the pulse sorter circuits (Fig. 7), and marily for reasons explained under Anti-
the corresponding scalers (Fig. 8). Three coincidence Circuit below) until the
discriminators of the Schmitt type (22) plate of V8 swung negatively to its
14 G. J. D o y l e , u n p u b l i s h e d results. normal condition on the trailing edge of
+ 500V
C24
I(:X)JJ.p.f
(1) P10
(Femole) R123 R122
R74 3.3 tO 5~
304M 47'
Rl10~
5 l Test
Point ~ Test Point
C16,.05 (us)
R 105
47
GL5654 ]Rt17
Point
(SGS) I 292 Test 9
Point
, R120 (A1)
:: 50 Rlll
12AXT
Pulses) 9
R127 Chonnel5
I00
>
Ground Bus
R 8t
tO0 Channel2
Test J Test
Point~ Point
(SB Z) 1/2V12 20 (A2) ~q
,12AX7 :R89
R82A 15o 22
100 R91 V16
Test Point 292
(SG2]
V15
J 0.05
C15 Test .>SM~ Test Point
:C14 Pointo~L-~ . (u 2) 00[ C21
50~l.p,f
0.05 input Pulses (1) P10 ~Mu,q
(SP~85 R86 lo~3.3 I R98:
(Female) IC18 47 :
From Cathode 3.3 L _ _ -150V +300V
of V5 100~#.f
(1) PI1
(Femole)
FzG. 7,--Pulse Sorter Circuits.
Resistance values in ldlohms unless o~herwise specified.
Capaeitor values in #f unless otherwise specified.
the pulse. The univibrator, Vll, de- vibrator combination, in addition to pro-
livered a large positive pulse, > 200 v, viding a gate for a clamp (for reasons
of period around 0.8 millisecond con- discussed below), facilitated application
trolled by R66, to the cathode follower of a particularly simple and reliable anti-
(89 of VIO) which gated the triode clamp coincidence circuit in the pulse sorter of
V7 to restore the bias level of the Schmitt Fig. 7. Through the univibrators, the
tube by shunting the accumulated posi- two channels shown there are identical
tive charge from the coupling capacitor with channel 1 of the totalizer, with ex-
(C14 of Fig. 7) through the electronic ception that no additional cathode fol-
low impedance network (R70, 89of V6, lower clamp drivers were used, the 6J6
Fig. 6) to ground. The univibrator also of Fig. 6 being adequate for a large num-
+300
50 ~ <~ 50 vo PI3~A~ [ l / 4.7

I off~ sw~ ~ ~_%\ ~-~--~."i
O25
_ __11~
~ 470 ~o~
(2) PIO " --

(Female)
Be.too I J Bd%0 I I 25:

~'~ L t ~r~' ~ ~'~176
Totalizer Scaler Manual •
y, Reset
GND ~ -150
L
To Role
X
V22
Units ~ I
Be. 700 I ]
Z
Differential Scaler
Fro. 8.--Scaler Circuits.

Resistance values in kilohms unless otherwise specified.
Capacitor values in pf unless otherwise specified.
For missing connections to decades see preceding stage.
delivered a negative pulse at P10 which ber of stages. The only additions were the
energized the totalizer scaler. During the anticoincidence tube 1;22 and its asso-
univibrator delay period, the first grid ciated components.
of Vll was held strongly negative, and The principle of operation of the pulse
the diode V6 was nonconducting. This amplitude selector circuit is as follows:
prevented further triggering of the uni- When a pulse exceeds the bias on the dis-
vibrator by multiple pulses from the criminator of channel 2, but not channel
Schmitt which may occasionally occur by 3, the resulting rectangular positive
action of noise fluctuations superposed pulse from the first plate of the second
upon the signal. Thus, double or multiple univibrator, V16, is differentiated and
counting of a single pulse was avoided. applied to the triode amplifier section of
Anlicoincidence Circuil.--The above 1122, which delivers a 125 v negative
arrangement of the discriminator-uni- pulse to energize the second scaler. When
a pulse exceeds both bias levels, a rec- tire with increasing channel number, the
tangular pulse from the plate of the upper limits at which the discriminators are
(channel 3) univibrator, 1/21, is fed di- energized are successively more negative
rectly through the limiting resistor R106 with increasing channel number, as
to the cathode-follower section of V22, shown in a. It is readily seen that during
producing a large positive swing at the the positive excursion f of the differen-
common cathode. This cathode bias pro- tiated output from univibrator 2, the
duces cut-off of the amplifier section of anticoincidence amplifier section is ren-
V22. The upper channel discriminator dered inoperative by the rectangular
bias is always set higher than the lower, pulse c from univibrator 3. The clamp
(Negative Pulse) Time ----~
circuit is in action during the interval
-- -- T2 - - - - Discriminator 1 Limit rl and is turned off to prevent rectifica-
- - - - Discriminator 2 Limit tion of the random noise signal, which
J ~ I I - - - - Discriminator 5 Limit may be several volts when the instru-
I II ment is being used at highest sensitivity.
(b) I - - F First Plate of Discriminator 1 Such rectification would of course pro-
duce an undesirable d-c bias at the dis-
il
criminator grid (7). A longer clamp in-
terval can be introduced independently
{C)- - ~ ~Flrst Plate of Univibrator 3 of other adjustments when desired.
Regarding adjustment of the uni-
I
vibrator delay intervals r l , r2, and r3, it
First Plate of can be seen that it is only necessary to
(d) Univibrator 2
keep all the intervals greater than the
I I maximum possible difference, t3 -- t2 of
First Plate of Fig. 9, which depends upon the particu-
Univibrator 1
(o) (Clamp Signal) lar application. In this work the pulses
were roughly triangular, and of 1 milli-
I
] second duration, so a delay period of 0.8
{f} ~k I
Differentiated O^utput
of UmviaraTor L:
millisecond was conservatively chosen.
If the pulses were very fast or rectan-
g gular, anticoincidence action is still
achieved, as t2 cannot occur before t3.
FIG. 9.--Waveforms Illustrating Anticoinci- Adaptation for Multichannel Operation.
dance Operation.
By connecting another differentiating
and the totalizer is set lowest. Therefore, circuit from the first plate of the upper
the univibrators are energized in sequence univibrator to the amplifier grid of an
from the trailing edge of the pulse, be- additional anticoincidence tube (not
ginning with the uppermost channel. shown), and the univibrator output of
Hence, if the upper channel is energized another higher channel (not shown) di-
by the pulse, the differentiated pulse from rectly to the cathode-follower grid, an
the lower channel is not amplified by additional anticoincidence stage is pro-
V22. Thus, anticoincidence action is duced. Successive stages may be added
achieved. to produce a multichannel unit. In such
The sequence of events is illustrated applications, it may be preferable to em-
in Fig. 9, which is an idealized representa- ploy a crystal diode as a clamp device,
tion for the case of a pulse exceeding all rather than a gated triode, because of the
discriminator levels. Since the pulse base lower impedance of a crystal. Then the
level (bias) is progressively more posi- electronic low impedance clamp networks
(for example, R70 and 89V6 of totalizer) units. Switching and voltage divider net-
become especially advantageous. Since works and a standard cell, not shown in
V6 is a high-mu triode the operating the diagrams, facilitated accurate check-
cathode to grid potential difference is ing of important d-c voltages in the cir-
small (1.0 to 0.4 v over the 50 v dis- cuits with the aid of the Brown recorder.
criminator range) and it may be em-
ployed as a delay bias to prevent recti- ] ~ X P E R I M E N T A L 7VIATERIALS
AND P R O C E D U R E S
fication of noise. Such rectification would
be appreciable only in the lower channels
Latex H ydrosols:
of a unit designed to cover a wide range,
and would be negligible when the signal- The properties of the polystyrene latex
to-noise ratio is high. hydrosols1~employed in the present study
Scalers.--The counting and timing ar- are summarized in Table I as communi-
rangements are shown schematically in cated by the manufacturer.
Fig. 8. Each. of the two scalers consisted The electron microscope technique
of a series of four decimal counting used for determining the particle size of
units. 15 In the totalizer scaler, two dec-
ades which recorded the hundreds and TABLE I.--PROPERTIES OF POLYSTY-
RENE LATEX HYDROSOLS.
thousands of counts respectively were of
the preset type (model 730). By appro- Stan- arnb~
Mean dard
priate circuitry involving these units, a now Run Designation Diam- Devia- Mea: Solids,
~terj # tion, ure- 3er cent
positive gate was delivered after the er cent aent~
registering of any preset integer number
of hundreds of counts in the range of 1 LS-067-A . . . . . . . . 1.17: 1.1 315 11.0
to 99. The gate discontinued the count- LS-066-A . . . . . . . . 0.81~ 1.35 357 11.5
LS-063-A . . . . . . . . O. 55: 2.0 373 13.0
ing by blocking the pulse amplifier, and, 15 N - 8 . . . . . . . . . . 0.51: 1.35 359 8.3
at the same time, activated a relay, RL1, LS-061-A . . . . . . . . 0.36~ 2.2 438 11.3
to stop an electric clock connected to the
timer plug, P13. A push-button, SW4,
was provided to reset the scalers and the the latices has been described in a recent
timer while inactivating the pulse ampli- publication (43).
fier. The index of refraction and density of
The arrangement described eliminated the polystyrene particles have been re-
the errors due to fluctuations in aerosol ported (44) as 1.625 and 1.057 g per cu
concentration and sampling rate en- cm respectively (at 25 C), the former
countered in single-channel instruments. value slightly decreasing with increasing
Furthermore, by successively recording particle diameter.
the time required for registering a certain
Pulse Amplitude Data and Signal-to-Noise
preset number of counts on the totalizer
Ratio:
scaler it was possible to follow, when
maintaining a constant sampling rate, The ratio of the count rates registered
the particle concentration changes oc- on the differential scaler to those recorded
curring in an aerosol system. concomitantly o n the totalizer scaler--
The power supplies employed for all both duly corrected for the background
Lhe circuits (,-t-300 and --150 v) were counts--was determined as a function of
conventional electronically regulated window voltage. In all the measurements
the window size was kept at 2 v. The
15 M a n u f a c t u r e d b y B e r k e l e y Scientific D i v i -
sion, B e c k m a n I n s t r u m e n t s Co., R i c h m o n d ,
mean pulse voltage and the standard
Calif. deviations from the means for the dif-
ferent latices were calculated in the usual adjustments in the slits and glare stops.
way (7). For this purpose, pulses within Hence no reliance was placed upon its
a given cell of the histogram were con- constancy. By measuring the photocur-
sidered to have the mid-window voltage. rent due solely to molecular scattering by
The signal-to-noise ratio was calculated gases within the scattering volume, the
for each experiment as the ratio of mean over-all sensitivity of the instrument was
pulse height to the 300 cpm noise level established for each experiment. Since
(7), the latter being measured under iden- the photocurrent from scattering depends
tical operating conditions but with the upon the scattering volume, adjustments
cell containing filtered air only. Suffi- which might affect the scattering volume
ciently low aerosol concentrations were were avoided in the course of each series
employed in all cases so that coincidences of measurements (A, B, C of Table II).
never exceeded 3.5 per cent. Pulse voltages were converted to multi-
plier anode currents by Eq 2 of Appendix
Photomelric Data:
I. Recorder deflections were converted to
At the beginning and end of each multiplier currents by use of appropriate
counting experiment the cell was alter- calibration data. Then, for each experi-
nately flushed with air and helium and ment, the value of the peak pulse photo-
the respective d-c signals were measured current, ip, was divided by i , , the photo-
at the operating conditions of the experi- current due solely to molecular scattering
ment. Dark current was excluded by tak- from air. Corrections for temperature
ing as zero the recorder deflection ob- and pressure variations were negligible,
tained with the multiplier voltage on and typically less than 1 per cent.
the illumination off. Drifts in light source The i~ to i, ratios computed by this
intensity, photomultiplier gain, etc., dur- procedure are independent of light source
ing the course of a counting experiment intensity, photocathode sensitivity, and
caused only minor changes in the magni- multiplier amplification. Gross changes in
tude of the d-c signals, typically about spectral response would affect the ratios
0.5 per cent from their mean values (7), but this effect was considered negligi-
adopted as representative for the whole ble because (a) the over-all sensitivity
experiment. Since the photocurrent due and the gain of the multiplier remained
to scattering from helium is known (7) essentially constant throughout the re-
to be 0.014 times that due to air, the dif- search, and (b) the tungsten light source
ference between the mean d-c signals ob- was stabilized by operation from a bat-
tained with air and helium in the cell tery and charger.
were multiplied by 1/0.986 to give the
d-c signal due solely to the scattering Optical Adjustment Procedures:
from the air contained in the total scat- Focusing of the image of the entrance
tering volume. The difference between slit $2 at the center of the sensing volume
the total d-c signal obtained with air in stream was achieved while passing ciga-
the cell and that due to the air alone rette smoke through the cell and observ-
represented the contribution of the stray ing the scattered beam through a window
light in the optical system. substituted for the end of the back-
ground trap T (Fig. 1). The in-plane
Computation Procedure: centering of $2 was accomplished while
In the course of the experiments, it observing the smoke stream through a
was observed that the stray light level glass window substituted for the back
was not reproducible, being sensitive to plate BP.
To adjust the collecting system, the placed in the direction of the axis of the
images of the smoke stream and of a fine illumination system and hence defined
wire inserted along the axis of the coaxial the scattering volume in conjunction
flow system were viewed on a translucent with unchanged area of $2 (2.4 by 1.1
screen substituted for exit slit SI1. ram).
T A B L E I I . - - M E A N P U L S E C U R R E N T S A N D P A R T I C L E SIZE.
A. S-11 = 1.2 by 2 . 2 s q m m
Mean Par- Signal-to- Mean Pulse ~Iean Photo-

Experiment ticle Di- Noise Standard
Current, amp, Deviation, current from ip/ia (ip/ia)ll2/D
ameter, Ratio 109ip ~ iAirscattering,
amp, 109ip
No. 66 . . . . . . . . 1.171 14.8 27.7 18.2 2.61 10.6 2.77

No. 69 . . . . . . . 0.814 11.2 32.9 18.3 5.22 6.32 3.09
No. 68 . . . . . . . 0. 557 5.5 31.6 18.2 10.8 2.91 3.06
No. 70 . . . . . . . 0. 365 2.60 29.7 18.4 23.2 1.28 3.10
No. 72 . . . . . . . 0. 365 2.40 26.9 18.9 21.2 1.28 3.10
B. S-11 = 2.3 by 3.8 sq m m
No. 73 . . . . . . . . 1.171 14.1 38.1 8.5 5.33 7.16 2.28

No. 75 . . . . . . . 1.171 13.2 23.7 8.6 3.05 7.77 2.38
No. 77 . . . . . . . 0.814 8.3 26.7 9.7 6.07 4.41 2.58
No. 74 . . . . . . . 0. 557 4.10 27.1 12.8 13.7 1.97 2.52
No. 76 . . . . . . . 0. 557 3.95 25.3 12.3 13.0 1.95 2.51
No. 78 . . . . . . 0. 365 1.78 24.6 21.1 29.1 0.85 2.52
c. S-1l = 1.1 by 1.9 sq m m
No. 79 . . . . . . . 0.814 10.0 25.0 12 3.03 8.27 3.54

No. 81 . . . . . . 0.814 10.0 35.1 12 4.11 8.55 3.59
No. 80. 0.511 3.83 26.0 15 8.03 3.24 3.52
No. 81 . . . . . . 0.511 3.65 12.8 16 4.11 3.10 3.45
D. Previous D a t a (reference (7), footnote 4)
No. 61 . . . . . . . . 0.986 13.5 a 16 ~ 11.05 3.38

No. 61 . . . . . . . . 0.514 3.6 a 14 a 2.95 3.34
No. 60 . . . . . . . . 0.514 3.4 a 13 a 2.89 3.31
No. 60 . . . . . . . . 0.333 1.8 a 15 a 1.50 3.68
No. 59 . . . . . . . . 0.333 1.6 a 15 a 1.40 3.56
VMues listed in the earlier publication had been normalized to a certain mul t i pl i e r amplifica-
tion, and therefore are not comparable.
EXPERIMENTAL RESULTS D = mean particle diameter, ~; S / N =

signal-to-noise ratio; ip = mean pulse
A summary of the results obtained
current (amp); a = standard deviation
with the five different latices particle
from mean pulse current, per cent; ia =
diameters is p r e s e n t e d in Table IIA, B, mean photocurrent from air scattering
a n d C. T h e t h r e e p a r t s of t h e t a b l e a r e (amp).
for three d i f f e r e n t s i z e s of t h e v i e w i n g Part D of Table I I contains previous
s l i t $11 ( s e e F i g . 1). T h e d i m e n s i o n s of data of O'Konski and Doyle (7) which
$11 a r e l i s t e d i n t h e t a b l e . I n a l l t h r e e have been recalculated according to the
c a s e s , t h e l a r g e r of t h e d i m e n s i o n s was computation procedure outlined above.
198 S Y M P O S I U M ON ]:)ARTICLE S I Z E ~/~EASUREMENT
TABLE III.--SUMMARY OF THE DATA which were different in the earlier study
FOR UNIFORM LATICES.
(7), the comparison was made as follows:
. . 1 a Mean
Namber of ratios of (ip/ia)VD for a given particle
Diameter, (*j*a)~/D Compari-
Deviatio: sons to the value of that quantity for the 0.814
/~ diameter particle were computed for
1.171 . . . . . . . . . O. 901 0.014 3 series A, B, and C, Table II. Employing
0.986b . . . . . . . . 0. 993 1
0.814 ........ 1. 0 0 0
the mean value of that ratio (0.511:
0.557 ......... 0.980 01007 3 0.814) from Table IIC, corresponding
0.511 ......... 0. 977 0.017 2 ratios were obtained for the 0.333/~ and
0.365 ........ 0. 994 0.012 3
0.333 ......... 1.064 0.018 2 0.986 ~ particles. The results are pre-
sented in Table III.
a R e f e r r e d t o u n i t y for t h e 0.814/~ spheres.
b Polyvinyltoluene. The others are poly-
A pulse amplitude histogram for the
styrene. case of a binary mixture of the homoge-
0.20 J
0.18
0.16 if3
2 O
t-
= 0.14 - m
0
(9
-5 0.12 O
.g
i- 0.10 m
"t-
"5 o w
to
,w
~"
0
0.08 - 123
J
0.06
ID
0.04
0.02
0
0 4 8 12 16 20 24 2 8 : 3 2 56 40 44 48 52
Discriminator Bias, v
FIG. 1 0 . - - P u l s e A m p l i t u d e D i s t r i b u t i o n of a M i x t u r e of 0.511 /~ a n d 0 . 8 1 4 / ~ D i a m e t e r P o l y -
s t y r e n e Aerosols.
The ratio between the pulse amplitudes neous aerosols (experiment No. 81 of Ta-
for the 0.814 and 0.511/, diameter par- ble IIC) is given in Fig. 10.
ticles was determined in experiments Nos. All of the above experiments were con-
79 to 81. Since the 0.814/~ particles were ducted with an aerosol flow rate, F1, of
used in each series of measurements 100 cu cm per min, and a sheath air rate,
above and the 0.511 ~ particles are the F2, of 300 cu cm per rain. After the im-
same preparation (15 N8) as the 0.514/~ proved flow arrangement was introduced,
particles used previously (series D), it is measurements were made to determine
now possible to compare all of the par- the effect of narrowing the aerosol
ticle scattering intensities. Because the stream, by reducing F1, upon the stand-
value of (i~,/ia) depends upon slit sizes, ard deviation. The results are sum-
O'KoNsKI E T AL O N P A R T I C L E S I Z E D I S T R I B U T I O N 199
marized in Table IV. The aerosol stream is excluded in this comparison, because of
diameter, d, was computed b y assuming the small difference in refractive index
streamline flow with the parabolic ve- (44), the corresponding deviations are 0.9
locity distribution prevailing in a long and 1.2 per cent. Thus, the present re-
cylinder of diameter equal to that of the sults generally confirm the previous ob-
sheath air and exhaust tube (F2 was 300 servation (7) with three sizes of the rela-
cu cm per rain). tively simple square-law dependence of
TABLE IV.--WIDTH OF THE PULSE AMPLITUDE DISTRIBUTION AS A FUNC-

TION OF THE DIAMETER OF THE AEROSOL STREAM, FOR 0.814 ~u DIAMETER
POLYSTYRENE LATEX.
Aerosol Stream ca Signal-to-Noise a(vp) b,
Experiment F1, CUminCmper Diameter, d, o(D), c
mm Ratio per cent
No. 82 ............ [ i00 1.12 8.3 15.1 9.3 0. 038

No. 83 ............ I 6 0.31 8.3 13.8 8.5 0.035
I
a N u m b e r of p a r t i c l e s p e r c u c m in t h e t e s t aerosol.
b S t a n d a r d d e v i a t i o n of t h e p u l s e a m p l i t u d e .
c S t a n d a r d d e v i a t i o n , in/~, of t h e p a r t i c l e d i a m e t e r .
TABLE V.--SENSITIVITY OF THE PHOTOMETER TO ,MALL PARTICLES.

Material Particle Diameter, Pmln, CU cm-1
Water Aerosol (n = 1.33) . . . . . . . . . . . . . . . . . . . 0.04 2.9 X 105

Water Aerosol (n = 1.33) . . . . . . . . . . . . . . . . . . 0.01 1.2 X 109
Water Aerosol (n = 1.33) . . . . . . . . . . . . . . . . . . 0.001 1.2 X 1015
Oil Aerosol (n = 1,50) . . . . . . . . . . . . . . . . . . . . . 0.01 5.6 X l0 s
Sulfur Aerosol (n = 2.00) . . . . . . . . . . . . . . . . . . 0.01 1.4 X l0 s
Hypothetical Aerosol (n = oo) . . . . . . . . . . . . . . 0.01 4.9 X 107
N2 gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (molecules) 2.5 X 10I7
(7.6 mm at 25 C)
C4I-It0 g a s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (molecules) i.i X 10IG
(0.33 mm at 25 C)
ClsH~6 g a s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (molecules) 6.6 X 1014
(0.02 mm at 25 C)
DISCUSSION signal upon diameter in this region. The

response for the 1.17 ~ particles was sig-
Counter Response Characteristics: nificantly less than would be expected if
From Table I I I it can be seen that the a square-law held over the entire region.
scattering power per particle rises mono- The response for the 0.333 ~ particles was
tonically with increasing diameter for all greater, b u t this cannot be considered
seven latices employed in this research. significant because of the uncertainty, at
For the 0.365, 0.511, 0.557, and 0.814 low S / N ratios, in the correction re-
polystyrene a n d the 0.986 ~ polyvinyl- quired for rectification of random noise
toluene, the square root of the pulse am- by the diode restorer employed in the
plitude is proportional to the diameter previous work (7). For the largest par-
with an average deviation of 0.8 per cent ticle diameter (1.171 ~), the magnitude of
and an extreme deviation of 1.2 per cent (ip/i,)89 was about 10 per cent lower
from the mean proportionality constant. t h a n the mean value obtained for the in-
If the 0.986 ~ diameter polyvinyltoluene termediate sizes. This shows t h a t ex-
trapolation of the square-law response to sidering the region up to 2.4 ~ diameter

larger sizes is not permissible; it is neces- as given in Gucker and Rose's curve for
sary to determine the response curve for the present right-angle system, ambiguity
particle diameters which cover the range of response would be avoided if the cells
of the size distributions to be examined. in the histogram were of arbitrary width
Once the response curve of an instrument up to 1.2 ~ diameter, then 1.2 to 1.5, 1.5
is determined for spherical aerosols of a to 1.8, and 1.8 to 2.4 u diameter. Gucker
given refractive index, that curve is ap- and Rose also made calculations of the
plicable to all materials of that refractive response for a small-angle optical system,
index providing the over-all sensitivity and their curves indicate that the cells
of a given instrument is determined by could be of arbitrary width up to 1.0/~
measurement of a single size. diameter and above 2.0 u diameter, but
In five cases (experiments 70 and 72, that a relatively wide region of ambiguity
73 and 75, 74 and 76, 79 and 81, 80 and exists between 1.0 and 1.9 ~ diameter.
81 in Table II) duplicate experiments The calculations suggest that there are
were carried out with the same particle more regions of ambiguity with the right-
diameters after a period of 1 to 2 months angle system than with a small-angle
had elapsed. The results show excellent system, but their widths, expressed as a
agreement for the 0.365 ~, 0.511 u, 0.557 percentage of the mean radius, are con-
u, and 0.814 u diameters. The agreement siderably smaller. This means that, for
for the 1.171 u particles was less satis- general use, the right-angle optics is to be
factory, amounting to about 4 per cent preferred. By increasing the solid angles
in mean pulse amplitude or 2 per cent in of illumination and collection, a smoother
particle diameter. I t is possible that the response would probably be obtained.
greater deviation observed with the 1.171
/z particles is partly due to fracture (7) Resolving Power and Sensitivity:
during atomization of the larger hydro- E~ect of Viewing Slit Dimensions.-
sols in the aerosol generator. Comparison of parts A and C with part
The theoretical response curve of this B in Table I I demonstrates the previ-
instrument for polystyrene latices is not ously suggested (7) effect of the dimen-
yet available, primarily because of the sions of S l l upon the standard deviation
tedious summations involved, so a direct from the mean of the pulse height dis-
comparison of the results with theory tribution for a given particle size. Ex-
cannot be made. A rough comparison can cepting the 0.365 u particles, a significant
be made by examining the curves for decrease in ~ resulted from the increase in
water computed by Gucker and Rose (17). slit size. This became the more marked
These indicate that the square root of the the larger the particle diameter. The de-
response is approximately proportional crease in ~ was associated with a reduc-
to the diameter from around 0.7 to 1.3 tion in the frequencies of the pulse ampli-
diameter. From 1.3 to 2.4 u diameter, the tudes smaller than the mean, while the
curves show oscillations of the response frequencies of the larger than mean pulse
amounting to about -4-10 per cent, which heights remained practically unaffected.
corresponds to around 4-5 per cent in I t is also evident that, as to be expected
radius. If this behavior is typical, it is (see Appendix I), the signal-to-noise ra-
clear that for high accuracy, discriminator tios for the same particle sizes were lower
levels should be judiciously selected in part B than in part A and C of Table
above 1.2 ~ diameter. For example, con- II. The superposition of relatively larger
noise pulses on the signals from the par- II may have been due in part to imperfect
ticles in experiments Nos. 73 to 78 caused alignment of the optics.
a greater spreading of the distribution PROPOSED VARIATIONS
curve and thus counteracted the decrease
The described instrumentation was de-
in r due to the enlarged aperture in the
veloped for laboratory studies of nuclea-
viewing system. With decreasing particle
~ize, the effect of the additional spread, tion kinetics in the formation of aerosols
by vapor condensation (4S).16 It is suffi-
caused by the noise, gained in importance.
ciently versatile to be readily adapted to
In the case of the 0.365 ~ particles, where
other aerosol problems, for example,
the signal-to-noise ratio was lowest, the
trend was actually reversed and the studies of air pollution (40). The concen-
tration range could be increased another
standard deviation even increased
tenfold, and the maximum count rate one
slightly when using the larger slit. On the
hundredfold, by increasing the linear flow
basis of all these considerations it is
rate 10 times, decreasing the input time
estimated that, by the increase of S l l in
constant 100 times, decreasing the en-
part B, the limiting diameter which can
be counted with adequate accuracy has trance slit width 10 times, leaving the
aerosol stream area unchanged, and de-
been raised from about 0.3 u to about
creasing the univibrator delay time 100
0.33 g. It is therefore concluded that, by
times. The disadvantage would be a ten-
proper enlargement of the exit slit, the
resolving power of the counter for larger fotd decrease of signal-to-noise ratio, so
the lower limit would correspond to par-
particles can be improved significantly
ticles 1 ~ in diameter. Conversely,
while its sensitivity to small particles will
be impaired to a minor degree only. The changes in the other direction would
effect was attributed to a small depend- make the instrument sensitive to smaller
ence of light collecting efficiency upon the particles, but to estimate a lower size
position of a scattering unit within the limit, calibration with smaller particles
would be required.
sampl e space, as a result of some shadow-
ing of rays by the exit slit. The essentially square-law response
from 0.3 to 1 ~ diameter means that in
Effect of Aerosol Stream Diameter.-
Since some improvement of resolving this region the photometer signal is pro-
power was realized with a larger viewing portional to the total surface area of the
slit, it was expected that with a given slit aerosol. This is of special interest for
studies of growth or evaporation proc-
combination the standard deviation
esses where rates depend upon surface
might be decreased by narrowing the
area. Also, analysis of sedimentation-
aerosol stream in the sample space (com-
scattering intensity measurements for
pare experiments No. 82 and No. 83, size distribution is greatly facilitated
Table IV). The slight decrease from 9.3 when the response follows a simple law
to 8.5 per cent suggests that something (4~).
other than variations of illumination and By means of an appropriately modified
light collecting efficiency is responsible optical system, the apparatus can be
for most of the standard deviations in adapted to studies of liquid systems. By
those experiments. The random noise using an ultraviolet source, replacing the
superposed upon the pulses is of the cor- illuminating achromats with quartz
rect order of magnitude to explain those
16 C. T. O'Konski and W. I. Higuchi, ac-
results, and the larger standard devia- cepted for publication in the Journal of Co',-
tions observed in series A and C of Table loid Science.
lenses, and incorporating suitable filters, light collecting system, an unusually high
the instrument would become a particle sensitivity can be expected.
counter based upon fluorescence, and a
A cknowledgments:
continuously recording fluorescence pho-
t o m e t e r for gases. Because of the low T h e support of the Office of N a v a l Re-
level of s t r a y light and the use of a fast search is gratefully acknowledged.
APPENDIX I
THEORETICAL CONSIDERATIONS OF THE SIGNAL-To-NoIsE RATIO
Let Ib be the background cathode emis- noise at the anode resistor was negligible.
sion current of the photomultiplier, exclusive Following the formulation of Hafstad (48)
of contributions from particles. Thus, the mean square shot noise associated with
the cathode photocurrent, Ir,~,~, may be ob-
h = I ~ + L + I, . . . . . . . . . . (1) tained from
where I~ is due to light arising from molecu-
lar scattering within the total scattering I~,~ = 2eI 1 + 4~~R~C2f~
volume, I , is from stray light in the optics,
tnd I , is the thermionic current. Let Ip he
since the frequency spectrum of interest is
the peak value of the additional cathode
determined by the anode circuit time con-
current due to light scattered by a particle stant, RC. If the shot fluctuations in the
within the sensing volume. Then the total
dynode emission are considered negligible,
cathode current of the multiplier, I, at the
the root-mean-square anode noise current,
peak of the response will be Ib + I~. If the i ..... is given by
anode load resistor is R, the multiplier gain
is ~, and the voltage amplification from the ira+ = #/rms 9
multiplier anode to a discriminator grid is A,
Since all but the insignificant low and the
the peak value of the voltage pulse at the
very high frequencies of the noise spectrum
discriminator will be given by
are passed by tile wide-band amplifier, the
V~ = ARip = ~ARI~, ....... (2) rms noise voltage at the discriminator, V,+,
can be written
where i~ is the peak anode pulse current.
This assumes that the amplifier is linear and V~ = A R i r m , .
that the time constant of the input circuit Performing the substitutions and the inte-
is small compared to the pulse length. Thus gration, we obtain
far, the random fluctuations have been ig-
nored so IF and Vp are to he regarded as V~ = ~AR(eI/2RC) 112 ...... (3)
average peak values. The d-c components of
Ib are not transmitted by the capacitively where e is the electronic charge and C is the
coupled amplifier. capacitance across the anode resistor R.
Consider now the random fluctuations Then the signal-to-noise ratio is given by
superposed upon the pulse peaks, where the
VF/V~ = Ip/ (eI /2RC) ~/2 . . . . . . (4)
total cathode current is I. Since I ~ , I F , L,
and I , are all the same sign, I may be treated In this research, it was experimentally
as a single component in computing the established that L and the leakage currents
shot noise. For this research, the amplifier were both negligible compared to (I= + I~).
bandwidth was large compared to the band- Hence
width of the over-all system. I t was demon-
strated experimentally that the thermal VF/V~ = I / [ e ( I = + L + I ~ ) / 2 R C W ~. (5)
From this equation it can be seen that in- use of the discriminator and counter cir-
creasing the light intensity or the luminous cuits alone. This was done by defining a
sensitivity at the photocathode x-fold will noise pulse count rate as standard and
increase the signal-to-noise ratio by x1/2. Re- experimentally determining the discrimi-
ducing (I~ + / ~ ) will improve the ratio by an nator level corresponding to that rate. The
amount depending upon the value of (Ia + reference rate was great enough so that
I8) relative to I ~ , which depends upon the counts due to occasional dust particles did
particle size. In cases where Ip >> (/~ + Is), not appreciably affect the measurements and
the ratio increases with Ip 1/2, that is, essen- the corresponding discriminator level could
tially linearly with particle diameter, for the be conveniently determined, but small
right-angle optics (see under Experimental enough to make dead time corrections negli-
Results). If Ia and I~ are reduced until their gible. The count rate selected previously (7),
sum becomes comparable to It (which may 5 cps, was employed throughout this work.
be feasible by further reduction of the sens- The resulting signal-to-noise figures are
ing volume) it would become advantageous around 30 per cent lower numerically than
to cool the multiplier to reduce I s , thereby equivalent signal-to-(tins) noise figures (Eqs
increasing Vp/V~ . The ratio Ip/(I~ + I~ + 4 and 5). This can be ascertained from pre-
ip)l/2 provided a convenient figure-of-merit viously reported (7) count rate data on noise
so that photometric measurements could be pulses. Since the particle pulses are approxi-
used in comparing various modifications of mately flat for around 0.4 millisecond, the
the optical system, as in the studies reported probability that a noise fluctuation will ex-
earlier (7). ceed the 5 cps noise level (for I~ < Ia + I~)
In earlier studies (2, the noise level was during this interval is about 0.002. Conse-
reported as the average a-c voltmeter read- quently, as was observed, reasonably small
ing at a specified point in the circuitry. In standard deviations may be expected even
this research, it was found possible to ob- when the reported signal-to-noise ratios ap-
tain quantitative measurement of noise by proach unity.
APPENDIX II
COINCIDENCE CALCULATIONS AND CONCENTRATION RANGE
Clearly, the minimum probability of a the total number of particles per unit volume
coincidence of the signals from two or more of aerosol, and v, is the sensing volume in the
particles is equal to the probability that more same units.
than one particle will be found within the From Eq 6. it follows that the upper limit
sensing volume of the instrument. If the in concentration, for a given coincidence
pulses are distorted or lengthened in any rate, is increased by decreasing the sensing
manner in the electronic circuitry, the coinci- volume, v,. This volume is equal to the
dence probability will be larger than this product of the area of the aerosol stream
(intrinsic) probability of coincidence within (where it traverses the illumination zone)
the sensing volume. In this work, the time and the height (see Fig. 2) of the image of
constant of the input circuit was kept small the entrance or exit slit, whichever is less.
compared to the duration of a pulse, and a The simplest method is to decrease the area
wide-band amplifier was employed, so the of the stream by reducing the sample rate,
two probabilities are essentially equal. For F1, as shown in Fig. 2. The linear flow rate
practicable conditions of operation (p << 1), remains constant if (F1 + F2) is held con-
stant. Concomitantly, the total scattering
they may be computed from the relation (7) :
volume may be reduced by decreasing the
p = n~v. . . . . . . . . . . . . (6) slit dimensions to decrease the background,
and improve the S - N ratio (see Appendix I).
where p is the fraction of coincidences, n. is When this is done, the pulse duration may
be reduced by decreasing slit height, where- are probably determined by the quality of
upon the input time constant should be de- the optical components, and were not
creased proportionately. The feasible limits reached in this study.
APPENDIX llI
SENSITIVITY OF THE PHOTOMETER TO SMALL PARTICLES AND GASES
From the well-known Rayleigh equation, at 25 C and 1 atmosphere pressure. This
the minimum detectable concentrations of corresponds to na 2 = 7.6 X 10-31, where n =
particles or molecules of various types can number of scattering centers per cu cm and
be computed when the particles are small a is their optical polarizability. For small
compared to the wavelength.
spheres of relative refractive index m, a
Previous work (7) established the lowest
detectable photometer signal with the de- (m 2 - 1)r~/(m 2 + 2), where r is the radius.
scribed instrument as 1 per cent of the The results given in Table V provide an in-
scattering intensity from pure nitrogen gas dication of sensitivity for typical examples.
REFERENCES
(1) F. T. Gucker, Jr., C. T. O'Konski, H. B. (7) C. T. O'Konski and G. J. Doyle, "Light
Pickard, and J. N. Pitts, Jr., "A Photo- Scattering Studies in Aerosols with a New
electronic Counter for Colloidal Particles," Counter-Photometer," Analytical Chemis-
Journal, Am. Chemical Soc., Vol. 69, p. try, Vol. 27, p. 694 (1955).
2422 (1947). (8) A. C. Guyton, "Electronic Counting and
(la) F. T. Gucker, Jr., H. B. Pickard, C. T. Size Determination of Particles in Aero-
O'Konski, and J. N. Pitts, Jr., "A Particle- sols," Journal Industrial Hygiene and Toxi-
Counting Smoke Penetrometer," OEM cology, Vol. 28, p. 133 (1946).
Report No. sr-282, Contract 10-212, Aug. (9) B. Vonnegut and R. Neubauer, "Detection
31, 1945. and Measurement of Aerosol Particles by
(2) F. T. Gucker, Jr. and C. T. O'Konski, "An the Use of an Electrically Heated Fila-
Improved Photoelectronic Counter for Col- ment," Analytical Chemistry, Vol. 24, p.
loidal Particles Suitable for Size-Distribu- 1000 (1952).
tion Studies," Journal Colloid Science, Vol. (I0) L. B. Loeb, "The Basic Mechanisms of
4, p. 541 (1949). Static Electrification," Science, Vol. 102,
(3) A. L. Thomas, "Development of a Particle p. 573 (1945).
Counter," Final Report, Chemical Corps (11) W. B. Kunkel, "The Static Electrification
Biological Laboratories, Project 439, Re- of Dust Particles on a Dispersion into
port 5, Contract No. DA-18-064-CML- Cloud," Journal Applied Physics, Vol. 21,
2101 (1953). p. 820 (1950).
(4) F. T. Gucker, Jr. and D. G. Rose, "A (12) C. T. O'Konski, "New Instrumental Meth-
Photoelectronic Instrument for Counting ods in Aerosol Studies," Ph.D. Thesis,
and Sizing Aerosol Particles," British Jour- Northwestern University (1948).
nal Applied Physics, Supplement 3, p. s138 (13) F. T. Gucker, Jr. and C. T. O'Konski,
(1954). "Electronic Methods of Counting Aerosol
(5) M. A. Fisher, S. Katz, A. Liebeman, and Particles," Chemical Reviews, Vol. 44, p.
N. E. Alexander, "The Aerosoloscope: An 373 (1949).
Instrument for the Automatic Counting (14) M. Kerker, "Scattering Functions for
and Sizing of Aerosol Particles," Proceed- Spherical Particles of Refractive Index of
ings, 3rd. Nat. Symposium on Air Pollution, 1.46-4.30i," Journal, Optical Soc. America,
Pasadena, Calif., April 1955, p. 112. Vol. 45, p. 1081 (1955).
(6) E. S. Gordon, D. C. Maxwell, Jr., and N. E. (15) F. T. Gucker, Jr. and S. H. Cohn," Nu-
Alexander, "Aerosoloscope Counts Parti- mericaI Evaluation of the Mie Scattering
cles in Gas," Electronics, Vol. 29, No. 3, p. Functions; Table of the Angular Func-
188 (1956). tions ~r,, and rn of Orders 1 to 32 at 2.5
O'KoNsKI ET AL ON PARTICLE SIZE DISTRIBUTION 205
deg Intervals," Journal Colloid Science, (30) E. Fairstein, "A Sweep-Type Differential
Vol. 8, p. 555 (1953). and Integral Discriminator," Review Scien-
(i6) G. Mie, "Beitrgge zur Optik trfiber Me- tific Instruments, Vol. 22, p. 76I (1951).
dien speziell kolloidaler MetallCsungen," (31) N. F. Moody, W. D. Howell, W. J. Battell,
Annalen der Physik, Vol. 25, p. 377 (1908). and R. H. Taplin, "A Comprehensive
(17) F. T. Gucker, Jr. and D. G. Rose, "The Counting System for Nuclear Physics Re-
Response Curve of Aerosol Particle Coun- search," Review Scientific Instruments, Vol.
ters," Proceedings, 3rd. Nat. Symposium on 22, p. 551 (1951).
Air Pollution, Pasadena, Calif., April 20, (32) E. Fairstein and F. M. Porter, "Fast Dif-
1955. ferential Pulse Height Selector," Review
(18) V. K. LaMer and D. Sinclair, "Progress Scientific Instruments, Vol. 23, p. 650
Report on Verification of Mie Theory-- (1952).
Calculations and Measurements of Light (33) G. G. Kelley, "Pulse Amplitude Analyzers
Scattering by Dielectric Spherical Parti- for Spectrometry," Nucleonics, Vol. 10, No.
cles," OSRD Report No. 1857, U. S. De- 4, p. 33 (1952).
partment of Commerce, Report No. 944, (34) W. E. Glenn, Jr., "A Pulse-Helght Distri-
Sept. 29, 1943, p. B. bution Analyzer," Nucleonics, Vol. 9, No. 6,
(19) W. H. Rodebush, I. Langmuir, and V. K. p. 24 (1951).
LaMer, "Report on Filtration of Aerosols (35) A. B. Van Rennes, "Pulse-Amplitude Anal-
and the Development of Filter Materials," ysis in Nuclear Research IV. Multichannel
OSRD Report No. 865, Part V, U. S. De- Analyzers," Nucleonics, Vol. 10, Oct., 1952,
partment of Commerce, Sept. 4, 1942. p. 50.
(20) W. A. Higinbotham, "Precision Regulated (36) C. W. Johnstone, "A New Pulse Analyzer
High Voltage Supplies," Review Scientific Design," Nucleonics, Vol. 11, No. 1, p. 36
Instruments, Vol. 22, pp. 429-431 (1951). (1953).
(21) R. W. Engstrom, "Multiplier Phototube (37) D. Taylor, "Trends in Nuclear Instrumen-
Characteristics; Application to Low Light tation," Nucleonics, Vol. 12, No. 10, p. 12
Levels," Journal, Optical Soe. America, (1954).
Vol. 37, p. 420 (1947). (38) T. D. Strickler and W. G. Wadey, "An
(22) W. C. Elmore and M. Sanda, "Electronics," Automatic Recording Gamma-Ray Spec-
McGraw-Hill Book Co., Inc., New York, trometer," Review Scientific Instruments,
N. Y. (1949). Vol. 24, p. 13 (1953).
(23) F. T. Gucker, Jr. and A. H. Peterson, (39) J. W. Thomas, V. V. Verbinski, and W. E.
"Simple Circuit for Adapting Thermo- Stephans, "Pulse Height Analyzer," Re-
couple Recorders to Measure Voltage in view Scientific Instuments, Vol. 24, p. 1017
High Resistance Circuits," Analytical (1953).
Chemistry, Vol. 25, p. 1577 (1953). (40) W. C. G. Ortel, "A Multichannel Pulse-
(24) H. F. Freundlich, E. P. Hincks, and W. Z. Height and Delay Time Recorder," Re-
Ozeroff, "A Pulse Analyzer for Nuclear view Scientific Instruments, Vol. 25, p. 164
Research," Review Scientific Instruments, (1954).
Vol. 18, p. 90 (1947). (41) W. A. Hunt, W. Rhinehart, J. Weber, and
(25) C. H. Westcott and G. C. Hanna, "A D. J. Zaffarano, "A Multichannel Pulse-
Pulse Amplitude Analyzer for Nuclear Re- Height Analysis System Utilizing a 35-ram
search Using Pretreated Pulses," Review Film Record," Review Scientific Instru-
Scientific Instruments, Vol. 20, p. 181 ments, Vol. 25, p. 268 (1954).
(1949). (42) S. Seely, "Electron-Tube Circuits," Mc-
(26) J. E. Francis, Jr., P. R. Bell, and J. C. Graw-Hill Book Co., Inc., New York,
Gundlach, "Single Channel Analyzer," N. Y., p. 95 (1950).
Review Scientific Instruments, Vol. 22, p. (43) E. B. Bradford and J. W. Vanderhoff,
133 (1951). "Electron Microscopy of Monodisperse
(27) W. E. Glenn, Jr., "Pulse Height Distri- Latexes," Journal Applied Physics, Vol. 26,
bution Analyzer," Nucleonics, Vol. 4, No. 6, p. 864 (1955).
p. 50 (1949). (44) W. Heller, J. N. Epel, and R. M. Tabibian,
(28) K. I. Raulston, "A Simple Differential "I.--Experlmental Verification of the Mie
Theory of Light Scattering," Journal Chem-
Pulse Height Analyzer," Nucleonics, Vol. 7, ical Physics, Vol. 22, p. 1777 (1954).
Oct., 1950, p. 27. (45) C. T. O'Konski and W. I. Higuchi, "Ki-
(29) H. O. Anger, "New Type Counting-rate netics of Nucleation in Turbulent Jets,"
Recorder," Nucleonics, Vol. 8, No. 2, p. 76 Journal of Physical Chemistry, Vol. 60, p.
(1951). 1598 (1956).
(46) G.J. Doyle and N. A. Renzetti, "Electronic and Size Distribution," Handbook of Aero-
Light Scattering Aerosol Analyzer Studies sols, Atomic Energy Commission, Wash-
of Air Pollution," Air Pollution Control ington, D. C., Chapter 8 (1950).
Association, Semi-annualTechnical Confer-
ence, Nov. 18-19, 1957, San Francisco, (48) L. R. Hafstad, "Applications of the FP-54
Calif., p. 82-92 (1957). Pliotrons," PhysicalReview,Voh 44, p. 201
(47) D. Sinclair, "Measurement of Particle Size (1933).
T U R B I D I M E T R I C P A R T I C L E SIZE D I S T R I B U T I O N T H E O R Y :
A P P L I C A T I O N TO R E F R A C T O R Y M E T A L
AND OXIDE POWDERS
BY ALLAN I. MICHAELS 1
SYNOPSIS
An industrial survey of particle size methods currently in use and a corre-

lation study on a group of tungsten metal powders were conducted to establish
the present state of affairs in the refractory metals industry. Results indicate
a wide diversity of techniques and no correlation between measurements, and
confirm the need for standardization in the measurement of the partide size
distribution of refractory metal powders. The turbidimetric sedimentation
technique is concluded to be most suitable for these powders.
The theories of turbidimetry, sedimentation, and turbidimetric sedimenta-
tion are thoroughly reviewed and the sources of error inherent in each are ana-
lyzed. The author concludes that the errors arising in the turbidimetric sedi-
mentation analysis of refractory metal powders tend to compensate each
other, giving a measured distribution which differs from the true value only by
an overestimation of the per cent weight in the 1 to 8 # size range.
The causes of poor correlation between measurements obtained on refrac-
tory metal powders by different laboratories are discussed. Various methods for
deagglomeration and suitable sedimentation media are described.
I n seeking to acquire accurate and Based upon the processing require-

reproducible methods for the measurements and physical properties of refrac-
ment and control of particle size, nearly tory metal powders, certain methods
every physical and chemical approach have been selected and developed, from
has been investigated and a long list of the m a n y available, which give the maxi-
instruments has been developed. One m u m useful information achievable with
salient fact has become evident, namely, the present state of knowledge.
that no technique or instrument can be The chief characteristics of these pow-
applied with equal success to all mate- ders which have been considered in the
rials, or, conversely, that each material selection of particle size techniques are
must be treated as a separate problem the presence of m a n y strongly sintered
requiring for solution one or more tech- agglomerates (1,2,3), 2 the extreme fine-
niques peculiar to itself. ness of the powders (largely below 10 ~),
1 Physicist, Metallurgical l~esearch Labora-
tory, Sylvania Electric Products, Inc,, Towanda, 2 The boldface n u m b e r s in parentheses refer
Pa. to the list of references appended to this paper.
207
Copyright* 1959 by ASTM Intemational www.astm.org
208 S Y Y I P 0 S l U M ON P A R T I C L E SIZE MEASUREMENT
and the fairly compact shape of the par- technique, while used extensively for
ticles (4). refractory metal powders, is limited in
Because of these special characteris- value since it gives only an average par-
tics, sedimentation methods, especially ticle size.
in liquid media and usually with very A broad variety of sedimentation
elaborate dispersion techniques, have methods are used in the refractory metal
come to dominate in the determination powders industry. These methods break
of the particle size distribution of refrac- down essentially into three classes:
tory metal powders. The compact shape cumulative weighing, direct incremental
of the particles is a good approximation sampling, and turbidimetric measure-
of the spherical shape assumed in Stokes' ment. Of these three, the turbidimetric
law and the ability to disperse and main- approach, probably because of its sim-
TABLE I.--SUMMARY OF REPLIES TO QUESTIONNAIRE.
Reproduci-
Modi- 9 Analysis bility, per cent
Company Instrument Used Range,
Number fied? Sample Size, g Time, min
>5~
No. 1 .... Photelometer No 1 t o 20 0.02 120 t o 180 10

No. 2 .... Photelometer Yes 1 t o 30 9.01 to 0.05 20
No. 3 .... Photelometer Yes 1 t o 50 0.02 30 t o 6 0
10
No. 4 .... Photelometer Yes 0 . 5 t o 10 <0.10 45 5
No. 5 .... Eagle-Picher No 1 . 5 t o 16 0.05 90
No. 6 .... Klett-Summerson Yes i t o 35 0 . 0 5 t o 0 . 1 5 20 t o 12C i,o
10
No. 7 .... Laboratory con- 0 . 2 t o 44 0 . 3 0 t o 0 . 5 0 ' 1 2 0 t o 180 Fair
structed
No. 8... Beckman B Yes 0 . 3 t o 15 0.10 60 t o 120
No. 9... Microscope
No. 10... Microscope
Roller analyzer
tain dispersion in a liquid medium en- plicity, rapidity, and small sample re-
ables some consistency to be achieved quirements, has become the most popu-
with respect to the degree of agglomera- lar.
tion measured. Recognizing the importance of corre-
Other techniques do not appear to be lating measurements between refractory
as satisfactory. The microscope loses metal powder producers and fabricators,
resolution at the finer end of the distri- Subcommittee II (Section B) on Refrac-
bution and, because of the spread of tory Metal Powders of ASTM Commit-
sizes encountered, requires excessively tee B-9 on Metal Powders and Metal
long counting times. In addition, the Powder Products has concerned itself
extreme agglomeration of these powders with the problem of establishing stand-
makes any microscopic count largely a ard procedures for particle size measure-
matter of guesswork. Elutriation meth- ments. The subcommittee appointed a
ods have the drawbacks of requiring task force on turbidimetric analysis to
large samples and of variable deagglom- study the problems of standardizing the
eration of the powder. The permeability method of turbidimetric sedimentation
MICHAELS ON DISTRIBUTION THEORY 209
TABLE II.--MODIFICATIONS MADE IN gree of correlation possible with existing

FIVE COMMERCIAL INSTRUMENTS.
techniques.
Instrument Modifications Twelve companies replied to the ques-
tionnaire. Of these, eight used some form
Automatic continuous
r e c o r d i n g (2).
of turbidimetric sedimentation, while
Increased distance be- four relied on microscopic counts. Of the
P h o t e l o m e t e r (3 m o d -
tween light source eight turbidimetric sedimentation instru-
ified) . . . . . . . . . . .
a n d cell.
S p r i n g s f o r h o l d i n g cell ments, seven were commercial (four were
fixed i n l i g h t b e a m . the Cenco photelometer) and one was
Klett-Summerson
p h o t o e l e c t r i c col- laboratory constructed. Five of the seven
orimeter ......... Slit size r e d u c e d a n d p o - commercial instruments had been modi-
tentiometric circuit
changed. fied to some extent. This information is
Beckman model B.. Cell h o l d e r a n d slit m o d - tabulated in Table I along with each
ified.
company's estimate of the range, sample
TABLE III.--SAMPLE PREPARATION METHODS AND MEDIA USED.
Number Medium Number

Preparation Method of Users of Users
None ......................................... ethyl alcohol ...........

S c r e e n i n g t h r o u g h N o . 325 sieve . . . . . . . . . . . . . . . . . acetone ...............
A g i t a t i o n in m e d i u m of a p r e v i o u s l y m i l l e d p o w d e r . . water .................
H a n d s p a t u l a t i o n of p o w d e r w e t t e d w i t h m e d i u m . . butyl alcohol ..........
G r i n d i n g in m o r t a r a n d p e s t l e . . . . . . . . . . . . . . . . . . . kerosene ..............
Spatulated between lapped carbide blocks ......... methyl alcohol .........
Light mortar and pestle then hand spatulated ..... xylene ................
dibutyt phthMate ......
and to initiate programs for the achieve- size, analysis time, and reproducibility of
ment of this end. their instrument.
The purpose of this paper is to outline Table II lists the modifications made
the work of this task force, to review in five of the commercial instruments
the principles, techniques, and problems and Table III gives the various sample
of turbidimetric sedimentation, and to preparation methods and sedimentation
present the most recent results obtained media used.
ill the laboratories of various cooperating As anticipated, considering the variety
companies. of techniques reported, the attempt at
obtaining some correlation of particle
EXTENT OF T H E P R O B L E M size measurements between companies
was a failure. Six companies made dis-
To evaluate the existing situation in
tribution measurements on four different
particle size measurement of refractory
sized tungsten metal powders (nominal
metal powders, a questionnaire was sent
sizes 1.5, 2.5, 6 and 10/z) using some form
to interested companies requesting in-
of turbidimetric sedimentometer. A sum-
formation on the particle size measure-
mary of the results is given in Table IV
ment techniques currently in use. In a
second study, six companies measured and the distribution curves are shown in
the particle size distribution of four tung- Figs. 1 (a, b, c, d).
sten metal powders to determine the de- Upon examining these data, it is ap-
210 SYMPOSIIY2Cf O N PARTICLE SIZE M E A S U R E M E N T
parent that the distributions measured parently must be surmounted in achiev-

on the same powders by different coming standardization of this technique,
panies are widely divergent. We may the question arises as to the specific
note also that the measurements do not problems and ultimate worth of the
maintain a consistent relative order. turbidimetric sedimentation method of
Company 1, for instance, obtained the particle size analysis. To answer this
coarsest distribution on the finer 1.5 and fully, it will first be necessary to review
the principles and sources of error of
T A B L E I V . - - S U M M A R Y OF D A T A F R O M turbidimetric sedimentation and then to
CORRELATION STUDY.
consider in turn the variations arising
Particle Size Distribu- from sample preparation methods, media
tion, weight per cent
Powder Com- Average
used, and other operational variables.
pany Size,a Iz
Less 1 to Above THEORY OF TURBIDIMETRY
than 10 ~ 10
Particles which are small compared to
l 1 8.0 6.0 51.0 43.0 the wavelength of light have an absorb-
2 1.2 36.0 64.0 0.0 ency in accordance with Rayleigh's law.
3 6.0 2.5 67.5 30.0
1.5/z. " " ' 4 0.5 80.5 19.5 0.0 The size below which such transmission
5 3.0 10.0 90.0 0.0 begins is given as about 0.1 ~ by Dalla-
6 2.2 1.7 96.7 1.6 valle (S), 0.5 v by Schweyer and Work
(6), 0.6 ~ by Stutz (7/, and 2.0 /~ by
t 1 9.0 0.5 53.5 46.0
2 2.3 3.0 97.0 0.0 Richardson (8,9). That such determina-
3 7.0 0.8 69.2 30.0
2.5/z. 9 " " 4 1.8 17.0 83.0 0.0 tions are highly dependent upon the op-
5 5.0 0.5 99.5 0.0 tical geometry of the instrument used is
6 3.1 3.0 96.4 0.6 indicated by the work of Skinner and
Withers (10).
.(1 1 9.0 0.3 51.7 48.0
2 4.4 0.8 91.2 8.0 The relation which governs the trans-
3 16.0 0.0 25.0 75.0 mission behavior in this region for a uni-
6.0 t~. 9 ' 4 3.9 2.5 95.5 2.0
5 7.6 0.0 62.0 38.0 formly sized suspension of particles is
6 8.2 0.0 60.8 39.2 given by Gamble and Barnett (11) as:
f 1 16.5 0.0 20.0 80.0
7.5 0.3 85.0 14.7 I = I0exp --kn ........ (1)
19.5 0.0 6.0 94.0
10.0~ . . . . 4 7.3 0.8 83.0 16.2
65 19.0 0.0 10.0 90.0
where:
12.2 0.0 33.3 66.7
I, I0 = transmitted and incident light
a Average size is the weighted m e a n size com- intensities,
p u t e d from the distribution. k = constant involving the refractive
indices,
2.5 v powders, while company 3 rated n = number of particles per unit
coarsest on the 6.0 and 10.0 ~ powders. volume,
Obviously, the differences in techniques v = volume per particle, and
can affect a distribution measurement to X = wavelength of light.
an almost unlimited degree as can be
seen in the data on the 1.5 ~ powder Examining this expression, we note
where companies 3 and 6 report 2.5 per that the transmission is dependent on
cent or less, and company 4 reports 80 the fourth power of the wavelength and
per cent below 1 ~. inversely dependent on the sixth power
Considering the difficulties which ap- of the particle diameter (square of the
I00
90
80
70
60
50
40 Coh~pony Symbol
.~ 30
2 x
u- 20 3 o
4 []
,o 5 a
~__~o 6 v
.~ ioo
"6 9O
80
o
70
60
50
40
30
I0
I I I I I E I I I
O0 5 I0 15 20 25 30 35 4010 5 I0 ,5 2'0 3'o 35 4o
Diameter,/z
Fro. 1.--Correlation Study.
(a) 1.5-/~ tungsten m e t a l powder.
(b) 2.5-/~ t u n g s t e n m e t a l powder.
(c) 6.0-/* ~ungsten m e t a l powder.
(d) 10.0-~ t u n g s t e n m e t a l powder.
approaches zero. The strong inverse de-

41|11 9 Glass Spheres
3 ~^
"O A Desert Sand I pendence of the transmission on the
~ 9 Ground Silica Sand J particle diameter in this region has been
o 2 ~' ~ .... x Polystyrene Spheres I
confirmed by other researchers (5,12,13).
For particles which are very much
larger than the wavelength of light,
i?l OI '1 I I I I I I [ I I
0 5 101520 30 40 50 60 70 80 transmission is generally considered to
Diameter, p. be governed by the "square law" of geo-
Fzo. 2 . - - P l o t of Extinction Coefficient v e r s u s metrical optics in which the light blocked
Particle Size. is proportional to the projected cross-
Solid line is based on experimental data; dot-
ted line is the theoretical curve. sectional area of the suspension of par-
ticles. With particles greater than 1 v,
particle volume). Consequently, longer the transmission has been shown to be
wavelengths will be transmitted more independent of wavelength (6,7,14,15).
freely and the total absorbency will de- The over-all transmission behavior of
crease rapidly as the particle diameter particles from near zero up to very large
sizes has been studied by Rose (13). Defin- using Cauchy's relation for irregularly
ing the absorbency in terms of an extinc- shaped, randomly oriented particles:
tion coefficient which gives the relative
A = 88 . . . . . . . . . . . . . . (3)
blocking power of various sized particles
as compared to the theoretical "square where So = surface area per gram of
law" value, he measured the extinction particles in the light beam. This gives us:
produced by a group of different size
Io Socl
powders. log T ---- ~ ............. (4)
The experimental plot of extinction
coefficient versus particle size which he In the most usual case however, a
obtained is given in Fig. 2 along with suspension of particles is not uniform
the theoretical curve for this quantity. but contains a distribution of sizes. A
The two curves coincide below 12 ~. more complete description, applicable to
Examining this figure we observe that a nonuniform distribution of particles, is
extinction is a maximum of 4 at about given by Rose (13) as:
1 ~, falling off below this value and going d
to zero in accordance with Rayleigh's log ~Io = Kcl ~0 K~nfl~ 2. . . . . . . (5)
law. Above 1 ~ the behavior is erratic,
the extinction coefficient rapidly falling where:
to a value of 2, rising to 3 and returning I 0 , I = incident and transmitted light
again to 2 at about 8 u- I t remains at 2 intensities,
and then gradually decreases (experi- K = constant,
mental curve) to approach the theoretical c = concentration of particles in the
value of 1 at about 80 u. light beam, g per cu cm,
The expression for the transmission of l = length of light path, cm,
light through a uniform suspension of K~ = Rose's extinction coefficient,
particles which is generally used (6,14,15) which equals the ratio of the
is a form of the Lambert-Beer law written actual obscuring power of a
as: particle of size d. to what it
log Io = A cl . . . . . . . . . . . . (2)
would be according to the
I "square law" of geometrical
optics,
where: n~ = number of particles of size d~ per
I , I0 = transmitted and incident light g of powder, and
intensities, d -- maximum size particle in the sus-
A = projected area per gram of par- pension, cm.
ticles in the light beam, and in- Comparing this to Eq 2 we see that
cludes all the optical factors in- d
volved, K ~ , n~d~ is related to the projected
0
c = concentration of particles, and area A, the extinction coefficient K~
l = length of light path.
converting it from the theoretical to the
With the modification of A in accord- true light blocking value. Since Cauchy's
ance with Rose's variable extinction co- relation connects the geometrical pro-
efficient, Eq 2 is applicable to any uni-
jected area of a suspension of particles
formly sized suspension of particles. to its specific surface we may write:
Equation 2 may, according to Hey-
wood (16) be converted to an expression a 1
K ~ n,d~ = ~ So . . . . . . . . . . (6)
for the specific surface of the particles by 0
~/~ICHAELS ON D I S T R I B U T I O N T H E O R Y 213
Let us consider now a suspended dis- 1

s~ - (log I1 - log 12) . . . . . . (9)
tribution of particles containing sizes K,~C1
between dl and d2 only, where dl < d2.
For this case the right side of Eq 5 be- where:
comes: Sm = total surface area of particles be-
d2 tween dl and d2 in diameter, and
Kcl Z K*n~'d*2 C a = proportionality constant.
dl
The surface area Sm of particles be-
which is related to the light blocked by
tween d~ and d2 in diameter in a suspen-
the suspension of particles between d~
sion has been shown (17,18) to be related
and d~ in size. This, however, is equiva-
to the weight of these particles, by the
lent to the differences in the amount of
expression:
light which would be blocked by a sus-
pension containing particles from 0 to da W m = Kidd,S . . . . . . . . . . . . . (10)
and one containing particles from 0 to
where:
d2. Thus:
d2 d2 Wm = weight of particles between d~ and
d2 in the suspension,
d1 0 K 1 = constant related to shape of par-
dr ticle, and
-- K d ~ K~u~d~2 d~ = mean particle size of the size in-
0
d l + d2
Io Io terval dl to d2 -
= ] o g ~ -- log I~ 2
We then have from Eqs 9 and 10
which reduces to:
d2 Cd,~
w~ = ~ 0og I1 - log I2) . . . . . (11)
Kcl Z K~n~d~ = log Ix -- log I2 .... (7)
di
K1
where I t and I~ are the transmitted light where C = constant -
C I"
intensities through the 0 to d~ and 0 to
d2 suspensions respectively, I1 > I 2 . Eq 11 states that the log difference in
If the interval dt to d2 is taken small the light transmitted through a suspen-
enough, the extinction coefficient m a y sion of particles up to d2 in size, and
be considered constant over the interval through one from which all particles be-
and factored out of the summation. Do- tween da and d2 have been removed, di-
ing this and also using Eq 6 we get: vided by the mean extinction coefficient
and multiplied by the mean size of the
Sod
K~ ~ - = log It - log I2 . . . . . . (8) removed particles, is proportional to the
weight of the removed particles. If such
where K m = the mean value of the ex- a measurement is made for every size
tinction coefficient in the size interval interval in the suspension, then the per
from da to d2. cent weight of each size interval in the
Sod . distribution is given by:
The term ~ is proportional to the
total surface area of all particles between d~ (log I~ - log 12)
Km
d~ and d~ in the suspension. Thus Eq 8 Per cent W~ = ...(12)
m a y be rewritten as: ~'~
K~
(log I1 - log I5)
214 SYm, OSllm ON PARTICLE SIZE MEASUREMENT
Actually it is a more common practice, sedimentation regions are not absolutely

in measuring particle size distribution, defined but vary with the material and
to assume that the extinction coeflScient medium employed.
is a constant independent of particle The turbulent region, described by
size. Thus Wagner (17), States (19), and Newton's law of turbulent motion, is
Kopelman and Gregg (2) use the forms: defined by Davies (20) as involving
Reynold's numbers of the order of 80 and
W,~ = C&,~ (log I1 - log I~)
larger. Dallavalle (S) gives it as including
&~(log I1 - log 12) particle sizes over 2000 ~. Since refrac-
Per cent W,, = E d~(log I1 -- log I2)" (13) tory metal powders seldom exceed 40
in size, this region of behavior is outside
C our sphere of interest.
where C = constant = ~ of Eq 11.
The region of transition flow is stated
This assumption introduces large in- by Dallavalle (5) to extend from the
accuracies into the results but does not turbulent region down to 85 u for quartz
seriously affect comparative measure- (density 2.6 g per cu cm) in water. Davies
ments made on similar materials for the (2o) defines it as including Reynold's
purpose of determining relative fineness. numbers between 0.5 and 80, and has
developed the following empirical equa-
T~IEOgY o ~ SEDIMENTATION
tion for the terminal velocities of spheres
A solid particle falling in a medium of falling in any fluid, which is valid for
lesser density rapidly accelerates to a values of Re less than 4.
terminal velocity, descending thereafter
Re2
at this constant rate, determined, for a Re = ~ ~ - -- 2.336 X 10-4(~/'R~) 2 + 2.015
particular medium, by the size and den-
sity of the particle. There exist three X 10-~(r 3 -- 6.911 X 10-9(~bR,2)'.. (15)
distinct modes of fall; the viscous, tran-
sition, and turbulent, which are defined where:
by (1) purely viscous, (2) a combination
of viscous and inertial, and (3) purely ~b = drag coefficient = 4 d ( ~ - - o)G
3pv 2
inertial resistance forces respectively.
The limits of each of these regions are
determined by Reynold's number which and Re -- the Reynold's number - vdp
is related to the velocity of the particle giving:
with respect to the medium, to the size
of the particle and to the viscosity and 4#(~ - p)pG
~R.' . . . . . . . . . . (16)
density of the medium as follows: 372
vdo where:
d = diameter of the spherical par-
ticles,
where:
v = terminal velocity,
R, = Reynold's number, ~, p = density of particle and fluid re-
v, d - - t e r m i n a l velocity and diameter spectively,
of the particle, = viscosity of fluid, and
p -- density of the medium, and G = gravitational acceleration.
= viscosity of the medium.
Since ~bR,~ involves only the physical
Thus the diameter limits of the various constants of the fluid and particle, Eq
15 m a y be solved for Re, from which where K~ = constant dependent on

the terminal velocity for a given sized a
particle m a y be directly determined. shape = h7 G.
For a given material and medium the 7r/6 G
maximum size particle for which Eq 15 For spheres Ks - 3rr G = ~ and
is valid, is that size corresponding to a Eq 19 reduces to the familiar form of
Reynold's number of 4. Thus for quartz, Stokes' taw for sedimenting spherical
of density 2.6 g per cu cm, the maximum particles:
size would be 104 u in air or 190 ~ in
water. For particles of density 14 g per d~(~ - o)G
v- . (20)
cu cm the maximum limits are 58 ~ in 187
air and 92 # in water. I t should be noted that in this small
For particles which are small enough, particle size region, the higher power
we leave the transition zone and enter a terms in Davies' (so) empirical equation
region where resistance forces are purely
viscous, flow is streamlined and the fluid TABLE V.--PER CENT ERRORS IN
motion occurs relatively far from the S T O K E S ' L A W F O R P A R T I C L E S OF V A R I -
OUS D E N S I T I E S A N D SIZES S E T T L I N G
particle. IN WATER.
The expression for sedimentation in
M a x i m u m Diameter in Microns
this viscous region is derived (21,13,5) for Accuracies of:
from Stokes' law for the resistance ex- Particle Density in g
perienced by a particle in streamline per cu cm lO I 5 I 1
Per Cent I Per Cent [ Per Cent
flow given as: (R,= / (eo= I (e,=
0.82) [ 0.38) 0.074)
R = Kdv~ . . . . . . . . . . . . . (17)
where: 5.0 ............. 7s / s7 r 33
10.0 . . . . . . . . . . . . 57 / 4a / 2s
R = resistance to flow, 14.0 . . . . . . . . . . . . sx / as [ 22
K = constant dependent on shape of
particle = 3 ~r for a sphere, and (Eq 15) vanish and the equation reduces
d, v, ~ as previously defined. to:
For a particle falling in a medium ~R, 2
Re = - - . . . . . . . . . . . . . (21)
which is at rest, the net force on the 24
particle due to gravity and buoyancy is:
Substituting the values of R , , and
F = o~dS(~ -- p ) a . . . . . . . . . . (18)
r 2 from Eqs 14 and 16 we get:
where:
d~(, - p)G
F = net force, V
18.q
a = volume factor = z c / 6 for a sphere,
and which is identical to Eq 20 above.
other symbols as previously defined. The size at which the purely viscous
When the particle reaches its terminal region described by Stokes' law (Eq 20)
velocity all forces are in equilibrium. begins has been set by Dallavalle (.5) at
Thus F = R and we get from Eqs 17 about 85 v for quartz (density 2.6 g per
and 18 the expression for Stokes' law of cu cm) settling in water. Davies (20)
sedimentation: states that pure viscous flow begins at
Reynold's numbers below 0.5. He has
v=K,(~Z~-)d2 ......... (19) calculated the maximum size particles
which obey Stokes' law to accuracies
216 SYMPOSltrg ON PARTICLE SIZE MEASUREMENT
within 1, 5, and 10 per cent; in air and h, into the light beam. No other particles
in water for various particle densities. of this size will then be above the level
Table V gives a partial list of his com- of the beam. Consequently, when the
puted values for the case of sedimenta- last dm~x particles settle below the beam,
tion in water. the concentration in the beam will have
With molybdenum (density 10.3 g per decreased, and the light intensity will
cu cm), for instance, we would expect a have increased by an amount related to
minimum accuracy of 5 per cent for the the initial concentration of all dm,~xpar-
coarsest material (about 40 ~) usually ticles in the suspension. The slower mov-
encountered, while for tungsten (density ing, smaller particles from the top surface
19.3 g per cu cm) the 5 per cent accuracy of the suspension will still be above the
extrapolates to approximately 35 ~. beam level and will continue to replace
particles of the same size which descend
PRINCIPLES O F TURBIDIMETRIC
below the beam.
SEDIMENTATION
A second reduction of concentration
Theory: and increase in light intensity at the
Turbidimetric sedimentation is a non- photocell will occur for the next smallest
contact, incremental sampling, sedimen- size particle at a time h (ll > l) required
tation process involving the combination for it to fall a distance h from the top
of the two methods of turbidimetry and surface of the suspension, and, similarly,
sedimentation described above. for each additional size in the distribu-
In this technique, a small sample of tion, at the appropriate times. The differ-
the powder to be studied is dispersed in ence in the light intensities registered at
a liquid medium contained in a fiat, the photocell at any two times 11 and t2
parallel faced glass cell. A thin, approxi- (t2 > ll) corresponding to particles of
mately parallel beam of light, originating sizes dl and d~ (dl > d2) is therefore
in a bulb, lens, and slit system, passes related to the initial concentration of all
through the cell at a height h below the particles between d2 and dl in size in the
surface of the suspension and falls, suspension. The relationship is as given
through an additional slit (and some- in Eq 13, assuming the constancy of the
times lens) system, upon a photocell extinction coefficient. Thus for the sizes
whose output is registered on a meter or dl to d2 we have:
recorder. W~12 = Cd,~a2 (log 12 - log 11) . . . . . (22)
Initially the dispersion of particles is where:
uniform throughout the cell. As sedi-
mentation proceeds, the distribution of Wml~ = the weight of all particles be-
particles in the light beam, and thus the tween d2 and dl in size in the
light intensity at the photocell, remains suspension,
unaltered for a period of time since each din12 = mean size of the d2 to dl size
particle falling below the beam is re- d2 + dl
interval = . - -
placed by an equal size one falling into 2 '
the beam from above. 11 = light intensity at the photocell
The rate of fall of the particles, gov- at time l~ when all particles
erned by Stokes' law (Eq 20), is propor- greater than dt have settled be-
tional to the diameter squared, so that low the light beam, and
larger particles fall more rapidly. At some I2 = light intensity at time h when
time t, the largest particle, d . . . . . in the all particles greater than d2 have
distribution will have fallen from the settled below the light beam,
top surface of the suspension a distance, Is > 11.
The per cent weight expression for this stant voltage to the light source, Lt. The
size interval becomes: light passes through a heat filter, F, then
through an iris diaphragm, I and lens,
dm12(log I s - - l o g 11)
P e r c e n t W~12 = E d.aj(log I i - tog I i )
.(23) L, which produces an approximately
parallel beam, defined by slit, $1, of
where: width 0.1 cm. This thin beam then passes
through the sedimentation celt, S, is
dmii = the mean size of the interval limited by shielding slit, $2, of width
dj to d~ (d~ > d~.), 0.3 cm and falls on the photocell, Pc.
di + di The current output from the photocell is
- 2 , and
taken through a potential divider to
r P lL
H
sI 5z M
FIG. 3.--Schematic Diagram of the Cenco Photelometer.
TABLE VI.--TIME OF FALL IN MINUTES AND SECONDS.

Fine tungsten, d e n s i t y , 19.3 per cu cm, in distilled water
Temperature,
deg Cent
Diameter.. i# 2# 3# 4# 5# 6# 8# 10# 12# 14# 16#
20 31 a - 26 5 7 - 52 3 - 30 1 - 58 I - 15 52 29 19 13 I0
25 27 - 58 7 - 0 3- 7 1 - 45 1 - 7 47 26 17 12 9
30. 25 - 3 6 - 16 2 - 47 1 - 34 1 - 0 42 24 15 10 8
35. 22 - 37 5 - 39 2 - 31 1 - 25 54 38 21 14 9 7
a Minutes.
b Seconds.
I.i, I i = light intensities at times when microammeter, M , which has a 15-#a

all greater than di and all full scale (100 divisions) deflection.
greater than di particles re- Procedure:
spectively have settled below
the light beam. The first step in making an actual
particle size determination is to calculate
The summation is taken over all size the time schedule for measurements. I t
intervals in the distribution. is customary, with refractory metal pow-
ders, to take readings at 1 or 2 u inter-
A pparalus:
vals for particle sizes up to 20 u and at
The Cenco photelometer, which may larger intervals for the coarser sizes.
be taken as a prototype of turbidimetric A particle settling at a terminal veloc-
sedimentation instruments, is basically ity, v, will fall the distance, h, in a time,
constructed as shown in Fig. 3 (taken t, given by v = hit. Using this and solv-
from States (19)). ing Stokes' law, Eq 20, for the time of
The transformer, T, supplies a con- fall, we get, in the usual set of units,
with d in v, t in sec, ~ in poise, h in cm, as the recorder pen stabilizes. Using a

and p in g per cu cm and g = 980 cm meter, it is customary to take the first
per sec per sec: reading at a predetermined size which
experience has indicated is the largest
18 X 10S~h
t - (24) particle size present to a significant de-
d2(~- p)G
gree. With most tungsten powders this
Using Eq 24, the time at which all top size is 20/z or less.
particles of each size interval will have Although the temperature is not usu-
settled the distance h (to the light beam) ally controlled, it should be read imme-
is calculated, and readings are taken at diately before and after the run with too
these times. Table VI is an example of large a change invalidating the data.
such a time schedule, calculated for fine Readings are made at the calculated
tungsten powder in distilled water. The times and recorded. The differences be-
height of fall, h, used was 1.87 cm. tween the logs of adjacent readings are
computed. Each difference value is mul-
7O tiplied by the mean diameter of the cor-
Tungsten Types responding particle size interval and is
~
MIO * divided by the sum of all such products
M 2 0 >~
.o_ MSO o to obtain the per cent weight for each
M40 particle size interval. The data is usually
M50 ,
plotted as per cent weight versus mean
interval diameter and the points joined
~=.-_ Ill/ J\ ' by straight lines. A cumulative weight
,\ curve can also be plotted.
Typical distributions are shown in Fig.
0 I 2 5 4 5 6 7 8 9 I0 4 in which the average distributions ob-
Diameter, if,
tained on five standard Sylvania tung-
FIG. 4.--Particle Size Distributions of Five sten metal powders are plotted.
Standard Tungsten Metal Powders.
SOURCES OF ERRORS AND VARIATIONS
The powder is next treated according Errors Inherent in Turbidimetric Meas-
to a previously determined "best" de- urements:
agglomeration scheme and then placed The Lambert-Beer law, given in Eq 2
in the chosen medium (if not treated in as:
the medium), shaken vigorously, and the
proper volume transferred to the sedi- tog lo = Acl
mentation cell. The cell is shaken, placed I
in the light beam, and a reading taken.
requires that, for a suspension of a par-
I t is general practice to add powder or
medium to the suspension to bring the ticular material, log I0 be proportional
initial reading close to 30 per cent of full
scale deflection (the transmission through to c and to 1. This proportionality was
the clear medium having been previously established by Skinner and Boas-Traube
adjusted to give a full scale deflection). (14) who found that, for silica, the quan-
The cell is again shaken, to provide an tity
initially uniform suspension, a timer
started (at the instant shaking stops), log~~ constant ~---2100
and the cell put back into the light beam.
With a recorder, readings start as soon for concentrations c of 1.083 X 10-a g
per cu cm and 3.264 X 10-4 g per cu cm which occurs at high concentrations.

and for path lengths l varying from 1.03 However, with the photocell subtending
cm to 4 cm. For carbon black the same a sufficiently small solid angle, most of
authors found that this quantity re- this forward scattered radiation is pre-
mained constant at about 19,000 for a vented from reaching the photocell and
concentration of 1.112 >( 10~5 g per cu the relation remains linear to much
cm and path lengths from 1.03 cm to 4 higher concentrations.
cm. Confirmation of this effect is given by
In addition they determined the con- Skinner and Boas-Traube (14). They dis-
I0 / covered that removing the shielding slit
stancy of the quantity log 7 / c for con- in front of the photocell of their instru-
centrations ranging from 3.641 >( 10-5 ment increased the measured transmis-
to 27.65 X 10-5 g per cu cm for silica, sion through a silica suspension from the
and from 4.116 X 10-6 to 3.096 X 10-5 original 75 up to 83 per cent, which is
g per cu cm for carbon black. equivalent to a specific surface decrease
Schweyer and Work (6) state that their from 31,500 to 20,400 sq cm per g. They
experiments on ground materials of then measured the transmission of two
widely differing particle size have con- materials on a standard apparatus, with
firmed the linear relation between log a parallel light beam and small sub-
Io/I and cl, provided I/Io is not less than tended solid angle, and on an instrument
30 per cent. At below 30 per cent trans- in which the beam was not truly parallel
mission they suggest a breakdown due and the photocell unmasked. The read-
to forward (multiple) scattering. ings obtained were 36,500 and 29,000 sq
Rose and Lloyd (22) confirm the linear- cm per g respectively for ground coke,
ity of the Lambert-Beer law, but main- and 8100 and 6000 sq cm per g respec-
tain that its validity extends to as high tively for silica powder.
as 99.5 per cent extinction and this view A similar study was made by Rose (13)
is supported by Skinner and Boas- on silica powder, ilmenite, and zircon.
Traube (14). An additional confirmation With a subtended solid angle of 0.00024
is provided by Talvitie and Paulus (18) solid radians, he found that for silica the
who found no deviation from linearity Lambert-Beer law remained valid up to
for a wide range of concentrations of 0 Io/I = 103 (c ~ 0.2 g per liter). When
to 3--~ quartz suspended in water. the solid angle was increased to 0.0115
The disagreement between the various solid radians, the relation became non-
authors cited regarding the upper con- linear at Io/I> 10 (c > 0.05 g per liter).
centration limit at which the Lambert- With a subtended angle of 0.00024
Beer law breaks down clearly arises from solid radians, the equation was obeyed
differences in the optical geometries, and up to Io/I ~ 106 for ilmenite and to only
especially in the solid angles subtended I o / I = 103 for zircon. Since the black
by the photocells, in the instruments ilmenite would naturally give rise to less
used. Schweyer and Work (6), for in- scattered radiation than the white zircon
stance, used an instrument in which the powder, this is a clear indication of the
photocell subtended a solid angle of 0.02 effect of forward scattering upon the
solid radians, while in Rose and Lloyd's linearity of the transmission-concentra-
(22) apparatus the solid angle subtended tion relation.
was only 0.0009 solid radians. Rose states the opinion that, for ac-
The deviation from linearity arises curate results, the solid angle subtended
from the forward (multiple) scattering should have a maximum value of 0.00024
solid radians. The Cenco photelometer, give relative opacities of 60 and 80 per
it should be-noted, has a rather large cent respectively.
subtended angle of the order of 0.05 solid The deviation in the blocking power
radians. However the requirement of an of a particle from the gedmetrical square
initial transmission of 30 per cent, as law was previously discussed in the
stipulated in the operating procedure sec- theory of turbidimetry section, and is
tion, limits the deleterious effects of for- taken into account by the size dependent
ward scattering. A smaller shielding slit extinction coefficient k, of Rose's (13)
is also easily installed. form of the Lambert-Beer law, Eq 5.
A further source of error in the Lam- If the simplified assumption of a size
bert-Beer relation can arise from trans- independent extinction coefficient is
parency of the particles in the suspension. made, as is customary, this will introduce
For a spherical, transparent particle, the large inaccuracies into the measured dis-
solid angle, a, of the cone of rays which tribution. For instance, were a constant
leave the particle, after having been extinction coefficient value of 2 chosen
transmitted through it, is given by Rose (referring to Fig. 2) we note that the
(13) as:
TABLE VII.--PER CENT ERRORS IN
a = 2 tan -1 2(u~ -- u~) ....... (25) S T O K E S ' D I A M E T E R S AS A F U N C T I O N
OF T R U E D I A M E T E R A N D D E N S I T Y ,
FOR SEDIMENTATION IN WATER.
where up, uf = refractive index of par- Errors are all ne ga t i ve ( t h a t is, calculated
ticle and medium respectively. diameters are less t h a n t rue diameters).
If the photocell subtends a solid angle,
Density, g per cu cm
fl, at the center of the particles, then for
values of (up -- us) for which/~ > a all True Diameter... 10# 20# 30# 40# 50# 60t*
the light transmitted through the par-
titles will fall on the photocell, severely . . . . .................. . . . o20'Io.5oL1.5
2 2.3oi3.6o,5.1o
h I"
reducing the absorptivity of the suspen- lo. ........... io. 1o.8o11. oj3.2oi .ool7.oo
sion. However, for values of (up -- us)
for which a >> fl, very little of this trans-
mitred light will reach the photocell and concentration of particles below 0.5 t*
the particles will behave as though they and above 12.0 v would be underesti-
were opaque. mated, while the concentration of 0.5- to
Thus, a suspension of transparent par- 8.0-t~ particles would be overestimated.
ticles will obey the Lambert-Beer law in One further, small source of error
the same manner as a suspension of worth mentioning is the fact that the
opaque particles, provided that there is emf developed across a photocell is pro-
a sufficient difference between the refrac- portional to the light intensity falling
on the cell only if both the light intensity
tive indices of the particles and the me-
striking the cell and the resistance con-
dium, and the photocell subtends a suffi-
nected across the cell are very low. Thus,
ciently small solid angle. This condition care should be taken to keep these quan-
will be met, according to Rose, with a tities as small as possible.
subtended angle of 0.00024 solid radians Errors Inherent in Sedimentation Meas-
and a refractive index difference of 0.2 urements:
for an 80 per cent, or of 0.6 for a 100 The upper particle size limit to the
per cent relative opacity. With a sub- validity of Stokes' law was previously
tended angle of 0.0115 solid radians the discussed under "theory of sedimenta-
0.2 and 0.6 refractive index differences tion." Table V listed Davies' (20) esti-
M I C H A E L S ON D I S T R I B U T I O N T H E O R Y 221
mates of the m a x i m u m size particles portant and the Stokes' diameter begins
of various densities for which Stokes' law to deviate from the true value.
was accurate to i, 5 and l0 per cent. The slip effect occurs when the par-
Another estimate of the per cent errors ticles are small compared to the molecu-
in Stokes' law for various size particles lar mean free path of the medium. In this
as given by Rose (13) is shown in Table case, the particles m a y slip between the
VII. molecules, encountering less resistance to
I t should be noted that the per cent motion and thus falling at a higher ter-
errors of Table V I I are somewhat lower minal velocity than is predicted by
than in Table V. For example, a 43-u Stokes' law. Cunningham's correction for
particle of density 10 g per cu cm is listed this is given by Dallavalle (5) as:
in Table V as having a 5 per cent error.
The comparable particle of Table V I I V ~ ' = V~,(1-I- K ~ ) . . . . . . . (27)
would have an error of about 3 per cent.
where:
TABLE VIII.--PER CENT ERRORS IN
OSEEN'S DIAMETERS AS A FUNCTION Vm', Vm = true and Stokes predicted,
OF TRUE DIAMETER AND DENSITY,
FOR SEDIMENTATION IN WATER. terminal velocities,
Positive errors indicate calculated diameters K = constant dependent on me-
are greater than true diameters. Unmarked er- dium,
rors are negative as in Table VII.
X = mean free path of molecules,
Density, g per and
cu cm
d = diameter of particle.
True For sedimentation in a gas this error
Diameter.. 60
"_A can be important. For 1.0 ~ particles in
2.7 . . . . . . 0.2olo.4olo.551o.751 o.sc 0.50 air, Davies (20), for instance, gives a cor-
4.0 . . . . . . D.2010.5010.75 0 . 4 5 + 0 . 2 ( +0.80
rection factor value of
10.4 . . . . . . 2 10 010 5510 +2.40
V,,~' = 1.164V,~
A correction to Stokes' law known as and Rose (13), using a value of K = 1.8,
Oseen's correction is given by Rose (13). calculates a 5 per cent error in the diame-
With this correction factor, Stokes' law ter. However, the mean free path of a
becomes: liquid is essentially zero (20, 13), and thus
V 18nv ll/2 (1 + 0.095R~)...(26)
d = [_(~ _ p ) a I
the slip effect is of little significance in
turbidimetric sedimentation which is cus-
tomarily performed in liquid mediums.
The Oseen correction renders Stokes' The other lower limit source of error in
law valid for Reynolds numbers up to liquid sedimentation is diffusion due to
one. The errors in Eq 26 for various Brownian motion, convection currents,
densities and particle sizes as estimated and thermal forces.
by Rose (13) a r e listed in Table V I I I . A study of Brownian motion was made
The Oseen diameters are apparently by Gibbs (23). From his observations we
far more accurate than the uncorrected m a y conclude that the net effect will be
Stokes' diameters, with all errors below to oppose the sedimentation of the finer
1 per cent with one exception. sized particles, resulting in an apparent
A lower size limit to the validity of decrease in the calculated Stokes' diame-
Stokes' law also exists. Below a certain ters. Heywood (24) and Davies (20) esti-
size, diffusion and slip effects become im- mate that Brownian motion becomes sig-
222 S ~ l , OSlly~ ON PARTICLE SIZE MEASUREMENT
nificant only for particles below 0.1 u in errors in the calculated Stokes' diame-
size. ters arise from the failure of the suspen-
Convection currents and thermal sion to meet the Stokes' law requirements
forces both result from the existence of a of a relatively infinite extension of me-
temperature gradient in the suspension. dium about the particle and of a spheri-
Both have greater effects on finer par- cally shaped particle.
ticles and tend, as with brownian motion, A limited extent of medium can lead
to decrease the calculated diameters of to wall and bottom effects and interac-
the fines. tion of particles. For cases in which the
Convection currents arise from the ratios d:D and d:L are not negligible,
relative decrease in density of hotter (where d, D are the diameters of the
portions of the medium, with a conse- particle and sedimentation cell respec-
quent rise of these portions and descent tively and L is the height of the liquid in
of colder portions. Fine particles are the cell) we Lave trrors introduced into
carried along more readily by these cur- Stokes' law which may be estimated by
rents. Thermal forces result from a com- Ladenburg's correction, given by Dalla-
bination of thermal gradient with normal valle (S) as:
brownian movement. In brownian move-
ment, the net molecular impact on larger Vow= V [ 1 + 2 . 4 d ] [ 1 + 1.7d]...(28)
particles is normally zero. If however, a
thermal gradient exists, bombardment is where:
no longer random, since there is a higher
kinetic energy on the hotter side, and V~ = the calculated Stokes' velocity,
particles will be impelled away from the based on an infnite extension of
hotter side. medium about the particle, and
For these two effects, the exact tem- V = the true velocity of the particle.
perature gradient at which errors become The first term in brackets in Eq 28 is
serious is not known by the author. the correction for wall effects and is only
Rose (13) recommends control of tempera- approximate at large values of d:D. The
ture to +0.01 C. Our own experience at second term in brackets is the correction
the Sylvania-Towanda Metallurgical Lab- for bottom effects.
oratory has revealed no serious effects For the Cenco photelometer where the
from temperature variations of several smallest cell diameter is 1 cm, the liquid
degrees centigrade, provided that the height about 3 cm and for the usual
changes occur fairly uniformly about largest size refractory metal powder par-
the sedimentation cell. ticle (about 30 u), the error introduced
Two studies have been made which by these effects is on the order of 2 per
confirm the lower limit validity of cent (1.4 per cent error in diameter), the
Stokes' law. In one, Perrin (zs) obtained calculated diameters appearing to be
agreement down to 0.3 u, on monodis- smaller than the true values.
perse fractions of gamboge, between sedi- The magnitude of these errors has
mentation results and measurements been experimentally verified by Rose (is).
made by two different microscopic meth- He found that for a suspension of par-
ods. Westgren (26), in the second study, ticles 50 ~ in diameter, settling in a tube
found good agreement between ultra 5 cm in diameter, the computed diame-
microscope and sedimentation measure- ters of less than 10 per cent of the par-
ments for gold sols about 0.1 u in size. ticles were in error to the extent of 1 per
Additional effects which may cause cent or more. For 10-u particles in a 2-cm
tube, 2 per cent of the particles were in concentrations are never in excess of 0.5
error 1 per cent or more. He also estab- per cent and usually less than 0.1 per
lished that no significant error due to cent so that the corrections are negligible.
liquid height occurred as long as the The second manifestation of particle
sampling level was not less than 1 cm interaction is the increase in flocculation,
above the bottom of the tube. especially of finer particles, which oc-
The interaction of particles manifests curs with increasing concentration. The
itself in two ways. First of all, each par- rather severe effect of this is illustrated
ticle in a suspension experiences a degree in Fig. 5, taken from Rose (13), in which
distributions obtained on the same
TABLE IX.--CORRECTION FACTORS powder for concentrations from 0.2 g per
FOR PARTICLE INTERACTION EFFECT.
liter to 21 g per liter are plotted. The dis-
Concentration by Correction Factor tributions are seen to become rapidly
Volume, per cent for Terminal Velocity
coarser as the concentration increases.
0.I .............. O. 9935 The final source of error to be con-
0.5 .............. O. 9693 sidered is the effect of particle shape. The
1.0 .............. 0.9400
5.0 .............. 0.7320
commonly used form of Stokes' law, Eq
10.0 . . . . . . . . . . . . . . O. 5325 20 above, applies strictly to spherical
particles. For nonspherical particles the
equation should be used in the form of Eq
12
19:
E--~ Curve A 0.2g per liter
::LIO "i. , I I Curve B l.Og per liter
I~ ON, A I I CurveC 5gperliter
Q- Ili ~, J ~ CurveD lOg per liter
-~'o 8 l'l~
I,/, "~l',C
ft~ rI [ I CurveE 219 perliter
Ill B.~\,q ~ / CurveA Obtained by Dallavalle (S) arrived at values of K,
6 .I ~1 ~ [ ~' , - - Photo Ekt nc:t on equal to 36.0 and 35.0 for irregular
;- .4' ~'
" I I~ ] t/1~ . Curve BtoEOblained quartz and coke respectively, as com-
] i \ ; ;"~ ~, ~ by use of an
g= 4 ~ [ \ j ] ~ \. \Andreosen Apparatus pared to Ks = G/18 = 54.5 for a spheri-
cal particle. Less severe deviations are
indicated by the work of other re-
searchers.
0 '.g ~ I i "~"'~""~-~-"~
0 tO 20 30 40 50 70 80 Davies (20), for example, conducted an
Stokes' Diameter, extensive study of the influence of par-
FIO. 5 . - - S i z e D i s t r i b u t i o n s O b t a i n e d b y Sed- ticle shape on the rate of sedimentation.
i m e n t a t i o n , for V a r i o u s C o n c e n t r a t i o n s . He concluded that in the viscous flow
(Stokes' law) region all reasonably com-
of down-drag from the fall of adjacent pact (not flat or elongated) particles, al-
particles and of up-drag due to the up- though possessing sharp edges, would
ward counter flow of liquid. The net ef- show no tendency to orient while settling,
fect will be upward, tending to decrease but would fall in a random pattern and
the apparent size of the particle. This has at a rate very close to that of spheres of
been found, by Steinour (27), to give rise the same density and volume.
to comparatively insignificant errors in The accuracy of Stokes' law for both
diameter for low concentrations. Typical spherical and irregular particles was also
correction factors which he computed are investigated by Roller (28) using a method
given in Table IX. of air elutriation rather than sedimenta-
For turbidimetric sedimentation meas- tion, and comparing results to a micro-
urements of refractory metal powders, scopic count. He found the law exact
for glass spherelets and for smooth, regu- Errors Inherent in Turbidimetric Sedi-
lar nonspherical shapes such as cubes, mentation:
plates, and rods provided that the micro- The combination of turbidimetric in-
scopic size was defined as the cube root of cremental sampling with sedimentation
the product of the three principal dimen- introduces one final source of error,
sions. For rough textured, irregular par- characteristic of most incremental sam-
ticles, on the other hand, he found the pling methods. This error arises from
microscopic size to be somewhat larger the fact that the sampling region (the
than that calculated from Stokes' law, light beam in turbidimetric sedimenta-
but accounted for this as primarily due tion) is of finite height. The effect of this
to occlusion of air in surface pockets. finiteness is variously defined as the
"resolution" (19,24) and the "discrimina-
TABLE X.--AVERAGE DIAMETERS IN tion ratio" (18) of the measurement.
MICRONS CALCULATED FROM THE The error which results from a finite
MEASURED DISTRIBUTIONS FOR sampling zone is, according to States (19)
THREE SIZED FRACTIONS OF GROUND
FLINT. and Heywood (24), analyzed as follows:
The incremental (here turbidimetric
Fraction Microscope Sedimentation sedimentation) method of particle size
measurement assumes that sampling is
1 ............... 11.32 11.34
2 ............... 1 6 . 0 7 1 6 . 0 4 done at an infinitely thin plane surface, a
3 ............... 22.84 22.68 distance, h, below the surface of the sus-
pension. In reality, the sampling zone has
a height, a, with center at h, equal to the
TABLE XI.--AVERAGE DIAMETERS beam, or defining slit, width.
IN MICRONS CALCULATED FROM THE
MEASURED DISTRIBUTIONS FOR FOUR
As sedimentation proceeds, a particle
SIZED FRACTIONS OF GLASS SPHER- size gradient forms at the top of the
ULES. suspension with a descending leading
Fraction Microscope Sedimentation
(plane) edge above which there exist only
particles smaller than the maximum di-
1 ................ 10.7 10.1 ameter particle in the suspension. This
2. 6.5 6.6 gradient eventually reaches the sampling
3. 3.1 3.9
4. 2.1 2.5
zone and passes through it. As each size
level of the gradient falls below the
sampling zone the particle concentration
Additional confirmation of the ap- in the zone decreases and the light trans-
plicability of Stokes' law to slightly ir- mission increases.
regular, nonspherical particles was ob- For an infinitely thin sampling zone
tained by Andreasen (29). He determined each light increase would correspond to
the distribution of three sized fractions of that size particle which has fallen exactly
ground flint by sedimentation and micro- a distance h from the top of the suspen-
scopic count. His results are listed in sion. In actuality the sampling zone, at
Table X. any instant, contains a gradient of sizes
This data may be compared to similar between dl at hi, at the top of the beam,
results obtained by Bishop (30) on four and d2 at h2, at the bottom of the beam.
sized fractions of glass spherules as shown If the gradient per unit depth in the beam
in Table XI. is given by (Ad/Ah) then the size range
It is apparent that the agreement is as in the beam is equal to:
good for irregular particles as it is for
Ad = a . . . . . . . . . . . . (29)
spherical ones.
x~/[ICHAELS O N D I S T R I B U T I O N THEORY 225
where: distiibution is as follows: A given size

particle, falling from the top surface of
Ad = d2 -- dl, and
the suspension, reaches the top of the
a = h 2 - hi. light beam and begins to cause an in-
From Stokes' law, for a given medium crease in transmission before it reaches
and powder, we have: h ( a / 2 below). Thus it registers as a par-
ticle of larger size. After passing h, it re-
h mains in the light beam until it falls an
V = -= Kd 2
t additional distance a / 2 , thus registering
h . . . . . . . . . . (30)
Kt=-- as a finer particle. For a particle of size
d~ d, the spread of the measured size is from
Thus: a maximum of d (1 + ~h ) to a minimum
( G~ ) = ~ &i = T a
~ ........ (3,) of d (1 - ~).
So that the spread of sizes in the sampling In a distribution, the largest particles
zone is: present will therefore register as larger,
stretching the distribution somewhat to
the coarse side. These larger particles
Ad = a = --. ........ (32)
2h also, after passing h, register as finer par-
ticles. However, this is cancelled by the
The "resolution" is then defined as the next smaller size which has meanwhile
reciprocal of the size spread: entered the top of the beam and regis-
2h tered as larger. Thus the body of the
R = a-d. . . . . . . . . . . . . . (33) distribution runs at the correct value.
Finally, when the finest particles pass h,
This gives a measurement of the error they remain for an extra time in the
introduced for each size particle by the light beam, thus appearing to be finer.
finite depth of the sampling zone. A more The net effect is to spread out the distri-
useful expression for the per cent error, bution at its ends.
which is independent of particle size and To evaluate these effects, Heywood
determined only by the physical dimen- (24) made tests on a 2- to 6-/~ graded
sions of the measuring system, is the powder and a 0- to 6-g ungraded powder
"relative size variation" obtained as fol- at various h : a ratios. He found that in
lows: both cases the coarsest particles regis-
Relative size variation (RSV)
tered considerably larger with h : a = 1
than with h : a = 6.
Ad Talvitie and Paulus (18) measured the
= -- X 100
d RSV (or "per cent discrimination ratio")
for quartz dust settling in water at 25 C,
= ~/~---x
d
loo with a slit width of a = 0.05 cm on an
instrument of their own construction.
ad/2h They found that at a sampling height of
= X 100 h = 0.86 cm the RSV was 30 per cent,
d
the diameter of 0.5 ~ particles registering
1003 as 0.425- to 0.575-~ particles.
RSV = 2h per cent ...... (34)
States (19) has computed the resolu-
tions of various size particles for the
The effect of this error on the measured Cenco photelometer (slit width = 0A
cm) and the Wagner turbidimeter (slit obtained (computed from the measured
width = 1.27 cm). His results are shown distributions in the case of the photelom-
in Table X I I along with calculated values eter and microscope) are given in Table
of the RSV (dependent on a and h only). XIII.
Two studies of the accuracy of turbidi- The photelometer and subsieve sizer
metric sedimentation measurements, es- give very close agreement, but the mi-
pecially as applied to refractory metal croscope registers a consistently finer
size. This discrepancy is accounted for by
TABLE XII.--RESOLUTIONS AND PER the large amount of strongly sintered
CENT ERRORS (RSV) OF THE CENCO
PHOTELOMETER AND WAGNER TUR-
agglomerates present. These agglomer-
BIDIMETER.
TABLE XIV.--COMPARISON OF MEAS-
Photeiometer Wagner Turbidimeter UREMENTS BY TWO PARTICLE SIZE
Particle INSTRUMENTS ON A VARIETY OF
Size, , I o I Rsv,
_ _cm
--~' ix per cel
h c I R I Rsv, METAL AND INORGANIC POWDERS.
J, m _ _ p e r c e n t
Average Diameter,
60 .... 31 1.03/ 1.6 15.010.3941 4.2
30 .... 3.1 2.07[ 1.6 15.010.7881 4.2 Material Photelom-
25 . . . . 3.1 2.48[ 1.6 13.110.827 / 4.8 S lbsieve eter
7.5.. 3.118.271 1.6 2.11o.44o 1 302 Sizer (Calcu-
lated)
TABLE XIII.--COMPARISON OF MEAS- No. 1 ......... 1.8 2.0

UREMENTS BY THREE PARTICLE SIZE Tungsten No. 2 ......... 3.5 3.6
INSTRUMENTS ON TUNGSTEN METAL No. 3 ......... 5.9 5.8
POWDERS. Molybdenum ............ 3.4 3.3
No. 1 ......... 2.7 3.0
Average Diameter, tt Zirconium N o . 2. 5.5 5.3
No. 3 ........ 14.6 13.6
Sample Beryllium ............... 21.0 21.3
Subsie~ Photelom- Micro- Rhenium ................ 2.3 2.1
Sizer eter scope
Germanium .............. 12.5 11.6
Tungsten trioxide ........ 1.1 1.4
1 .............. 3.55 3.57 Zireonium hydride ........ 6.4 6.2
2 .............. 4.40 4.56 3.94 Red phosphorus .......... 5.6 6.2
3 .............. 4.80 4.67 3.52 Titanium hydride ........ 6.0 6.7
4 .............. 4.65 4.59 3.81 Tantalum carbide ........ 1.9 2.7
5 .............. 3.50 3.20 2.79 Germanium dioxide ....... 2.0 2.4
6 .............. 4.90 4.84 4.26 Aluminum oxide .......... 6.6 6.2
7 .............. 5.90 5.83 3.68
8 .............. 4.15 4.20 ,..
9 ............. 4.15 4.41 3.83
10 ............. 4.90 5.03 3.71 ates act as single particles in sedimen-
11 ............. 4.15 4.22 3,45
4.80 4.57 ...
tation and permeability, while on the
12 .............
microscope the individual particles con-
stituting the agglomerate are counted
powders, based on comparison of the re- separately. This question is discussed
suits obtained with a variety of particle further in the section on agglomeration.
size analysis techniques, were conducted In the study conducted by Gregg and
by Gregg (31) and by Gregg and Kopel- Kopelman (32), a large group of metal
man (32). and inorganic powders were analyzed
Gregg (31) measured the particle size of with the photelometer and subsieve sizer.
twelve tungsten metal powders on the Excellent agreement between the two
Cenco photelometer, the Fisher subsieve instruments was found for most of the
sizer air permeability instrument, and powders as shown in Table XIV.
the microscope. The average diameters They also obtained distributions on a
typical tungsten powder using the pho- finer or coarser size. Furthermore, any
telometer, microscope, Andreasen pipet uniform errors are easily compensated
and the roller air elutriator. Figure 6 for by constant correction factors. Conse-
shows the results of these four measure- quently, the most significant question to
ments. consider at this point is the net effect of
It will be observed that, as before, the all the particle size dependent errors upon
microscope gives a finer distribution than each distinct size range in a distribution.
the photelometer, accountable for in 0.0- to 0.5-~ Particles.--Assuming a
terms of the powder agglomeration. The constant value of two for the extinction
Andreasen pipet and roller analyzer both coefficient, then the concentration of ma-
terial will be seriously underestimated
100 since k= is between 0 and 2 in this regiom
Some intermolecular slip may occur,
90 making the near zero particles appear
slightly coarser, but this will not affect
80 the range as a wholei Flocculation will
cause many of these particles to act as
c. 70
iT. greater than 0.5-~ particles, adding sig-
6o nificantly to the underestimation.
o The diffusion effects of Brownian mo-
~, 50 tion, convection currents and thermal
forces have a fairly large effect in this
40 region but chiefly serve to shift particles
.of
I II x Photelometer to the finer end of the region. Some few,
= 30
C) o Andreosen greater than 0.5-~ particles will, however,
Pipet be shifted into this range giving a slight
a Roller overestimation. Wall and bottom effects
Analyzer and particle drag will.have a small effect
I0 on greater than 0.5-~ particles and will
transfer some of these into the finer range
0 I I I I I
o 2 4 6 8 10 12 14 adding to the overestimation. The in-
Diameter, /x fluence of resolution depends on the size
Fie. & - - C o m p a r i s o n of Distributions Ob- at which the measurement is terminated.
tained on a T u n g s t e n MetM Powder by Four I t would tend to shift some particles
Different Particle Size I n s t r u m e n t s . down into this range if the run is cut off
at 0.5 ~.
produce coarser distributions. These two
Though some cancellation occurs, the
instruments, however, use considerably
net result of all errors is to cause serious
larger sample concentrations that the
underestimation of the concentration in
photelometer and, as may be recalled,
the 0- to 0.5-/z range.
increasing concentrations lead to a coars-
0.5- to 1.0-~ Partides.--Diffusion ef-
ening of the distribution as shown in Fig.
fects will shift a few particles into the
5.
below 0.5-~ region causing underestima-
Summary of All Inherent Errors in Tur- tion.
bidimetric Sedimentation: All other factors contribute to over-
Most of the errors which have been estimation. The extinction coefficient is
discussed tend to distort a distribution between 2 and 4 adding seriously to the
rather than to shift it uniformly to a apparent concentration in this range.
Flocculation is=smaller at these sizes and The net effect in the 1- to 8-~ range is
thus more flocculates from the finer sizes a fair degree of overestimation, especially
will be added than are lost to the coarser at the finer end.
region. Similarly, the transfer of parti- 8- to 13-~ Particles.--In this range, the
cles due to wall and bottom effects and extinction coefficient is equal to 2, giving
particle drag will be greater from the the true concentration. Forward scatter-
coarser than into the finer ranges. ing may become more serious, giving rise
Finally, if the measurement is termi- to some underestimation. A small degree
nated at 1 ~ as is customary, resolution of overestimation may result from wall
may add to the overestimation. and bottom effects, particle drag and the
The net effect in the 0.5- to 1.0-~ range entry of flocculates from the finer sizes.
is thus a serious overestimation of con- All other previously mentioned errors are
centration. The over-all effect on the negligible.
0- to 1.0-~ range will not be severe. The The measured concentration in this
underestimation occurring for 0- to 0.5-~ range will therefore lie close to the true
particles will be largely cancelled by the value.
0.5- to 1.0-v range overestimation, the 13- to 20-~ Particles.--The extinction
resultant measured concentration being coefficient is slightly below 2, giving a
close to the true value. small underestimation. Forward scatter-
1- to 8-~ Particles.--Diffusion effects ing will be somewhat larger, possibly
are very small giving at most a slight making a significant contribution to
underestimation by shifting particles to underestimation. Resolution will shift
the finer range. If the run is cut off at 1 some particles to above 20 u if the meas-
~, resolution will also shift some particles urement is begun at 20 u. Some over-
below this range. estimation will be produced by wall and
A new underestimation effect may be- bottom effects, particle drag, and influx
gin to operate at this size. At the time of flocculates.
when the 0- to 1.0-v particles are regis- A new factor may enter at this point.
tering a decrease in the light beam, the This is the deviation from Stokes' law
concentration of particles in the beam which occurs due to the onset of some
(all greater than 1.0-~ particles no longer nonviscous flow for larger particles. For
present) is very low and no forward scat- tungsten and molybdenum, the error at
tering is likely to occur. For the l- to 20 u is below 1 per cent, but some greater
8-~ region, the concentrations are higher than 20-~ particles may slow down and
and with an instrument with a moder- register as tess than 20 ~.
ately large photocell subtended solid The measured concentration in the 13-
angle, such as the photelometer, some to 20-~ range will thus be slightly below
forward scattering may occur, giving a the true value.
slight underestimation of concentration. Greater Than 20-~ Particles.--In this
The extinction coefficient value in this region, the extinction coefficient de-
range varies from 4 to 2, up to 3 and creases gradually to reach a value of 1
back to 2, resulting in a fair amount of at about 80 ~, thus giving an underesti-
overestimation. Wall and bottom effects mation which increases slowly with size.
and particle drag are more serious above Forward scattering will also increase rela-
8 ~ and shift some particles down to this tively as the initial concentration is ap-
region. The influx of flocculates from the proached with increasing size. Wall and
finer sizes is a third source of overestima- bottom effects, particle drag and espe-
tion. cially the deviations from Stokes' law
will all add to this pattern by shifting For refractory metal powders (usually
particles from the coarser to the finer end less than 20 v), the net effect will be to
of the range and perhaps shifting some increase the apparent per cent concentra-
particles to below 20 ~. At the largest tion in the 1- to 8-~ range.
size, resolution will introduce a shift to
VARIATIONS ARISING FROM SAMPLE
the coarser.
PREPARATION TECHNIQUES
In the greater than 20-tz range, under-
estimation will therefore be small at first In the previous sections we have con-
and will increase rapidly with increasing sidered the inherent errors of the turbidi-
size except at the very top size where it metric sedimentation method. All meas-
FIO. 7.--Electron Micrograph of a Sintered Tungsten Agglomerate (X 10,000).
will be counteracted somewhat by the urements made by this method, especially

resolution effect. if run on similar instruments should
Errors arising from such factors as be equally subject to these errors.
transparency and nonspherical shape Consequently, they should in no wise
affect all sizes uniformly and may thus interfere with the reproducibility of the
be taken into account by constant cor- technique or with the ability to correlate
rection factors. the measurements of different labora-
Summary.--A given distribution from tories.
0 to 80 u will be essentially unaffected in We must now explore those sources of
the less than 1-u range, somewhat over- variation which are related primarily to
estimated between 1 and 8 g, unaffected the physical properties of the materials
from 8 to 20 ~, and increasingly under- investigated rather than to the technique
estimated at greater than 20 ~. of measurement, and are the chief cause
of the poor reproducibility and poor cor- must decide, on the basis of general ex-
relation of measurements made by this perience or specific experimental results,
method. whether it is most fruitful to measure
First in this classification we will con- (a) the "as is" (agglomerate and floc-
sider the previous treatment of the culate) size, (b) a size based on all mod-
powder; that is, the amount of deag- erately strong agglomerates, (c) a size
glomeration to which it is subjected be- containing only the strongest sintered
fore measurement. Secondly, the sedi- agglomerates, or (d) the individual grain
mentation medium used will be examined size.
since this will largely determine the The first choice is seldom made, since
amount of flocculation or deflocculation some dispersion of the flocculates is
occurring, and finally, some small miscel- necessary in most cases. The other three
laneous sources of variation will be all have their valid applications. In some
briefly discussed. cases a measure of the agglomerate
Agglomeration in Refractory Melal Pow-

ders:
Basic to the whole problem of particle
,4f
12
size measurement is the question of what ~I0

particle size property of a powder is most .4 8
(,9
meaningful. This is especially important x O.I-g Sample
6 o Miscellaneous Weights
for refractory metal powders, such as
tungsten and molybdenum, which are
usua:lly hydrogen-reduced at high tem- 2
peratures and thus contain numerous 0 I I I I I I I I
large, strongly sintered agglomerates. An 0 2 4 6 8 10 12 14 16 18 20
Spatulation Time, min
electron micrograph of a typical sintered
tungsten agglomerate, as obtained by FIG. 8.--Deagg]omeration of Tungsten M e t a l
Gregg (31), is shown in Fig. 7. Powder by Spatulation.
An agglomerate such as this would act
as a single particle in a manufacturing strength is important and measurements
process which does not involve heavy of more than one kind are required.
physical working. Kopelman (1), for in- In order to illustrate the degrees of ag-
stance, states that in the pressing and glomeration possible and the approach to
sintering of compacts, only a relatively the determination of a particular ag-
small fraction of two particles need be glomerate size we shall consider three
sintered together in order for the two to materials; tungsten metal powder, tung-
act as one particle in the process. Thus if sten trioxide, and ammonium paratung-
a particle size measurement is to be used state.
for control of these processes, it is clear A series of tests were performed by
that the agglomerate size would be the Kopelman and Gregg (2) on a tungsten
significant property to measure. metal powder. The powder was damp-
If, on the other hand, the process used ened and worked with a metal spatula
involves a heavy milling step or similar on a glass plate, using a firm pressure and
treatment, the powder may emerge es- a rotary motion, for various periods of
sentially single grained and a previous time. The particle size distribution of the
measurement of individual grain size worked powder was then measured with
would be required. the Cenco photetometer using distilled
Thus for each material and process one water as a medium. Figure 8 is the plot
of the average size (computed from the ble, since fairly large variations in work-
measured distribution) v e r s u s the spatu- ing time produce little change in size.
lation times, which ranged from zero Lesser working times or a gentler working
(hand shaken in medium only) to 20 method would be used were a more fully
rain. Samples were mostly 0.1 g, al- agglomerated size desired. Similarly a
though several random weights were used much greater working force technique
with no deviation from the curve. would be required to produce a more
Figure 8 reveals an extremely rapid nearly single grain size.
decrease in size in the initial period of Figures 9(~) and (b), based on work
working time. At 6 min the size has done by the author, show average parti-
dropped to 3 u from an " a s is" value of cle size v e r s u s working time curves, simi-
over 13 u. Thereafter it remains essen- lar to Fig. 8, for tungsten trioxide and
tially unchanged for working times up ammonium paratungstate. The working
to 20 rain. It is fairly obvious that during technique used for these powders (which
20
(o) (b)
15
~L
.N
ml0
g
o
0 L I L
0 5 IO 15 2(3 5 10 15 20 25 30
Agitation Time, min
FIG. 9.--Deagglomeration of (a) WO3 and (b) Ammonium Para Tungstate by the Waring Blendor
the first 89min of spatulation, flocculates are less strongly agglomerated) was agi-
and weakly bonded agglomerates are tation in a Waring Blendor.
rapidly dispersed. The reduced slope of In both cases we see, as for the tung-
the curve from 89 min to about 3 min sten metal powder, an initial rapid drop
indicates that somewhat stronger ag- in size, followed by a tapering off in the
glomerates are succumbing to the spatu- rate of decrease, and finally (at 10 rain
lation force. At 6 min, for all practical for WO3, 15 min for paratungstate) a
purposes breakdown ceases, suggesting flattening of the curve with essentially no
that we have reached a point where the further reduction in size. The interpreta-
powder consists almost entirely of very tion is the same as for Fig. 8.
strongly sintered agglomerates, chemi- It is apparent from the above that a
cally bonded aggregates and individual careful choice of deagglomeration tech-
particles, all too strong to be broken niques and times is essential to the
down by the working force involved. achievement of the maximum meaning-
For most applications, this level por- fulness and reproducibility of results.
tion (6 min or greater spatulation time) Consequently, we shall consider next
would be the most significant size. It is some of the deagglomeration methods
also, by this working method, the region presently in use or under investigation
where results would be most reproduci- in the refractory metal powders industry.
232 SYMPOSlLrlVt ON PARTICLE SIZE MEASUREMENT
The data in the following discussion is Spatulation by a Metal Spatula on a Glass

taken from unpublished material made Plate:
available to the author by the various
This technique has already been men-
member companies of ASTM Subcom-
tioned under "Agglomeration in Re-
mittee I I (Section B) of Committee B-9,
fractory Metal Powders." Figure 8
or from the author's own research.
showed the relation between working
METHODS OF DEAC-GLOMERATION time and size as obtained on a tungsten
metal powder by this method.
Hand-Shake in Flask or Cell:
For use on tungsten metal powders,
This technique, consisting of a vig- sample sizes of 50 to 100 mg (depending
orous shaking of the powder in the me- upon the fineness of the powder) are
dium in which it is to be run, results weighed out. The criteria here is the
only in a dispersion of flocculates bound amount of material required to obtain
by weak electric forces. The results of an initial transmission in the neighbor-
50
Company 1 - - x Company I - - x
*- 40 Company 2 - - , Company 2 - - 9
t-
oo
} - 20
10
o 5 IO 150 5 I0 15
Diameter, p.
(a) Powder 1. (b) Powder 2.

FIG. 10.--Distributions of Tungsten Metal Powders Obtained by Two Companies, Using a Hand-
Shake Dispersion Technique.
necessity are variable since it is difficult hood of 30 per cent on the photelometer.
to regulate the amount of work involved The powder is placed on a flat glass
in manually agitating a suspension. In plate, dampened with a few drops of the
addition the degree of deflocculation same medium in which it is to be run
achieved for a given agitation is highly (distilled water or acetone usually) and
dependent on the properties of the me- then worked for 6 rain with a flat, flexi-
dium used. The author has found it ble metal spatula using a heavy pressure
impossible to obtain good reproducibility and a rotary motion which is frequently
by this method. reversed. Additional drops of medium
In a series of tests designed to compare are added as needed to maintain damp-
the particle size measurements of two ness. After spatulation, the powder is
companies, made on the same powders washed into an Erlenmeyer flask and a
and with the same type of instrument, small amount of medium added. I t is
one testing phase utilized a hand-shake then shaken vigorously, a sample poured
pretreatment. The poor agreement into the sedimentation cell and the trans-
achieved for two tungsten metal powders mission read. If the transmission is be-
is illustrated in Fig. 10. low 25 per cent, the sample is returned
1VIICHAELS ON DISTRIBUTION T H E O R Y 233
to the Erlenmeyer flask, more medium in general) due to the variable human
added and the process repeated. If the factors involved. Figure 11 illustrates
initial reading is greater than 40 per cent the reproducibility obtainable between
a new, larger sample must be spatulated. two different operators using this tech-
/
A ~176176176
f~l I
Operotor2---x II, Operotor2---x
XX I
'~ l; ,k Ij ),
~o r I/ ~ I ti l,
Diameter,ff
FIC. ll.--Reproducibility of Spatulation Technique for Two Operators on Tungsten Metal
Powders.
60
50 Operatort--O ~~ OperatorI--o
~40 ,/~ Operator2--X Operator2--x
'~. 3O
7=
~2o
I0
0 I I I I I I I I I I
0 I 2 3 4 5 6 0 I 2 3 4 5
Diameter,P-
Fla. 12.--Reproducibility of Carbide Block Spatulation for Two Operators on Tungsten Metal
Powders.
With the correct transmission, the sus- nique on two samples of tungsten metal
pension is shaken in the cell, the timer is powder.
started and the run commences.
The reproducibility of this method is Spatulation by Carbide Blocks:
considerably superior to that achieved by The following description was sup-
a hand-shake agitation, but is still poor plied by D. A. Pearson of the Carmet
(about 10 per cent or greater variation Division of Allegheny Ludlum Steel
234 SYMPOSIUM ON I~ ~IZE ~V[EASUREMENT
Corp.: ent laboratories. Figure 13 shows the dis-

A given weight of dry powder is placed tributions obtained with this method by
on the larger of a pair of lapped carbide the same two laboratories and on the
blocks (one 5 in. by 2 in., the other about same two samples of tungsten metal
2 in. square). The smaller block is placed powder as in the hand shake treatment
on top of the powder and spatulation correlation tests which were illustrated
proceeds by applying a heavy hand pres- in Fig. 10. As can be seen, the agreement
sure to the top block while moving it in is considerably better in Fig. 13 than in
a circle of about 89to 1 in. in diameter for Fig. 10.
20 sec. The sample is then brushed into
the cell and the medium added. The Mechanical Mortar and Pestle:
weights used depend upon the fineness of In an attempt to establish a mechani-
the powder. cal deagglomeration technique, free of
The reproducibility of this method ap- human variables such as entered into the
50
Company I - - X
4O Company 2 - - e
o
.o 2 0 //,.
tO
t cc
.;;:yy;::,• // ~\
2
0 ~'~"~ i ,,, I.~ 0 5 I0 15
0 5 tO
Diometer ,/x
FIO. 13.--Distributions Obtained on Samples of T u n g s t e n M e t a l Powder by Two Companies
Using Carbide Block Spatulation.
pears to be somewhat better than that previously described approaches, we in-

achieved by the metal spatula technique. vestigated the use of the Fisher mortar
Compare, for example, Fig. 12, which grinder with a Mullite mortar and pestle.
shows the distributions obtained by two A series of tests were performed in which
operators on two tungsten powders using the criteria for evaluation were the re-
carbide block spatulation, with Fig. 11 producibility of results and the achieve-
where runs were made by the same opera- ment of maximum deagglomeration. The
tors on the same powders by the metal procedure recommended on the basis of
spatula method. most satisfactorily fulfilling these criteria
Upon examining Figs. 11 and 12 it will is as follows:
also be noted that the distributions in the A 125-mg sample of tungsten metal
latter are somewhat coarser, the carbide powder is placed in the mortar. The
block technique apparently working the pestle stroke is set at medium and in the
powder less severely and giving a more tight position, with the mortar slightly
agglomerated size than does the metal off center. The powder is dampened con-
spatula method. tinuously during grinding, using a 50 per
The carbide block treatment was also cent alcohol-water mixture, and grinding
tested for its suitability in correlating continues for 1 hr.
the particle size measurements of differ- The distributions so obtained are finer
than those produced by the metal spatula weighed out and run in the photelometer
method. Reproducibility was also some- after being dispersed in Daxad No. 115
what superior. However, the length of by a 2-min shake in the photelometer
time required and the existence of some cell. The standard weights used are based
evidence that the grinding operation on the Fisher subsieve sizer reading of
shatters and flattens m a n y individual the "as produced" powder as shown in
particles, are both deterrents to a general Table XV.
use of this technique. An extensive series of tests were con-
ducted by W. A. Buerkel in order to
Rod Milling: determine the reproducibility of this
This technique was devised at the method. Eight different tungsten metal
laboratories of the Cleveland Wire Plant powders were analyzed, six to twelve runs
of General Electric. The description of being made on each. The average of all
the technique and the experimental re-
TABLE XVI.--REPRODUCIBILITY OF
REPEAT RUNS ON A TUNGSTEN METAL
TABLE XV.--STANDARD WEIGHTS POWDER BY THE ROD MILLING TECH-
AND READING RANGES FOR VARIOUS NIQUE.
FISHER SUBSIEVE SIZE TUNGSTEN
METAL POWDERS. Weight Per Micron Size, per cent
Sample Run
Sample Number Numbel
Fisher Number, Weight, Micron Sizes Read 1# 2~ 3~ 4~ 5~
mg m
1 ....... 21.4 43.7[ 1 8 . 8 7.1 4.2

0 to 0.80 ..... 10 1 to 10 o n l y 1 ....... 22.2 41.21 19.6 7.8 3.1
0.80to 1.80 ..... 15 1 to 10 o n l y 2 ....... 22.8 43.81 16.7 7.3 6.4
1 . 8 0 to 3.00 ..... 25 1 to 10 o n l y 2 ....... 20.7 42.5[ 20.7 7.6 4.0
3 . 0 0 to 3.75 ..... 50 1 to 10 p l u s 15, 20 3. 25.5 44.51 17.0 7.1 3.3
a n d 25 3 ....... 23.4 43.4 i 18.8 7.4 3.3
3 . 7 5 to 5 . 5 0 . . . . . 75 1 to 15 plus 20 a n d 4 22.4 41.81 17.5 8.9 4.3
25 4 ....... 22.7 43.91 16.6 8.9 4.2
5 . 5 0 to 7 . 0 0 . . . . . 100 1 to 15 p l u s 20 a n d 5 ....... 23.8 43.11 17.5 8.2 3.2
25 5 ....... 23.2 43.71 17.2 7.2 3.2
7.00 up ......... 150 1 to 15 plus 20 a n d 6 ....... 24.2 44.21 16.3 9.3 2.2
25 6. 24.2 43.41 17.3 7.5 3.3
sults were suppl!ed by W. A. Buerkel of per cent deviations for duplicate runs
said company. was about 6 per cent which is consider-
Thirty grams of powder are put into a ably better than is obtainable by the
250-ml "No-Sol-Vit" glass bottle 3 con- spatulation methods. Table X V I lists the
taining fifty 0.150 in. by 3 in. cleaned data for one of these eight powders.
tungsten rods. The bottle is sealed with As a further check on the consistency
a screw cap that has had the inner seal and reproducibility of the rod milling
removed, and placed on a laboratory jar technique, various portions of the above
roll mill. 4 The bottle is then rotated for eight tungsten metal powders were
1 hr at 145 rpm. After milling the powder blended to produce new distributions.
is immediately sieved through a 20-mesh These new distributions were then de-
screen to remove the milling rods, and termined by calculation based on the
then placed in a sample bottle. A stand- blending weights (using the average dis-
ard weight of sample is then immediately tribution previously obtained on each
component powder of the blend), and
3 C h e m i c a l R u b b e r Co. No. T-1825. also by a direct measurement (using rod
4 G e n e r a l u t i l i t y model, 175 rpm, U. S. Stone-
w a r e Co. 5 D e w e y a n d A l m y C h e m i c a l Co.
236 S'ZMI~OSIUM ON PARTICLE SIZE MEASUREMENT
milling) on the blended powder. A total Table XVIII, for example, gives the dis-
of eighteen such blends were made and tributions obtained on the same tungsten
the agreement between the calculated powder by the metal spatula and the rod
and measured distributions were found milling techniques.
to be excellent. Table XVII lists the It will be observed that rod milling has
calculated and measured distributions of produced more 0- to 1-~ particles, indi-
four of these blends. cating a severer working force, but has
A limited number of tests of this tech- also left some particles in the 3- to 4-#
nique were made by several of the co- range, with the probable explanation that
operating companies of Subcommittee II a portion of the powder has been sub-
TABLE XVII. MEASURED AND CALCULATED DISTRIBUTIONS
OF TUNGSTEN METAL POWDER BLENDS.
Number Weight Per Micron Size, per cent

Mix of Com- Distribution
ponents 2# 3# 4# 5#
_ _ m
A .............. Measured 32.9 4 1 . 3 13.3 5.3 2.0

A .............. Calculated 32.3 43.5 13.2 5.3 2.7
g .............. Measured 32.8 41.0 14.3 5.0 3.5
K .............. Calculated 31.0 40.1 14.6 7.0 3.5
M ............. Measured 34.7 44.6 13.0 3.4
M ............. Calculated 29.2 46.9 13.4 4.6
~V. . . . . . . . . . . . . . Measured 35.5 42.6 14.6 2.6
Calculated 34.6 43.8 13.3 3.8
TABLE XVIII.--DISTRIBUTIONS FOR jected to less work than is provided by

TUNGSTEN METAL POWDER BY SPAT-
ULA AND ROD MILLING TECHNIQUES.
the metal spatula technique.
Weight Per Micron Size Range, Ball Milling:

Deagglomeration per cent
Technique A ball milling technique for the deag-
. 0-1. # . 1-2. # . 2-3. # 3-4 #
glomeration of tungsten metal powder is
M e t a l S p a t u l a . . . I 11"011 8 0 . 2 0 8 . 9 0 ]
described by Power and Kakascik (3). In
R o d M i l l i n g . . . . . 1 2 1 . 8 8 1 70.151 5 . 4 9 / 1 . 9 2 this procedure 300 g of tungsten metal
powder are dried and then ball milled for
(Section B) of Committee B-9. All con- 3 hr at 80 rpm in a 1-qt mill using 400 g
firmed the good reproducibility of the of flint pebbles having diameters be-
method. However, various difficulties tween 89and 1 in. No data on reproduci-
were encountered, especially in regard to bility is given. They report, however,
uniform milling of the powder. Several that this method produces a more com-
companies, for instance, reported that a plete deagglomeration, without fragmen-
portion of the sample would invariably tation of individual particles, than is
move into the neck of the milling bottle possible with a hand spatulation tech-
and thus escape the milling action of the nique. The large sample and long time
rods. We did not observe any serious required would probably prohibit exten-
amount of this at the Sylvania Metal- sive use of this method.
lurgical Laboratories, but nevertheless, Eagle-Pitcher Stirrer Housing:
the data obtained indicated that the
amount of work done on the powder was A special pump stirrer used by the
not uniform throughout the sample. Eagle-Pitcher Research Laboratories is
1VilCHAELS ON DISTRIBUTION THEORY 237
described by Musgrave and Harner (33). may be excessive. Figure 14, for instance
This instrument is reportedly designed to shows the plot of average size versus
provide a vigorous circulation and agita- working time for a metal spatula deag-
tion action without introducing air into glomeration of ammonium paratung-
the suspension. They state that the 1800- state.
rpm propeller effectively breaks up ag- Compare this graph to Fig. 9(b) where
glomerates without shattering particles. dispersion has been achieved by the
A number of the cooperating compa- gentler method of agitation in the Waring
nies of Subcommittee II (Section B) of Blendor (the same powder was used for
Committee B-9 tested this stirrer on both tests). First of all we note that 15
tungsten powder. The general conclusion min of agitation in the Waring Blendor is
was that the action was not sufficiently required to reduce the particle size to 7
vigorous for proper deagglomeration, ~, while this same size is reached after 89
rain of spatulation. Secondly, the curve
20 remains level at 7 ~ from 15 to 30 rain
of Waring Blendor agitation, indicating
that essentially complete deagglomera-
:k 15 tion has occurred and making high re-
\
.'2_
u) 10
g
•
producibility achievable in this region.
In the spatulation case the curve is flat
for only an additional 89rain of working
time and then begins to fall again.
reaching a size of about 4 ~ at 3 min.
The 89 1-min region is clearly the deag-
glomerated size, which, because of the
0 I I
smaller spread, would be more difficult to
o I 2 reproduce. The decrease in size beyond 1
Spatulation Time, rain min of spatulation time indicates that
FIG. 14.--Deagglomeration of A m m o n i u m fracture of individual particles is occur-
P a r a t u n g s t a t e by the Metal Spatula Technique. ring. Thus the Waring Blendor, or a
similar method, is advisable for materials
and for the coarser sizes was not violent of this sort. Figure 9(a) showed the aver-
enough to prevent some powder from age size versus working time curve for
settling to the bottom during agitation. WOa worked in the Waring Blendor.
For the lighter, less strongly agglomer- The reproducibility generally achieved
ated oxides its usefulness may be greater. for WO3 and ammonium paratungstate
Waring Blendor: by this method is about 5 per cent, which
is definitely superior to the spatulation
For materials such as tungsten trioxide
methods and comparable to the rod mill-
and ammonium paratungstate which pos-
ing technique used for tungsten powder.
sess comparatively weak agglomerate
bonds and are in addition rather friable, VARIATIONS ARISING :FROM TtIE
severe working techniques, such as de- USE OF DIFFERENT MEDIA
scribed above, are unsuitable. With spat- In making a choice of a medium for
ulation and milling the achievement of a the sedimentation of a particular powder,
particular state of agglomeration is diffi- it is necessary to meet certain criteria, as
cult because of the extremely rapid follows:
breakup which occurs, and also because 1. The medium must not dissolve or
the fragmentation of individual particles react chemically with the powder.
238 SYmpOSiUM ON PARTICLE SIZE MEASUREMENT
2. The medium should be reasonably alcohol, acetone, water, butyl alcohol,

transparent. kerosine, methyl alcohol, xylene and di-
3. The viscosity and density of the butylphthalate. Most of these would
medium should have values, depending serve equally well for molybdenum.
upon the density and size of the powder, In the author's experience water, or
which will give a satisfactory rate of water plus a small amount of wetting
sedimentation. agent, gives excellent results on the
4. If the powder is not completely finer tungsten and molybdenum powders
opaque, the index of refraction of the (up to 20/~ top size). For coarser powders
ii
x Benzene
I0
'S
W- Hexone
g~8
p~
Carbon Tetrachloride
E
~iethyl Ether
7
Nitrobenzene 1
o
r~
(3. Acetic Acid Butyl Alcohol x .
5
Methyl Alcohol )
, i , , A,ceton~-~---~{--
0 4 8 12 16 20 24 28 32 136 81
Dielectic Constont of Liquid
FIG. 15.--Average Size of a Tungsten Metal Powder in Liquids of Different Dielectric Constants.
medium must differ substantially from a 10 g per liter aqueous solution of low
that of the powder. viscosity cellulose gum has proven satis-
5. The medium should be safe to factory.
handle and reasonably inexpensive. For WOa a 1 per cent NasPO4 aqueous
6. The medium should thoroughly dis- solution has shown good dispersion and
perse the powder. reproducibility. Ammonium paratung-
For tungsten Cadle (34) has suggested state which is somewhat soluble in water
such media as water, acetone, acetone has been run in a 6 per cent NH4CI
and vegetable oil, water and glycerol, aqueous solution.
water and electrolytes such as sodium Kopelman and Gregg (2) made a study
pyrophosphate, calcium chloride, and po- of the dispersing ability of various media
tassium citrate added to concentrations for tungsten metal powder. They meas-
of about 0.1 mole per liter or less. ured the size distribution of the same
Referring to the results of the question- powder on the Cenco photelometer using
naire circulated by the turbidimetric task eleven different media with dielectric
force of Subcommittee II (Section B) of constants ranging from 2.29 for benzene
ASTM Committee B-9 which are given to 81.07 for water. The powder in each
in Table III, we see that the mediums case was previously deagglomerated by
reportedly used for tungsten are ethyl a 3-min metal spatula treatment.
Figure 15 shows the relation between sample by taking a number of random

the dielectric constant and the average small samples from the batch. The num-
particle size of the powder (computed ber of samples chosen depends upon the
from the measured distribution). The size desired precision of sampling, defined by
is seen to decrease smoothly with increas- Cadle (34) as:
ing dielectric constant until at ethyl alco-
4S,~2
hol, dielectric constant = 25.8, it reaches _P~ . . . . . . . . . . . . . . (35)
a value of 4.4 ~. Thereafter, the size re- N
mains essentially constant as the dielec- where:
tric constant increases, indicating that
deflocculation and dispersion are com- 4 - p = the precision desired to within a
plete in all associated 6 media with dielec- certainty of 95 per cent,
tric constants greater than 25. This then N = number of samples taken, and
100
,
r-
4
" 80
Q.,
6O
4O
r L~
-t-
O
E zo
O
i i I I I I
0
0 2 4 6 8 I0 12 14 16 18
Diameter,
Fro. 16.--Particle Size Distribution of a T u n g s t e n Metal Powder in Liquids of Different Dielec-
tric Constants.
would be a requirement for a medium to S m = standard deviation of the mean

be used for the dispersion of tungsten. sizes of the samples taken, from
Figure 16 gives the different distributions the mean size of the gross batch.
obtained on the same powder when run
in four different mediums. The distribu- This large sample is then reduced to
tion in water would be the deflocculated, test size by another random sampling
correct distribution. plan as above, or by a thorough blending
followed by a single sampling. In some
~VIISCELLANEOUS S O U R C E S OF V A R I A T I O N cases where very small samples are re-
quired (as in turbidimetric sedimenta-
Sampling:
tion for tungsten--50 to 100 ms), the
The selection of a small sample from a test sample must be further reduced, and
large batch of powder requires the ut- at this size a blending plus single sam-
most thoroughness and care if the sample pling is most convenient.
is to be truly representative. In general I t has been the author's experience
one proceeds by compositing a large that care must be taken to select the
6 N i t r o b e n z e n e is n o t a n a s s o c i a t e d liquid. test samples shortly after blending, since
240 SYMPOSlU~ ON PARTICLE SIZE MEASUREMENT
it has been found that upon standing for by the particles will not necessarily cor-
any length of time the samples tend to respond to that of spherical particles of
segregate with the finer particles moving the same diameter.
to the bottom of the container. We have frequently, in this paper,
made use of an average diameter for a
Particle Statistics: powder, calculated from the measured
For an irregular particle, such as is distribution. This diameter is the
generally encountered in refractory metal weighted mean diameter, day computed
powders, no diameter can be chosen as follows:
which is related by a definite geometrical
expression to the surface or volume of ~o~ ~w,~, (37)
the particle. Instead a diameter is usually ~w,
selected which is based upon some aver- where:
age physical property of a statistical
collection of irregular particles. Wi = weight of particles of size d~ in
Two such diameters, called the nomi- the distribution, or weight of
nal diameter, and the effective or Stokes' particles in the size interval
diameter, are defined respectively as the whose mean size is di, and
diameter of a sphere of the same volume ZW~ = total weight of particles.
as the irregular particle, and as the diam- This is a convenient expression for the
eter of a sphere which falls at the same average size and has some physical
rate in a medium as does the irregular significance as was seen, for instance, in
particle. Table X I V where the weighted mean
The nominal diameter can be deter- size was compared to an air permeability
mined from the volume of water dis- measurement of average size with very
placed by a given weight of powder, close agreement.
provided that the number of particles Mention should be made of a certain
per unit weight is known, by means of practice, used in the plotting of a per
the following expression (5) : cent weight distribution, which, while
not strictly incorrect, can lead to a mis-
= A/ 6 ........... (36)
'F ~r~N interpretation of results. This practice
arises from the manner in which readings
where: are usually taken in turbidimetric sedi-
mentation. The coarser particles (about
d, = nominal diameter,
20 u or larger) fall very rapidly as com-
= density of the particles g per cu
pared to the finer sizes. Consequently it
cm, and
is customary, especially if 11o recorder is
N = number of particles per g.
used, to take readings at larger size inter-
The effective diameter is the diameter vals in the coarser region than in the finer
actually measured in sedimentation if one. If the data is then plotted as per
the usual form of Stokes' law is used. cent weight per micron size range and the
I t is obvious that due to shape and readings are not corrected to a uniform
surface factors, two particles of the same size interval, the curve as plotted will
nominal diameter and density can easily frequently rise to a false maximum at the
have different effective diameters. T h u s coarse end, giving a misleading picture
in interpreting the diameters measured of the distribution. Of course the use of
in turbidimetric sedimentation it is well a cumulative per cent weight plot avoids
to remember that the volume occupied this problem, but does not give so saris-
factory a representation as does a fre- what larger weight per cent in the 1- to
quency plot. 8-~ range, this error being easily cor-
rected for if desired. The inherent errors,
Contamination: in addition, do not interfere with the use
Some deviations in distribution results of the method for control and develop-
which occurred when tungsten metal ment purposes or for correlation of meas-
powder was handled carelessly led to a urements between companies.
brief study of the effect of contamination On the other hand, large variations in
of the powder by perspiration from the the measured distributions are intro-
hands during spatulation. Duplicate runs duced by the techniques of deagglomera-
were made on two types of tungsten tion and the sedimentation media used.
metal powder using the metal spatula Consequently, if standardization of
deagglomeration technique and in one particle size measurements is to be
60 40
~
9 Uncontaminated 9 Uncontaminated
X Contaminated
i X Contaminated
30
o,T, 4 0
o.
20
4=
o 20 x
iO
0 ' X-. ol
o 5 IO o 5 I0 15
Diometer,~ Diameterdx

Fia. 17.--Effect of Contamination on the Measured Distribution of T u n g s t e n Metal Powders.
case deliberately contaminating the achieved with the technique of turbidi-

powder, in the other taking care not to metric sedimentation, some program
do so. The result was an apparent in- such as the following will need to be
crease in the per cent of coarse particles established.
present when the powder was contami- 1. A common instrument should be
nated. This is illustrated in Fig. 17. adopted. The Cenco photelometer or
some very similar instrument is recom-
CONCLUSION
mended.
We have seen that the method of 2. A common deagglomeration tech-
turbidimetric sedimentation particle size nique for each type of powder must be
analysis is applicable to and can give used. The rod milling method or some
accurate results for refractory metal new mechanical spatulation method,
powders and oxides. The inherent errors using mechanically loaded and rotated
of the method have been shown to largely carbide blocks for instance, are two
compensate each other, giving a meas- possibilities for this.
ured distribution which deviates from 3. A common medium for each type
the true value only by indicating a some- of powder should be adopted.
4. All laboratories should preferably Charge, Metallurgical Research Labora-

use the same computational and plotting tory, Sylvania Electric Products, Inc. for
technique. their encouragement and assistance in
the preparation of this paper. Acknowl-
A cknowledgments: edgment is also due to H. I. Davidson
The author wishes to thank C. O. of the Physical Testing L a b o r a t o r y for
Young, Research Manager, Metals Sec- his help in performing m a n y of the ex-
tion and R. C. Nelson, Engineer-in- periments reported in this paper.
REFERENCES
(1) B. Kopelman, "Nature of Metal Powders Inst. Mining Engrs. (London), Vol. 105,
Prepared by Reduction of Oxides," in "The pp. 676-703 (1946).
Physics of Powder Metallurgy," edited by (11) D. L. Gamble and C. E. Barnett, "Scatter-
W. E. Kingston, McGraw Hill Book Co., ing in the Near Infrared, Measure of Par-
Inc., New York, N. Y., pp. 307-308 (1951). ticle Size and Size Distribution," Industrial
(2) B. Kopelman ajad C. C. Gregg, "Particle Engineering Chemistry, (Analytical Edi-
AgglomerationinTungsten Metal Powder," tion), Vol. 9, pp. 310-314 (1937).
Journal of Physical and Colloid Chemistry, (12) J. Alexander, "Colloid Chemistry," Vol. 1,
Vol. 55~ April, 1951, pp. 557-563. Chemical Catalogue Co., New York, N. Y.
(3) A. D. Power and I. M. Kakascik, "Particle (1926).
Size Distribution of Tungsten and Molyb- (13) H. E. Rose, "The Measurement of Particle
denum Powders," in "The Physics of Pow- Size in Very Fine Powders," Chemical Pub-
der Metallurgy," edited by W. E. Kingston, lishing Company, Inc., New York, N. Y.
McGraw-Hill Book Co., Inc., New York, (1954).
N. Y., pp. 311-319 (1951). (14) D. G. Skinner and S. Boas-Traube, "The
(4) C. J. Smithells, "Tungsten," Chemical Light Extinction Method of Particle Size
Publishing Company, Inc., New York, N. Estimation," Symposium on Particle Size
Y. (1953). Analysis, Supplement to Transactions, Inst.
(5) J. M. Dallavalle, "Micromeritics," Pitman Chemical Engrs. (London), Vol. 25, Feb. 4,
Publishing Corporation, New York, N. Y. 1947, pp. 57-63.
(1943). (15) R. C. Tolman et al, "Relation Between In-
(6) H. E. Schweyer and L. T. Work, "Methods tensity of a Tyndall Beam and Size of Par-
for Determining Particle Size Distribu- ticle," Journal, Am. Chemical Soc., Vol. 41,
tion," Symposium on New Methods for pp. 575-587 (1919).
Particle Size Determination in the Sub- (16) H. Heywood, "Measurement of the Fine-
Sieve Range, Am. Soc. Testing Mats., pp. ness of Powdered Materials," Proceedings,
1-22 (1941). (Issued as separate publica- Inst. Mechanical Engrs., Vol. 140, pp. 257-
tion ASTM STP No. 51.) 308 (1938).
(7) G. F. A. Stutz, "The Scattering of Light (17) L. A. Wagner, "A Rapid Method for the
by Dielectrics of Small Particle Size," Determination of the Specific Surface of
Journal, Franklin Institute, Philadelphia, Portland Cement," Proceedings, Am. Soc.
Pa., Vol. 210, pp. 57-85 (1930). Testing Mats., Vol. 33, Part II, pp. 553-
(8) E. G. Richardson, "An Optical Method for 570 (1933).
Mechanical Analysis of Soils," Journal, (18) N. A. Tatvitie and H. J. Paulus, "Record-
Agricultural Sot., Vol. 24, pp. 457-468 ing, Photometric Particle Size Analyzer,"
(1934). Review of Scientific Instruments, Vol. 27,
(9) E. G. Richardson, "Turbidity Measure- No. 9, Sept. 1956, pp. 763-767.
ments by Optical Means," Proceedings, (19) M. N. States, "Specific Surface and Par-
Physical Soc. (London), VoL 55, pp. 48-63 ticle Size Distribution of Finely Divided
(1943). Materials," Proceedings, Am. Soc. Testing
(10) D. G. Skinner and A. G. Withers, "Sam- Mats., Vol. 39, pp. 795-808 (1939).
pling and Analysisof Dust Raised in Suspen- (20) C. N. Davies, "The Sedimentation of Small
sion in Coal Mines, with Special Reference Suspended Particles," Symposium on Par-
to the Fineness Factor," Transactions, ticle Size AnaIysis, Supplement to Tram-
DISCUSSION ON DISTRIBUTION THEORY 243
actions, Inst. Chemical Engrs. (London), trial Edition), Vol. 36, pp. 618-624, 840-
Vol. 25, Feb. 4, 1947, pp. 25-39. 847, 901-907 (1944).
(21) S. W. Martin, "The Determination of Sub- (28) P. S. Roller, "Metal Powder Size Distribu-
Sieve Particle Size Distribution by Sedi- tion with the Roller Analyzer," Symposium
mentation Methods," Symposium on New on Testing Metal Powders and Metal
Methods for Particle Size Determination in Powder Products, Am. Soc. Testing Mats.,
the Sub-Sieve Range, Am. Soc. Testing pp. 54--65 (1952). (Issued as separate publi-
Mats., pp. 66-88 (1941). (Issued as sepa- cation A S T M S T P No. 140.)
rate publication A S T M STP No. 51.) (29) A. H. M. Andreasen, "Validity of Stokes'
(22) H. E. Rose and H. B. Lloyd, "On the Laws for Nonspherical Particles," Kolloid-
Measurement of the Size Characteristics Zeitschrift, Vol. 48, pp. 179 (1929).
of Powders by Photo-Extinction !Vlethods,"
Journal, Soc. Chemical Industry, Vol. 65, (30) D.L. Bishop "A Sedimentation Method for
the Determination of the Particle Size of
pp. 52-58 and 65-74 (1946).
Finely Divided Materials," Journal of Re-
(23) W. E. Gibbs, "Clouds and Smoke," Blaki-
search, Nat. Bureau of Standards, Vol. 12,
stone Co., Philadelphia, Pa. (1924).
pp. 173 (1934).
(24) H. Heywood, "The Scope of Particle Size
Analysis and Standardization," Symposium (31) C. C. Gregg, "Particle Size Analysis of
on Particle Size Analysis, Supplement to Tungsten Powder," Sylvania-Bayside Re-
Transactions, Inst. Chemical Engrs. (Lon- port, Feb. 17, 1948 (unpublished).
don), Vol. 25, Feb. 4, 1947, pp. 14-24. (32) C. C. Gregg and B. Kopelman, "Particle
(25) J. Perrin, In "Dispersoidanalyse," edited Size Analysis of Metal Powders," Sylvania-
by F. V. Hahn, Vol. 3, Theodor Steinkopff, Bayside Report YE51-0422, March 2, 1951
Dresden (Germany), pp. 271-272 (1928). (unpublished).
(26) A. Westgren, "Bestimmung der Avogad- (33) J. R. Musgrave and H. R. Harner, "Turbi-
roschen Konstante durch Messungen der metric Particle Size Analysis," Technique
Brownschen Bewegung der Teilchen in and Technology Bulletin, Eagle-Pitcher Re-
Gold Hydrosolen," Zeitschrift fur anorga- search Laboratories, No. 1 (1947).
nisehe Chemie, Vol. 93, pp. 213-266 (1915). (34) R. D. Cadle, "Particle Size Determina-
(27) H. P. Steinour, "Rate of Sedimentation, tion," Interscience Manual 7, Interscience
Industrial Engineering Chemistry (Indus- Publishers, Inc., New York, N. u (1955).
DISCUSSION
MR. R. D. CADLE.I--I would like to angle of acceptance changes. Therefore
make one comment a b o u t Rose's or any it is necessary to calibrate a n y particular
other correction factors for particles, for instrument, not only in the size range
example, in the 2 to 20 or 30-t, range. below 2 ~ b u t also in the size ranges
Considerations of light-scattering greater t h a n 2 t~.
theory show t h a t the reasons for the MR. A. I. MICHAELS (aulhor).--I am
errors Rose noted and studied result to a little surprised to hear t h a t Rose's
a v e r y large extent from forward scatter- determination of available extinction
ing from the particles. This t y p e of error coefficient was the result of forward
can be minimized, of course, b y decreas- scattering, because in the instrument on
ing the angle of acceptance b y the photo- which he performed this work he used a
cells, as mentioned in the paper. How- solid angle of about 0.00024 radians. A t
ever, it is i m p o r t a n t to notice t h a t the this angle you should get v e r y little
correction for this effect will not be the forward scattered radiation.
same from instrument to instrument if MR. CADLE.--I a m thinking of some
the geometry changes from instrument of the statements in Rose's book particu-
to instrument and p a r t i c u l a r l y if the larly and the papers t h a t he referenced
1 Section Manager, Stanford Research Inst., in t h a t book. I t is true t h a t Rose did
Los Altos, Calif. work with a v e r y small angle, b u t unless
244 SYMPOSIUlVI ON PARTICLE SIZE MEASUREMENT
you happen to have precisely the same the relative variation with size would
angle you would have different correc- differ significantly from Rose's results.
tion factors. This is the only point I was MR. K. T. WHITBY3--Did I under-
trying to make. This effect of forward stand you to say that photometric meas-
scattering is thoroughly discussed by D. urement is restricted to opaque or ab-
Sinclair in the AEC Handbook on sorbing particles?
Aerosols3 MR. MICttAELS.--No. I said that it was
MR. MICHAELS.--I a m u n f o r t u n a t e l y applicable to transparent materials pro-
not familiar with this particular work. vided that you had a small subtended
M y impression is that the variation in solid angle and used a dispersing medium
extinction coefficient arises from a size with a refractive index sufficiently differ-
dependent interaction of the particle ent from that of the particles.
with the incident radiation rather than MR. WmTBu should like to com-
resulting from a multiple scattering pliment the author on the presentation
effect. I assume therefore that the for- of what appears to be excellent data on
ward scattering you refer to is this sort the relationship between working, that
of individual particle scattering effect. is, the mechanical agitation of the sam-
This is of course dependent upon angle ples, and dispersion. We have noted this
of observation and consequently the characteristic with m a n y materials.
optical geometry and especially the solid There are many mineral materials be-
angle subtended at the photocell will sides the refractory metals where we have
effect the absolute value of these correc- observed this type of thing. However,
we have never made a thorough study
tion factors. I doubt, however, that for a
of it.
solid angle as small as 0.00024 radians
Assistant Professor of Mechanical Engineer-
2 "Handbook on Aerosols," Atomic Energy ing, Mechanical Engineering Department, Uni-
Commission, Washington, D. C., 1950. versity of Minnesota, Minneapolis, Minn.
S T P 2 3 4 - E B / A u g . 1959
E L E C T R O N I C SIZE ANALYSIS OF SUBSIEVE PARTICLES BY

FLOWING T H R O U G H A SMALL LIQUID RESISTOR
B Y ROBERT H. BERG 1
SYNOPSIS
This paper describes basically a new principle of particle content and size
analysis and reviews the principal theoretical points. The method is applica-
ble to sizes ranging from below 0.6 # to over 200 #. A suspension of particles
in conductive liquid flows through an aperture with simultaneous flow of
electrical current, resulting in a series of electrical pulses, each pulse being
proportional in magnitude to the volume of the particle causing it. The pulses
are amplified, scaled, and counted to provide direct data for plotting cumu-
lative particle frequency against particle size. Potentials and limitations are
discussed, and methods of calibration, sample preparation, and data reduction
are emphasized.
Particle-size distribution and concen- ago (1).3 Investigations during the past
tration are important properties of year have shown this new method to be
countless powdered, slurried, or emulsi- generally applicable to all forms of finely
fied materials as well as of biological divided material.
cells, fluid contaminants, and foodstuffs.
In processes involving particulate ma- RESPONSE PRINCIPLE
terials, particle size is a critical factor in The number and size of particles in an
dynamic process control, in equipment electrically conductive liquid are deter-
evaluation, in product quality control, mined by application of the Coulter prin-
and in research and investigation. Pres- ciple. This principle consists of forcing
ent methods of particle-size measurement the suspension to flow through a small
include microscope counting, sieving, aperture having an immersed electrode
adsorption and permeability, and a num- on each side, as shown in Fig. I. As each
ber of Stokesian methods. Although most particle passes through the aperture, it
of these methods have been automated replaces its own volume of electrolyte
to varying degrees in recent years with within the aperture, momentarily chang-
significant improvements in speed and ing the resistance value between the
accuracy, there is still need for instru- electrodes. This change produces a volt-
mentation to reduce frequently inherent age pulse of short duration having a mag-
tedium, time delay, and error. nitude proportional to particle volume,
During the past ten years a basically and the resultant series of pulses is elec-
new principle has been developed for tronically amplified, scaled, and counted.
particle-size analysis. It was first applied Voltage-pulse height is proportional
to blood cell counting about four years
i Process Control ServicesCo., Elmhurst, Ill. to the list of references appended to this paper.
245
246 SYMPosItI~ ON PARTICLE SIZE 1V[EASUREMENT
to amplifier gain, aperture current, and and aperture size, response is essentially
resistance change due to particle passage linear with particle volume, providing
(AE = G X I X AR). Expressing the high sensitivity of size measurement.
particle in electrical effect as a right cyl- (When size is expressed as diameter, error
inder, aligned with the aperture axis and is divided by 3.) Deviations are moderate
shorter than the aperture, it can be and usually correctable, and measure-
ment precision within 1 per cent on
diameter basis has been commonly ex-
perienced.
Changes in electrolyte temperature
change electrolyte resistivity by about 1
per cent per deg Fahr for common elec-
trolytes at room temperature; correction
is readily made if need be.
Particle resistivity has been found to
be effectively many orders of magnitude
greater than that of the electrolyte.
Metal powders and other apparently good
conductors behave like nonconductors.
This is hypothesized as being due to
oxide surface films and ionic inertia of
the Helmholtz electrical double layer and
associated solvent molecules at the sur-
faces of such particles. Electrical charges
on the particles have otherwise no ap-
parent effect on response.
Particle density does not affect re-
sponse but, where gross particle porosity
exists (as distinct from sealed internal
voids), the pores aligned with the aper-
ture axis may provide a degree of electri-
FIO. 1.--Basic Mechanism of Coulter Principle. cal translucency with proportionately
lesser pulse height.
shown (2,3) that the change in aperture As indicated in Eq 1, deviation from
resistance caused by a particle is: linear volumetric response becomes ap-
preciable for nearly spherical particles
AR=~• l-ao/p above 30 per cent of aperture diameter
(a/A ~_ 0.09). This effect is correctable
where: if need be. It is markedly reduced for
po = electrolyte resistivity, elongated particles, such as fibers, rods,
A = aperture area normal to axis, and flakes, as the prevailing streamline
v = particle volume (see discussion), flow in the aperture causes predominant
p = effective particle resistivity, and alignment of such particles with the aper-
a = area normal to aperture axis of ture axis.
equivalent right cylinder for parti- Thus, it is seen that particle shape and
cle as oriented in passage. structure have but little effect on re-
Thus, for given electrical conditions sponse. However, it is recognized that the
BERG ON ELECTRONIC SIZE ANALYSIS 247
FIG. 2.--Size Range of Coulter Method Compared with Coverage of Sieve, Sedimentation, and
Microscope Methods, and Overlap of Electron Microscope and Centrifuge Ranges.
FIG. 3.--Electronic Unit and Sample Stand.
FIG. 4.--Schematic Diagram of Laboratory Model.

distortion of the electrical field in the Closing the stopcock then isolates the
aperture by a particle will conform to system from the external vacuum, and
the essential surface of the particle the siphoning action of the rebalancing
rather than follow each crevice and mercury continues the sample flow.
wrinkle, thus sensing the "envelope vol- The advancing mercury column acti-
ume" of the particle much as though it vates the counter by means of fixed start
were wrapped in a thin film. and stop probes, thus providing a con-
stant suspension volume for all counts.
SIZE R A N G E
The volume between probes may be
Response correction is unnecessary chosen in a range from 0.02 to 5 ml, and
for most particulate systems if the few a fresh volume is drawn for each count.
largest particles do not exceed 40 to 50 A typical count requires from 3 to 30
per cent of the aperture diameter. This sec, depending on aperture size and ma-
is also a practical maximum to avoid nometer volume requirements.
excessive aperture blockage due to coin- The voltage pulses are amplified and
cidence of large particles. The noise limi- fed to a threshold circuit having an ad-
tations of electronic amplification justable screen-out voltage level, and if
prevent measurement below 1 to 2 per this level is reached or exceeded by a
cent of aperture diameter. Thus, a single pulse, the pulse is registered. Thus, each
aperture size provides a diametric meas- count represents the number of particles
urement range upwards of 20:1, with larger than the selected threshold-siz~
corresponding volumetric range upwards level in a given volume of suspension
of 8000:1. This range covers most mono- By taking a series of counts at various
caused particulate systems. Range ex- threshold settings, data are directly ob-
tension may be obtained by fractionating tained for plotting cumulative particle
samples and using two or three aperture frequency or concentration v e r s u s par-
sizes. ticle volume (or mass, given constant
The maximum size measurable by this density).
method is governed by the ability to keep The threshold level is indicated on an
particles in uniform suspension, using oscilloscope screen by brightening of the
agitation freely (Fig. 2). Aperture sizes pulse segments above the threshold.
now in use range from 10 to 1000 ~. Up (The pulse pattern also serves as a moni-
to the present, thermal noise generated tor for possible instrument malfunction.)
by electrical heating in the aperture has The oscilloscope picture, counter ca-
limited the minimum measurable size to dence, and aperture-observation micro-
about 0.3 g. Resolution potential reaches scope serve as excellent monitors of
somewhat lower since ionic dimensions aperture blockages which are usually
are near 0.0002 g. remedied by lowering the beaker and
wiping the aperture with a clean finger-
APPARATUS AND OPERATION tip or rubber-tipped rod.
The first embodiment of the Coulter Agitation of the beaker contents is
principle has been the general purpose used freely during measurement to main-
laboratory instrument illustrated in Fig. tain a uniform suspension and to assist
3, with schematic function as in Fig. 4. thorough dispersion. The momentum of
When the stopcock is opened, a con- heavy particles may require aperture
trolled external vacuum initiates flow orientation toward the particle stream.
from the beaker through the aperture Particles which might accumulate inside
and unbalances the mercury manometer. the aperture test tube can cause response-
signal interference and may be flushed without weighing, to satisfy coincidence

out periodically by means of an auxiliary limitations as described. However, where
internal inlet. Otherwise, the suspension solid content of slurries or data on a
downstream of the aperture has no effect significant weight fraction of material
on measurement and need only be con- beyond the range of measurement are
ductive. Thus, preparation for each desired, sample weight (or slurry volume)
successive sample merely involves rinsing and electrolyte volume used in sample
the exterior surfaces which are immersed preparation must be recorded.
in the sample beaker with a wash bottle Electrolyte resistivities generally range
of clean electrolyte. from 1 to 1000 ohm-cm, depending on
aperture size, and are usually kept as
SAI~PLE PREPARATION high as noise levels permit to take full
As in any analysis measurement, care advantage of the effect on response as
must be taken that the sample presented shown in Eq 1. For many purposes a 1
to the sensing element is quantitatively per cent sodium chloride solution in
representative, and the material from water, having a resistivity of about 55
which the test portion is taken must ohm-cm at room temperature, is quite
first be thoroughly mixed. Dispersing satisfactory.
agents are used as the need arises and Where the particulate material is water
do not affect measurement, provided con- soluble or is already suspended in an oil
centrations are reproduced so that elec- or other such medium, nonaqueous elec-
trolyte strength remains constant. A trolytes may be prepared with polar
few drops of dispersant solution may be compounds such as alcohols and ketones,
premixed with the sample portion or may with the ions furnished by materials such
be added to the body of the electrolyte as thiocyanates, quaternary ammonium
in the beaker. Within limits, additives salts, or strong acids. If particles are
for increasing electrolyte viscosity aid slowly soluble in a chosen electrolyte, the
effective suspension of heavier particles. voltage pulses may be recorded on mag-
The low particle-concentrations used netic tape immediately after adding the
further aid dispersion and reduce the sample and then analyzed for height
chances of coalescence or agglomeration. distribution. Solution rates and other
Particle concentration may range from time phenomena may be studied in this
1000 ppm to less than 1 ppm by volume manner.
and is governed principally by coinci- Background counts on the blank elec-
dence considerations and the count sizes trolyte may be taken and correction
desired for statistical protection. Varia- made if need be. For most purposes, care-
tion in repeat counts is a function of ful filtration and protection from dust
counted number, the standard deviation contamination will provide negligible
in a number taken from a Poisson distribu- background counts. If filtered aqueous
tion being nearly equal to the square root saline solutions are to be stored for long,
of the number. The amount of repeat it is well to add 0.1 per cent formaldehyde
data taken may be adjusted accordingly, to prevent the growth of microorganisms.
and sample dilution may be performed
during the course of measurement to COINCIDENCE EFFECTS
retain the statistical advantage of larger The primary effect of coincident par-
numbers in the low count-ranges. ticle passage is loss in count, and saris-
For relative size distribution, sample factory numbers of particles may be
dilution may be done approximately, counted while keeping coincidence cot-
250 SYMPOSllnVl ON PARTICLE SIZE MEASUREMENT
about 175 ml of well-filtered electrolyte

rections below 10 per cent. These correc-
tions are known functions of aperture of suitable properties for the material at
size and particle concentration and may hand. The beaker is then placed on the
be checked experimentally by counting a sample stand under agitation, and 10 to
100 ppm by volume (estimated) of par-
given suspension at successive dilutions.
Mattern (4) has shown that this proce- ticulate material is added (in some cases
dure confirms a Poisson distribution of premixed with a few drops of concen-
particles within the suspension and thattrated dispersant solution on a watch-
glass). At times, it may be useful to check
the electrically effective liquid-resistor
volume is about three times that of the the blank electrolyte first for background
aperture @inder. count.
As a secondary effect, coincident pass- In the absence of prior experience with
similar samples, it is well at first to ob-
ages involving only particles smaller than
threshold size may produce pulses reach-serve the oscilloscope pattern briefly at
ing above the threshold level, causing avarious aperture current' levels for suita-
bility of choice of aperture size, amplifier
false increase in count. This effect will
gain, and particle concentration. (Any of
thus vary with the size range of the sys-
tem being analyzed and with the point these may require adjustment which in-
in the distribution at which measurementvolves a few minutes at most.) At the
same time, the aperture-observation
is taken. If coincidence-loss corrections
microscope is used periodically to check
are kept low, 'this secondary effect will
for any occurrence of aperture blockage.
usually be negligible, but it may be quite
prominent for narrowly distributed sys- If need be, test counts may be taken to
tems near the frequency peak. Detection obtain indication of the distribution for
and remedy merely involve sample dilu- guidance in taking data and to check
tion to reduce coincidence levels. for suspension stability (no particle solu-
bility, agglomeration, etc.).
A further factor in particle concentra-
tion involves frequency response and Counts are then taken beginning usu-
relaxation speeds of electronic compo- ally at the largest threshold-setting and
nents. Six- to seven-thousand random progressing downward in successive size
pulses per second may be handled with settings (single-threshold procedure).
negligible loss, but when very small Replicate counts are taken,as indicated
by count size, that is 6 or 8 for counts
pulses are being measured in the presence
of very large pulses, the tent-shaped of 10 or less, 3 or 4 for counts in the low
bases of the large pulses may obscure a hundreds, and 2 or 3 for counts in the
sizeable fraction of the smaller pulses.thousands and higher. Satisfactory data
Again, the effect depends on the type ofresult if the size-level settings are chosen
such tlmt the points are separated by no
distribution and the point at which meas-
urement is being taken. The need for more than a factor of 2 to 4 in either
additional sample dilution may be particle volume or count. Points may be
quickly determined by trim and may be checked or additional size levels meas-
indicated by a ragged appearance of the ured at any time, and sample dilution
oscilloscope pattern. may be made (and noted) in the course
of measurement, should coincidence
TEST PROCEDURE levels so dictate.
A typical size-analysis on a known The "end" of the particulate system is
material of roughly known size range is usually reached when the counts increase
begun by placing in a 200-ml beaker by only 10 to 20 per cent or less, each
105
104
O3
g
o
O0
E
2
Z
~6
N
I0
I0 I02 103 io 4
Porticle V0[ume, ,u.3
I00
80
2 60
U3
o
o
z=
20
o
I 2 5 IO 20 50
Diameter,/z
FIC. & - - N a r r o w l y Sized Abrasive Grades Suitable for Calibration, Plotted with Comparative
Sedimentation Data.
251
time the particle volume setting is with the response range of over 8000:1,
halved. (The smallest particles form only makes logarithmic presentation of direct
a very small fraction of the total volume data most effective if not mandatory.
or mass of a system.) Thus, a range of Examples are shown in Figs. 5(a), 6, and
8000:1 in particle volume (20:1 diamet- 8(a). The upper end of such curves be-
rically) is covered by 40 to 50 counts comes horizontally asymptotic in the
among 12 to 15 size settings, requiring region of the finest particles, and the
I0~
104
e~
N
~D
103
o
m
I
~S i0 ~
E
Z
a: 10
1
io 2 IO 3 IO 4 Io 5
Particle VoLume ,/.L3
FIo. 6.--Bimodal System (Seeds, Pulp) in Log-Log Cumulative Frequency Plot. Curves B and
C represent two totally different sources.
about 15 min. Less time is required for lower end becomes vertically asymptotic
routine tests at a few points on similar in the region of the coarsest particles.
samples, and more time (up to several With a little experience in interpretation,
hours) can be taken on systems requiring such curves are often adequate, and
multiple aperture-sizes and in exhaustive further data reduction is not required.
research investigations. This method of presentation is especially
sensitive to minor percentages of large
DATA REDUCTION particles which is an important consid-
The numbers of particles counted eration in materials such as pigments
range from 1 to 100,000 and more which, and abrasives.
As may best suit a given material, data circuitry. These forms of presentation
may be converted for plotting particle include the use of multiple threshold-
diameter or volume v e r s u s frequency, levels, pulse integrators, and rate meters
surface area, or weight on either the to provide cumulative or incremental
cumulative or the fractional basis, using frequency rates, frequency ratios, and
linear or semitogarithmic paper. Data weight fractions or weight-fraction ratios.
may also be presented on probability
paper (linear or logarithmic). For the CALIBRATION
most part, process materials are reported Monosized particles are available in a
as cumulative or fractional weight (vol- number of diameters and serve as a use-
100
80
N
09
o
60
03
O
x~
40
tm
2O
o
5 IO 20 50 100 200
Diameter ,ft.
Fro. 7.--Cumulative Weight per Cent Plots of Fresh Catalyst Compared with Average Data
of the American Petroleum Institute.
ume) v e r s u s particle diameter. Examples ful means for calibration. They must
of these are shown comparatively in first be carefully measured by micro-
Figs. 5(b), 7, and 8(b). scope. Materials used include polystyrene
For various purposes, particularly in spheres in the range below 2 u, and blood
application to continuous measurement, cells, spores, and pollens in the range
data may be reduced automatically by from 5 to 80/z. Rapid calibration may be
suitable secondary pulse-analysis instru- made by observing the threshold level
mentation. The more complex digital required to screen out the single-height
computers may perform virtually any pulses on the oscilloscope or by observ-
type of mathematical operation on the ing the threshold level at which half of
pulse signals, but several useful forms of the total system count is found (such
automatic data presentation may be systems being normally distributed).
achieved with comparatively simple Calibration constants should be estab-
106
; III I I III I I
E~qualized Data
9(Counts Scaled to Common Point }
J !
iO 5 ,
"~ ~
',, = -%~,. ~ x " ~ , I
CO
fa)
03
o 104[__
' ' - - I
' k~ ~,-- "...~'-M/lled

EL
o
/lied ~ Passes ' ~ I

at 5 0 0 0 Ib on Rolls ~ \ , .
N 103
fi
Z
,, , _,,,,
M/lied 5 Passes
at B 0 0 0 Ib o n / ? e l l s
,~\~--,
\ \ " \ i
cr
I0 ~
\
\
F Vet YelLow Dye
iO~ I t111 i, \ \
0.I ~0 1oz
Particle Volume,/z 3
I0
o~
EL
~-4
o
0~
o
o I 2 3 4 5
Diameler ,/.z
FIG. &--Cumulative Frequency (a) and Incremental Weight Plots (b) Illustrating Effect of In-
creased Degrees of Milling on Dyestuff.
lished for each combination of electrolyte V, = total suspension volume,

and aperture size used. Wp = total weight of particles,
Calibration may also be made by pp = particle density,
measuring a system of known particle An = integration count increment, and
density and narrow distribution. Nar- = arithmetic average threshold value
rowly classified fractions of glass beads in a given count increment.
or abrasives similar to those illustrated
CONCLUSION
in Fig. 5 have been used. Since virtually
all the particle volume in such systems Results obtained by this method check
may be accounted for, integration of the closely with those of other methods, as
curve of cumulative frequency versus shown in Figs. 5 and 7. There is sub-
relative particle volume provides a rela- stantial independence of particle shape,
tive measure of the total volume of par- and particle properties other than volume
ticles in the metered suspension volume have no influence except for occasional
used in taking counts. The volume per cases of resistivity or porosity. Breadth
cent of particles may be determined be- of measurement range compares favor-
forehand by measuring sample weight and ably with that of any other single
electrolyte volume in sample preparation. method, although the lower size limit
The factor for converting threshold values does not reach as far as with the use of
to particle volume is thus: the centrifuge and the electron micro-
scope. The method has high sensitivity
(,Jv.)(w,/p,)
F . . . . . . . . . . (2) and speed, general applicability, sim-
~(~n)~
plicity of sample preparation and data
where: reduction, and low human fatigue ele-
v~ = metered suspension volume, ment.
REFERENCES
(1) W. H. Coulter, "High Speed Automatic and Sizing of Bacteria," Nature, Vol. 182,
Blood Cell Counter and Cell Size Analyzer," pp. 234-235, July 26, 1958.
paper presented at the National Electronics (4) C. F. T. Mattern, F. S. Brackett, and B. J
Conference, Chicago, Ill. (1956). Olson, "The Determination of Number and
(2) "Theory of the Coulter Counter," Coulter Size of Particles by Electronic Gating,"
Industrial Sales Co., Elmhurst, Ill. (1957). Journal of Applied Physiology, No. 10(1),
(3) H. E. Kubitschek, "Electronic Counting Jan., 1957.
DISCUSSION
MR. MORTON W . SCOTT.I--Has t h e level pulse height discriminator to dis-

author had any experience with liquid- play the data considered; the type of
liquid systems such as oil in water emul- thing that O'Konski uses, for example,
sions? in his aerosol counter?
MR. R. H. BERG (author).--Yes. MR. BERO.--Yes; the single adjustable
These are readily measured. The particle level discriminator represents the lowest
concentration is so low that even if there investment in electronic gear, is quite
is a tendency to coalesce, the particles rapid, and seems to be reasonably flexi-
seldom meet after they are dispersed in ble. Multiple simultaneous levels of
the conductive medium. Also, agitation pulse screening, counting between levels,
is freely used. Size distributions of vari- and integration of pulses (since each
ous types of oils in water have been done, pulse is in effect the mass of a particle)
including food extracts such as lemon can be used to determine mass concen-
oil, and also mineral oil emulsions. trations, ratios, and rates larger than, or
Mm FRED C. NAClmD2--Can erythro- between, selected size levels. There are
cytes be used as calibration material for perhaps five fundamental electronic cir-
the approximate 7-** yardstick? cuits of simple computing nature which
MR. BERG.--I do not know what elec- can be assembled in a variety of com-
trolyte you might require. Hemolysis binations to render continuous automatic
could be a problem. data presentation of a type required by
MR. NACHOD.--I believe you said 1 a given situation. Of course, a complex
per cent salt solution was used; since 0.9 digital computer of the $100,000 variety
per cent is isotonic with erythrocytes can do practically any mathematical
there would be very little hemolysis at operation.
that particular level. MR. DONALD PASTOR?---YOU men-
MR. BERG.--You should have no tioned that you could measure the par-
trouble in isotonic saline. I use my own ticle sizes in oil and water emulsions.
blood cells quite often. How do you distinguish between the
MR. NACHOD.--Do they give you water in the oil and any air bubbles
equal pulse heights? that are coming through?
MR. BERO.--Very nearly. A dearly M~. BxRo.--Air bubbles are ~ source
distinguishable level of nearly single of error and will act just like other par-
height pulses is obtained. For a quick
ticles. They must be removed. Water
calibration I would estimate that you
droplets in oil pose an entirely different
could get within 2 per cent or so on a
diametric basis. Incidentally, blood cells measurement problem than oil droplets
are about 95 **in volume, which is about in water. Since most oils are non-conduc-
a 5.7-** sphere, rather than the nearly tors and would require addition of some
7-** diameter of these wafer-like par- polar solvent to make them conductive,
ticles as seen in the microscope. it is doubtful that the water droplets
MR. R. D. CADLE.a--Was a multi- could be measured, since most polar sol-
1 Senior Scientist, Smith, Kline & French
vents would absorb the water droplets
Laboratories, Philadelphia, Pa. into solution.
2Sterling-Winthrop Research Inst., Rens-
selaer, N. Y.
a Section Manager, Stanford Research Inst., 4 Chief, Applied Research, Fram Corp.,
Menlo Park, Calif. Providence, R. I.
256
DISCUSSION ON ELECTRONIC SIZE ANALYSIS 257
MR. A. I. 1VIICHAELS.5--YOU men- diameter at the mass median on the

tioned limitations in the size of particles sedimentation basis were measured by
that could be measured on this instru- this method to be 15 t~ in diameter, which
ment. How can fairly large tungsten was confirmed by microscope check.
particles be kept in suspension long CHAIRMAN L. T. WORK.6--Have you
enough to complete a measurement? stiffened up the viscosity of the liquid
Tungsten particles of 10 to 15 g will medium, for example, by putting sugar
settle very rapidly. into the solution?
MR. BERG.--The method permits vir- MR. BERG.--Yes, we have done this
tually unlimited agitation during meas- and we have also used gelatin, since gela-
urement, short of whipping air into the tin particles are well below our range.
suspension. I might repeat that, for Viscosity increase helps a good deal when
heavy, large particles of fair momentum, measuring particles which are rather
the aperture must face toward the on- dense or large. The only limitation is that
coming stream of particles. If it is at the flow through the aperture must not
right angles to the stream, some particles be slowed too much. The electronic cir-
may refuse to turn the corner, and just cuitry is timed for pulses of about 10 to
skid and go past the aperture. We have 200 microseconds, and to date, a 10 to 1
experienced this a couple of times and variation in velocity through the aper-
can demonstrate this effect. ture has been tolerable, but the electron-
MR. MICI~AELS.--Have you made any ics might require adaption for a larger
comparisons with other particle size in- variation.
struments on refractory metals? (Author's closure).--The Coulter prin-
MR. BERO.--We have several sets of ciple represents what seems to be a new
data on tungsten, principally compari- class of particle size analysis method, no
sons with the Fisher subsieve sizer, and doubt fully as important as the sieves,
also some with the Micromerograph. In the Stokesian methods, and the micro-
general, the average size obtained with scopes (all of these being distinct from
the Fisher unit is much smaller than that single number methods such as perme-
obtained by this method, and I think it is ametry, radiation scattering, and gas
because we are not talking about the absorption). This new class of method is
same average. If the Coulter data is perhaps best characterized by the con-
given as a cumulative weight curve, it is cept of a flow of dilute particulate ma-
quite expectable for the mass median of terial through a sensing zone. Further
such a curve to be 4 or 5 tt on a sample intrinsic characteristics are that the pass-
for which the Fisher value is 189 t*, since age rate is extremely rapid, requiring
this is a surface mean diameter in theory. electronic instrumentation to handle the
Also, the Coulter method provides a com- signals from the individual particles, and
plete size curve rather than the single that the relationship between particle
value obtained from the Fisher unit. In concentration and sensing zone size must
the case of the Micromerograph we found provide reasonable limits of coincident
that either something happened to passage of particles. In the Coulter prin-
Stokes' law for this dense material or ciple, the sensing zone is electrical in
attrition might have occurred in the nature, and others have been devised
deagglomerator of the Micromerograph. (and proven useful) which utilize a
Particles that were apparently 5 tt in focused spot of light or ultrasonic energy
as the sensing zone. The automatic scan-
~Sylvania Electric Products, Inc., Metal-
Iurgical Laboratory, Towanda, Pa. Consulting Engineer, New York, N. Y.
ning of microscope slides also falls in microscope is a tedious, expensive, and

this category, especially the principle of not at all efficient or suitable use of the
oscillating the slide past a narrowly con- human as a measuring instrument. He is
fined beam of light. In this connection, better suited to the qualitative charac-
it should be recognized that, for quantita- terization of what he sees in a microscope
tive measurement of particle size distri- field, leaving the quantitative aspect to
bution, the human operation of a the inherently more applicable devices.
STP234-EB/Aug. 1959
T H E D E T E R M I N A T I O N OF P A R T I C L E SIZE
BY A D S O R P T I O N M E T H O D S
BY R. JAY FRIES 1
SYNOPSIS
This paper is essentially a survey of the methods and apparatus available

for determining the particle size and surface area of finely divided solids by
the adsorption of gases and liquids.
A general discussion of the calculation of particle size from surface area data
is given, followed by a consideration of the effect of particle shape, porosity,
and surface roughness on the validity of such a calculation.
The next section, dealing with gas adsorption methods, is devoted to a con-
sideration of the evaluation of the monolayer capacity from the adsorption
isotherm and the assignment of the area occupied by each adsorbate molecule.
This is followed by a detailed discussion of the experimental techniques of gas
adsorption and the various types of apparatus (volumetric and gravimetric,
routine and research) which can be used.
A rather general discussion of the advantages and disadvantages of surface
area determination methods based on adsorption from liquid solutions is then
presented, followed by a brief discussion of heat of wetting methods.
Finally, data from the literature are shown comparing the results of adsorp-
tion methods of particle size determination with several other methods, partic-
ularly electron microscopy.
BASIS AND LIMITATIONS where V is the volume, S is the surface

OF T H E M E T H O D S area, and d is the diameter of the sphere.
A consideration of the geometry of Similarly for cubes;
regular solid shapes reveals that the V/S = d3/6d ~ = d/6 ......... (2)
volume and surface of such solids are
simply related by a dimension character- where d here is the length along any one
istic of their particular shape. For side.
spheres, Thus a knowledge of the density and
specific surface area (surface area per
V / S = l~-#/~rd~ = d / 6 . . . . . . . (1) gram) of a particulate solid enables one
o
to calculate the average particle size by
1Research Associate, Department of Re- assuming a regular geometric shape. I t
search in Chemical Physics, Mellon Institute, is convenient to assume a spherical par-
Pittsburgh, Pa.; present address, University of
California, Los Alamos Scientific Laboratory, ticle shape, so that the formula for the
Los Alamos, N. M. surface average diameter, in terms of
259
260 SYMPOSIU~I ON PARTICLE SIZE MEASUREMENT
the density, O, and the specific surface In actual practice, it is found that
area, ~, becomes; most truly nonporous materials give sur-
face roughness factors (2)4 between 0.9
d3 = 6 / p ~ . . . . . . . . . . . . . (3)
and 1.5, 5 which is as good as the agree-
The adsorption methods of determin- ment between most of the other methods
ing the specific surface area of finely for determining average particle size.
divided solids give results which include The effect of particle shape can be par-
area contributions from both the gross tially corrected for by a knowledge of
external particle surface (geometric sur- the actual shape of the particles under
face) and also from any microscopic investigation. In general, it is found that
cracks, fissures, or pores present in the the errors introduced by surface rough-
particles. Since no reliable method (1)2'3 ness and nonspherical shape are not very
is available for separating the area at- serious, and one should expect adsorp-
tributable to pores from the total spe- tion-determined particle sizes to be as
cific surface, the particle size determined reliable as those from any other method,
from adsorption will have the signifi- provided the materials are nonporous.
cance of a real dimension only for non- Of course, the ultimate utilization of
porous solids. This is probably the most the material under investigation, more
severe limitation of the adsorption than any other factor, determines the
method. For porous materials it causes suitability of any method of particle size
discrepancies of up to several orders of evaluation. If properties such as chem-
magnitude between results from this and ical reactivity or solubility are important,
other methods, the adsorption method then an average particle size calculated
always giving the smaller particle size. from the total specific surface would be
In addition to porosity, both particle more indicative of the material's per-
shape and surface roughness can lead to formance than one calculated from only
incorrect particle size results. Since the the geometric surface. Similarly, if op-
adsorption methods determine the ex- tical properties or sedimentation are in-
tent of the surface area by filling the sur- volved, then the geometric surface di-
face with a unimolecular layer of atoms ameter would be more useful than the
or molecules, surface irregularities, even total surface diameter.
of molecular dimensions, contribute to
the specific surface and thus give rise to SURFACE AREA DETERMINATION
an average particle size which is too BY GAS ADSORPTION
small. Similarly, since a spherical particle As seen in Eq 3, a knowledge of the
has the smallest possible surface to vol- density, 0, and the specific surface area,
ume ratio, any deviation from spherical Z, of a solid permits the evaluation of the
shape (except for perfect cubes) will average particle size, provided an as-
lead to an increase in the actual surface sumption is made concerning particle
to volume ratio and thus again to too shape. Since in principle the density is
small an average particle size as calcu- easily determined, the problem that re-
lated by Eq 3. mains is to evaluate the specific surface.
to the list of references appended to this paper. 4 The surface roughness as defined in reference
s I n some cases gas permeability measure- (2) is the ratio of the surface area as determined
ments enable the total surface area to be divided by N2 adsorption to that calculated from the
into that contributed by the geometric surface, particle size distribution as determined by elee-
that contributed by continuous pores, and that tsron microscopic count.
existing as blind pores (reference (1)). 5 See Table I and references (1,2,30,31,32).
FRIES ON ADSORPTION M E T H O D S 261
To see how this is done, it is necessary amount of gas adsorbed in the monolayer
first to consider the adsorption process. could be calculated. From the B E T the-
Adsorption of a gas on a solid occurs ory, the adsorption of a gas on a solid
when the solid is exposed to the gas; m a y be represented by the following
some of the adsorbate molecules leave equation:
the gas phase and tend to adhere to the
VmCx 1 - (n + 1)x~ + nx~+~
solid and form a layer of molecules on its
V 1-- x 1 + ( C - - 1)x-- Cx ~+1"'(5)
surface. This process is known as phys-
ical adsorption when the adhesive forces where V is the volume of gas adsorbed
between the gas and the solid consist of at pressure P ; x is the relative pressure,
relatively weak forces such as van der P / P o , that is, the ratio of the equilib-
Waals forces. I t is called chemisorption rium pressure, P, to the saturation pres-
when the forces at the solid-gas bound- sure, Po ; Vm is the volume adsorbed in
ary, that is, the interface, are sufficient a monolayer; n is the number of ad-
to promote chemical reaction (3). I t is the sorbed layers, and C is a constant related
physical or van der Waals adsorption exponentially to the heat of liquifaction
which permits a determination of the and the heat of adsorption (reference
specific surface. (3), p. 154).
Experimentally, one determines at When n is infinite (the case most often
some constant temperature the amount encountered experimentally when nitro-
of gas adsorbed as a function of the gas gen is used as the adsorbate at - 195 C),
pressure, that is, the adsorption iso- Eq 5 reduces to:
therm. I n order to calculate the specific
surface, it is necessary to determine from x 1 ( C - 1)x
+ - - ....(6)
this isotherm the number of adsorbate V(1 - x) V,~C V~,~C
molecules required to just cover the sur-
A plot of x / V ( 1 - x) versus x is usually
face of the solid with a monomolecular
linear over the range of relative pressures
layer. Then if a knowledge of the area
from 0.05 to 0.35, with a slope, S, of
occupied by each molecule in this mono-
(C - 1)/VmC and an intercept, I, of
layer is available, the specific surface
1/VmC. Thus Vm can be evaluated from
area can be evaluated by:
1 1 C-1
= noNA .............. (4) + - - -s+i
v , ~ - vmc vmc
where m is the number of moles of gas
in the monolayer per gram of adsorbent, or
N is Avogadro's number (6.02 X 1023), vm = (s + x)-I . . . . . . . . . . . (7)
and Ao is the area occupied by each
molecule. Area Occupied per Molecule:
I n their original work, Brunauer,
Evaluation of the Monolayer Capacity: Emmett, and Teller (7) assumed that the
Several treatments lend themselves to adsorbate molecules are held in two-di-
a theoretical explanation of specifc ad- mensional close packing on the surface,
sorption data (4,5,6), but until 1938 no the area occupied per molecule being the
really general treatment had been pro- projected cross-section of the molecular
posed. In 1938 Brunauer, Emmett, and volume calculated from the density of
Teller (7) proposed a theory (known as the solidifiedor liquified adsorbate. This
the B E T theory) of multimolecular ad- assumption leads to a value for the area
sorption from which a value for the per molecule, Ao, of:
262 SYMPOSllnvr ON PARTICLE SIZE MEASUREMENT
F M ]~/a sq A. with an uncertainty of 4-3 per cent.

Ao = 3 464 ...... (8)
Livingston (10) considers the problem of
where M is the molecular weight of the assigning cross-sectional areas to adsorb-
gas, N is Avogadro's number, and d is ate molecules and gives a list of the best
the density of the solidified or liquified values to use for a large number of ad-
adsorbate. When Ao is calculated from sorbates.
Main Vacuum Line To Mercury
To Mc Lead
9 Diffusion
Gage <
Pump
osphere
Go~
(Hel
Nit
Stopcock
Sample -
Bulb A
Lc
Temp
B( sure
. ) Liquid )
FIG. 1.--A Basic Gas Adsorption Apparatus (From Emmett (11)).
this equation using the density of liquid EXPERIMENTAL METHODS OF GAS

nitrogen at - 1 9 5 C, a value of 16.8 sq ADSORPTION
/~ per molecule is found, while the use of
General Considerations:
the density of solidified nitrogen at
- 255 C leads to a value of 13.8 sq A per In order to determine the adsorption
molecule. Thus there is a difference of isotherm for a given gas-solid combina-
about 20 per cent between surface areas tion, it is necessary that any gases ad-
calculated from these two values for A o. sorbed on the solid prior to the experi-
However, during the past twenty years, ment be removed. Joy (9) states that if
considerable evidence has been accumu- the quotient Tb/T~ is greater than three
lated to indicate that the area occupied (where Tb is the boiling point of the ad-
by each nitrogen molecule in the adsorbed gaseous impurity and Ta is the
sorbed phase is much closer to 16.2 sq temperature of the experiment), the im-
than to 13.8 sq A- (s). Joy (9) concludes purity will not affect the B E T surface
that Ao for nitrogen at - 1 9 5 C is 15.8 area, but may alter the heat of adsorp-
F R I E S ON ADSORPTION M E T H O D S 263
tion. If this quotient is less than three, The section of capillary tubing extend-
the adsorbed impurity will probably af- ing from stopcock T to the buret and to
fect both Vm and C. the reference point on the left leg of the
Degassing is generally accomplished by manometer, known as the zero bulb vol-
heating and simultaneously evacuating ume, is generally calibrated by means of
the sample under high vacuum (10.4 mm gas expansion. With stopcock T closed
Hg or lower). For the most accurate and the mercury set at the lowest refer-
work, the sample should be degassed at ence mark on the buret, a quantity of gas
as high a temperature as possible. (helium or nitrogen) is admitted to the
The choice of a temperature at which system through the gas inlet stopcock un-
the isotherm is to be determined is in- til a pressure of about 150 m m is read on
fluenced by several factors. The tempera- the manometer. The left leg of the man-
ture should be such that the pressures to ometer is then adjusted to the reference
be measured (corresponding to P / P o = mark, and the pressure of the unknown
0.05 to 0.35) fall into an experimentally quantity of gas is read and recorded as
convenient range. In addition the bath Pi 9 Mercury is then admitted to the bu-
required to maintain the sample at the ret until the lower bulb is filled, the man-
desired temperature should be easy to ometer is again set to zero, and the pres-
prepare and maintain. When nitrogen gas sure P2 corresponding to the new volume
is used as the adsorbate, liquid nitrogen recorded. This procedure is repeated un-
forms a very good refrigerant, since the til a sufficient number of experimental
pressures to be measured then fall in the points has been obtained. If we denote
range of from 50 to 400 mm Hg. the zero bulb volume which is being cali-
brated as Vo and the buret volume,
Volumetric A pparalus: which is known from a previous calibra-
tion, as Vb, at constant temperature we
The apparatus used for obtaining gas have the following relationship:
adsorption isotherms is of two general
P(Vb + Vo) = c o n s t a n t = C
classes, that is, volumetric and gravi-
metric, depending on whether the vol- PVb + PVo = C
ume or weight of the gas adsorbed is or
measured in the experiment. This section
Pvb = -PVo + c .................... (9)
and the next will be devoted to a dis-
cussion of the apparatus and methods of Now, for each of the experimental
these two classes. points, the measured pressure, P, is mul-
Most modern volumetric designs are tiplied by the volume of the buret at that
based on the apparatus first used by Em- particular setting of the mercury, Vb,
mett (11), which is shown in Fig. 1. There and a plot of P X Vb with respect to P
are three essential components, namely, is prepared. A straight line is obtained
the sample tube, A, the mnltibulb buret, whose slope is the negative of the zero
B (which must be cal{brated before being bulb volume, Vo. Stopcock T remains
mounted into the system), and the mer- closed during this procedure, since the
cury manometer. In order to maintain a volume to the left of this stopcock will in
known system volume at all times, it is general be different for each sample, and
necessary to adjust the mercury level in thus this section, the so-called dead
the left leg of the manometer to some ref- space, must be calibrated for each new
erence mark before taking a reading on sample. The apparatus is now calibrated
the manometer. and ready for adsorption measurements.
264 SYMPOSIUM ON PARTICLE SIZE I~EASUREMENT
To make a measurement, the adsorp- PXF

tion bulb containing the desired amount V(ml at STP) = - - . . . . . . (ll)
T
of sample is sealed on to the apparatus at
the left side of stopcock T and then de- For precise work, it is desirable to check
gassed. The next step is to calibrate the the volume of gas taken at several differ-
dead space volume so that the amount of ent bulb settings.
unadsorbed gas present in the sample After the volume of helium taken has
tube to the left of stopcock T can be de- been determined, stopcock T is opened
termined. Since this calibration is best and the helium is allowed to expand into
made with the sample at operating tem- the sample tube. When thermal equilib-
perature, it is necessary to use a gas rium is established, the pressure is read
which will not be adsorbed by the sam- and the volume of helium remaining in
ple. Helium is generally used for this the buret system is calculated. The vol-
purpose because at temperatures of ume of helium present in the sample tube
--195 C or higher the amount of helium is the difference between the total volume
adsorbed on most materials will be negli- of helium in the system and the quantity
gible. The liquid nitrogen bath is placed remaining in the buret system at the
around the sample bulb, and the sample equilibrium pressure. For convenience in
is isolated from the measuring system by later calculations, a "dead space factor"
closing stopcock T. A volume of helium f is calculated from:
is then admitted to the buret through the vt- vb
gas inlet stopcock, and the amount of gas f - - . . . . . . . . . . . (12)
Pc
taken determined by measuring the pres-
sure and temperature of the gas at a where Vt is the total volume of helium
given buret bulb setting. The volume of taken, Vb is the volume remaining in the
gas is calculated from: buret system at equilibrium, and Pc is the
equilibrium pressure corrected to 0 C. If
V(ml at STP)6 the helium is not adsorbed by the sam-
(22,414)(Vb + Vo)(P) X do pie, this dead space factor will be a con-
= R x r ~ . (10) stant and its constancy should be estab-
lished by determining f at two or more
where 22,414 is the standard gas volume different pressures (by changing the set-
in milliliters per mole, (Vb + Vo) is the ting of the mercury in the buret). At the
volume of the system, P and T are the conclusion of the dead space calibration,
measured pressure and temperature, and the helium is pumped out of the adsorp-
do/d2~ is the ratio of the density of mer- tion system.
cury at 0 C to that at the operating tem- With the sample prepared for nitrogen
perature (taken as 25 C), This last fac- adsorption, the dead space factor deter-
tor corrects the pressure reading of the mined, and the sample tube and buret
mercury manometer to standard condi- system evacuated, stopcock T is closed.
tions. I t is convenient to prepare a table Next an appropriate volume of nitrogen
of values of (22,414)(Vb.:-~ Vo)do/Rd2~ is admitted to the buret system and its
(denoted as F) for each of the various volume determined by noting the pres-
possible buret bulb settings, so that the sure and temperature for a given buret
STP volume of gas in the buret system bulb setting and employing Eqs 10 or l l .
can be calculated simply from the equa- Stopcock T is then slowly opened and the
tion: system is allowed to equilibrate. For ni-
6 Standard temperature and pressure. trogen surface area determinations, this
FRIES ON ADSORPTION METHODS 265
first adsorption point can conveniently tercept determined, and the monolayer
be taken at an equilibrium pressure of capacity, Vm, calculated by means of
about 100 m m Hg and the mercury level Eqo7. The specific surface, assuming 16.2
in the buret should be so adjusted. After sq A as the cross-sectional area of the nitro-
equilibrium has been established, the gen molecule, can then be calculated from
pressure, temperature, and buret setting
should be recorded along with some (4.38) (Vm)
2~(sq m per g) = .. (15)
measure of the bath temperaturC which Sample weight in g r a m s
is needed to establish Po, the vapor pres- Generally three or four experimental
sure of nitrogen at the operating temper- points in the relative pressure range 0.05
ature. The amount of gas adsorbed, Va,
measured in milliliters at STP, is then To Kryptonand Helium
calculated from: Storage
V,, = V ~ - V~- Vd . . . . . . . . (13)

( ~ - T o High
where V, is the total volume of nitrogen ~j'~Vocuum
in the system, Vb is the volume of gas re-
maining in the buret section as calculated
by means of Eqs 10 or 11 and Va8 is the
volume in the dead space which is calcu-
lated from:
vd~ = (f) (Po)(~) . . . . . . . . . (14)
w h e r e f is the dead space factor (Eq 12),
SaT~PI: IJJ McLeod
Gage
Pc is the equilibrium pressure corrected

to 0 C, and/3 is a correction for the non-
ideality of nitrogen gas at the bath tem-
perature (12). To obtain the second ad-
sorption point, the mercury level in the
buret is increased so as to give a pressure
increase of 30 to 40 mm Hg. If insuffi- FIO. 2 . - - A Simple K r y p t o n Adsorption Ap-
cient nitrogen remains in the buret sys- p a r a t u s (Mter Bloecher (13)).
tem to accomplish this, stopcock T is
closed and the gas volume remaining in to 0.30 are sufficient for the determina-
the buret is determined. A second "dose" tion of a surface area.
(quantity) of nitrogen is then added, the Use of Krypton as an Adsorbate.--From
new volume of gas in the buret deter- Eq 13 it is seen that in order to maintain
mined, and the new total amount of ni- a reasonable degree of precision in the de-
trogen in the system calculated. By termination of the volume adsorbed, the
means of a repetition of this procedure, amount of unadsorbed gas in the sample
values of Va and P / P o for a sufficient tube, Ve,, should be small compared
number of points on the isotherm are col- with Va 9 Since increasing the sample size
lected. Then, using Eq 6, a B E T plot of also increases the dead space volume, the
the data is prepared, the slope and in- amount of gas adsorbed on samples with
a specific surface of about 1 sq m per g or
7 Several m e t h o d s are available for measuring smaller cannot be determined using ni-
the bath temperature, such as oxygen or nitro-
gen vapor pressure thermometers, t h e r m o -
trogen without considerable error, even
couples, or resistance thermometers. when using relatively large samples.
One method of circumventing this diffi- A basic volumetric adsorption system us-
culty is to use some combination of ad- ing krypton as the adsorbate is shown in
sorbate and bath temperature for which Fig. 2 (13). There are only two essential
the value of Po is much smaller than 760 parts of this system, a sample tube and a
m m Hg. Then for a given value of rela- McLeod gage of known volume, con-
tive pressure, P/Po, the absolute pres- nected by wide bore tubing. The McLeod
sure will be correspondingly reduced, as gage doubles as the gas buret and is
will the volume (STP) of gas in the sys- used to calibrate the other sections of the
M
N
FIG. 3.--Diagram of a Volumetric Gas Adsorption Apparatus Suitable for Both Routine and
Research Studies (17).
tem but not adsorbed. Krypton, which system and also to measure the amounts
has a vapor pressure of about 3 m m Hg of krypton used in the adsorption meas-
at liquid nitrogen temperature ( - 195 C), urements.
has been found to be a good choice for After the apparatus has been assem-
low area materials. The amount of un- bled, the volume of tubing enclosed by
adsorbed gas in the system is reduced by stopcocks 1, 2, 3, and 4 is calibrated by
a factor of 3/760 or about 0.004 while expansion of a known volume of helium
the volume adsorbed per unit area is from the McLeod gage into the connect-
about 80 per cent of that for nitrogen. ing tubing and application of the perfect
The use of this adsorbate has made pos- gas laws. With a sample in place and
sible the measurement of surface areas ready for adsorption measurements, the
as small as 50 sq cm with good precision. dead space factor (Eq 12) is determined
in the same way as for the nitrogen meas- made by admitting more helium to the
urements. An amount of helium is ad- system and repeating the procedure.
mitted to the measuring system with The method of determining the experi-
stopcock 1 closed, and its volume (ml, mental points of the adsorption isotherm
FIG. 4.--The Volumetric Gas Adsorption Apparatus Shown in Diagram in Fig. 3.
STP) is determined by means of the is just the same as that already described
known system volume, the gas pressure, for the nitrogen system, except that the
and the temperature. The helium is then working pressure range is from 0.15 to 1.0
expanded into the refrigerated sample mm Hg. The calculations are identical to
tube, and the volume of gas remaining in those for nitrogen except that the non-
the McLeod gage and connecting tubing ideality correction factor, ~ (see Eq 14),
is determined. A check determination is can be set equal to one, since only low
pressures are involved. However, it is be obtained with only one (the initial)
necessary for the most precise work to admission of nitrogen gas to the system
correct the measured equilibrium pres- The burets are jacketed so that they can
sures for thermal transpiration effects be thermostated by circulating water
(14,15). from a constant temperature bath.
The bath temperature (and thus Po for The manometer is equipped with two
krypton) can be determined by one of devices which facilitate the adjustment
the same methods listed for nitrogen ad- of the mercury level to the reference
sorption, or at the end of the experiment mark. The reference mark itself consists
krypton can be condensed in the sample of a tungsten contact, T, sealed into the
tube and the vapor pressure determined manometer. This contact and another
with the McLeod gage. However, since one located in the mercury reservoir are
krypton is a solid at - 1 9 5 C and the Po connected in series with a voltage supply
required is that for the liquid (16), it is and a neon indicator lamp. The mercury
necessary to convert the measured value level is adjusted to within 1 cm of the bot-
to that appropriate for the supercooled tom of the reference contact by applying
liquid at the same temperature. either pressure or vacuum through stop-
Once the value of Vm has been deter- cock 16 to the mercury reservoir. Then,
mined from the B E T plot and Eq 7, the by means of the fine control E (essen-
specific surface (assuming a cross-sec- tially a rubber-tube and pinchcock ar-
tional area of 19.5 sq A per krypton rangement), the mercury is raised until
atom) can be calculated from: it just makes contact with the tungsten
tip as indicated by the lighting of the
(5.2S)(Vm)
~(sq m per g) = .. (16) neon lamp.
Sample weight in grams
For measurements with krypton, the
Modification of the Basic Types of Vol- dead space is first calibrated in the nor-
umetric Apparatus.--A large number of mal manner using the burets and manom-
different types of volumetric systems eter system. The krypton adsorption
have been reported in the literature, some data are then obtained using the cali-
suitable for almost any type of adsorp- brated doser G and the manometer C for
tion research, others suitable only for sur- measuring a dose of gas, which is then
face area determinations on one specific admitted to the sample tube A through
type of material. A few of these different stopcocks 7a and 6. The equilibrium pres-
types are discussed below. sure is measured with the three stage
The apparatus of the Department of McLeod gage K. With this doser system
Research in Chemical Physics at Mellon it is necessary to admit a separate dose
Institute (17), which was designed for gas of gas for each point to be determined.
adsorption research and also routine sur- The refrigerant bath (liquid nitrogen)
face area determinations with either ni- temperature is measured with a nitrogen
trogen or krypton, is shown in Figs. 3 vapor pressure thermometer consisting of
(diagram) and 4. The nitrogen system thermometer bulb L, manometer I, and
consists of the sample tube A, burets B the uncalibrated gas holder H which is
and B r, and the mercury manometer C, used to compress the gas in the system
which is backed by a graduated mirror so that liquid-vapor equilibrium is es-
scale. tablished in the thermometer bulb at the
The use of two burets enables data for operating temperature. A gas thermome-
a complete surface area determination ter, which measures the vapor pressure
(and often for a complete isotherm) to of the adsorbate gas, Po, directly, is very
FRIES ON ADSORPTION M E T H O D S 269
convenient to use, since this quantity en- which enables several points to be taken
ters directly into the B E T surface area for each dose of krypton.
calculation. The major disadvantage of the volu-
The auxiliary equipment incorporated metric gas adsorption methods as de-
into this apparatus includes several 3- scribed above is the length of time re-
liter bulbs F for the storage of purified quired for a determination. Even by
gases, and a two-trap (glass beads and outgassing several samples simultaneously
ToThermostot~ T h e r m i s t o r
C N
Krypton C
11
To McLeod
Goge 1 S-2
F To Vocuum
To Atmosphere
FIO. 5.--Apparatus Used for Krypton Adsorption on Very Small Surface Areas (From
Rosenberg (15)).
Courtesy of Journal Am. Chemical Soc,
charcoal) gas purification train (not overnight, an experienced operator can

shown). run only three or four samples in a work-
Rosenberg (IS) has described a krypton ing day. However, for routine determina-
adsorption apparatus suitable for accu- tions where an error of 10 to 15 per cent
rately measuring areas as small as 50 sq is not objectionable, several steps can be
cm. This apparatus is shown in Fig. 5 and taken to speed up the procedure. The
is unique in that it employs a thermistor great majority of inorganic adsorbents
vacuum gage to measure the krypton give rise to B E T plots with quite small
pressures. In addition, the apparatus em- intercepts, which enables a surface area
ploys mercury cutoffs instead of stop- to be computed from one experimental
cocks and also a multibulb buret system point by assuming that the B E T plot
passes through the origin. Emmett (see cluded in the system can be calculated
reference (12), Chapter 1) states that the from a knowledge of the position of the
slope of an adsorption curve using a zero mercury. The gas measuring buret con-
intercept and one experimental point us- sists of a single fixed calibrated volume,
ually differs by less than 5 per cent from since only one adsorption point is to be
the slope determined by three or four determined. In addition, the samples are
points. outgassed for 10 to 20 min at room tem-
An apparatus designed to take ad- perature with a mechanical pump to a
vantage of this and several other time- pressure of 10-2 mm Hg or less. With
saving steps has recently been described these modifications, Starkweather and
Palumbo report a time per determination
of about 1 hr with an error (always nega-
Silica
•['III•Cop tive) of usually less than 10 per cent as
compared to the standard B E T method.
I I I-wa,erJocke,
ToGosl I ~ I I Gravimetric Apparatus:
Storage l I ~ II ~,90Higuh
The gravimetric methods of studying
gas adsorption are in general much sim-
pler than the volumetric ones. Since the
amount of gas adsorbed is observed di-
rectly, the volume of the adsorption
~Sd~ system is immaterial, which eliminates
volume calibrations and dead space de-
terminations. The major disadvantage of
the gravimetric methods arises from the
ample
fact that rather small changes in weight
must be determined. The apparatus re-
quired is accordingly more fragile and
difficult to construct than volumetric
types.
The original design of McBain and
Mercury
Manometer
Bakr (19), which utilized a fused silica
FIo. 6.--A Basic Gravimetric Adsorption helix as the balance, has served as the
Apparatus. prototype for the majority of the mod-
ern gravimetric systems. The apparatus
by Starkweather and Palumbo (18). In shown in Fig. 6 (patterned after that of
their system, sample tubes of known vol- McBain and Bakr) is a simple gravimet-
ume are attached to the apparatus by ric system suitable for nitrogen adsorp-
means of a ground glass joint. A knowl- tion studies. Its essential parts are a fused
edge of the density of the adsorbent un- silica helix in a thermostated s balance
der study then enables a calculation of case and a mercury manometer. The sam-
the dead space correction and thus elimi- ple is placed in a thin-shelled glass bucket
nates the helium calibration. Their man- and attached to the helix by a long fused
ometer is made from precision bore tub- silica or vycor fiber so as to isolate the
ing which eliminates the necessity of balance spring from the extremes of tern-
adjusting the mercury in the pressure leg
s A good discussion of the errors introduced
of the manometer to a reference mark, by changes in the temperature of ~he helix is
since the volume of the manometer in- given in reference (20).
FRIES oN ADSORPTIONMETHODS 271
perature present in the vicinity of the plot is prepared from the data using Eq
sample. Easy access to the sample is pro- 6 (substituting weights Wa and W,~ for
vided by the ground glass joint in the volumes V~ and V~), and the monolayer
lower section of the balance housing. capacity, I/V~, calculated from Eq 7. The
The change in weight of the sample is specific surface (assuming 16.2 sq 2t as
determined by measuring the elongation the area of a nitrogen molecule) is then
of the helix with a cathetometer (0.1 mm) calculated from:
or a traveling microscope (0.001 mm).
3.50Win
The helix, of course, must first be cali- ~(sq m per g) = .. (18)
brated by attaching a series of known Sample weight in grams
weights and observing the extensions where W,,~ is the weight adsorbed in a
produced. For most work at low tempera- monolayer expressed in milligrams.
ture (liquid nitrogen), it is necessary to Modifications of the Basic Gravimetric
correct for the bouyancy effect of the gas A p p a r a t u s . - - W i t h the gravimetric spring
present in the balance case. balance, it is possible to determine iso-
To determine a nitrogen adsorption therms for several samples simultane-
isotherm, a sample is prepared, placed ously, by assembling the desired number
in the apparatus, and then degassed un- of balance cases and helices in parallel,
der high vacuum at an appropriate tem- and arranging the optical system so that
perature. This accomplished, the refrig- each of the springs can be observed in
erant bath is placed about the sample and turn. Milligan et al (21) have described
the zero point of the helix is noted. an apparatus suitable for simultaneous
Nitrogen gas is then slowly admitted adsorption measurements on 15 samples.
to the system through stopcock 1 until Their balance units were arranged lin-
the desired pressure is reached; stopcock early so that the extension of any of the
1 is then closed and the system allowed quartz helices could be determined with
to equilibrate. Because of the large vol- a micrometer microscope which was
ume of the measuring system, the pres- mounted on a horizontal screw-driven
sure change caused by the adsorption is platform. The elongation of a given helix
generally quite small, and the equilibra- was determined by measuring the total
tion must be followed by observing the length of the spring in order to eliminate
extension of the helix. When the system the effects of any change in the vertical
has equilibrated, the final position of the position of the microscope platform as
helix, the pressure, and the bath tempera- it was shifted horizontally to the various
ture are noted. The net weight gain, W~, samples.
of the sample is determined from the cali- A further advantage of the spring bal-
bration data for the helix. The total ance apparatus is the ease with which it
amount adsorbed is then: can be made to be recording. Klevens et
Wa = W,~ + V.d . . . . . . . . . (17) al (22) have recently described such a re-
cording adsorption system. The balance
where V~ is the volume of the sample and used was a conventional silica helix in an
the sample bucket and d is the density apparatus much like Fig. 6. The record-
of the gas around the sample in the bal- ing feature was obtained by attaching
ance case. the core of a linear variable differential
This procedure is repeated, adding a transformer (LVDT) 9 to the silica fiber
suitable increment of gas for each ad- midway between the helix and the sam-
sorption point, until a sufficient number
of data have been obtained. The B E T 9 Schaevitz Engineering Co., Camden, N. J,
pie. The transformer coil (in the shape that, as the solute concentration is in-
of a hollow cylinder) was placed around creased, the amount adsorbed increases
the outside of the balance case and ad- but asymptotically approaches a con-
justed vertically to enclose the core. stant value, which is usually considered
With the L V D T primary winding ap- to result from the complete coverage of
propriately energized, the position of the the surface with a monomolecular layer
core relative to coil is measured by the of the solute. In many cases, the adsorp-
output from the secondary winding of the tion data can be fitted to the Langmuir
transformer coil, which can be rectified equation:
and fed to a recording potentiometer.
aWoc
With this system, both the helix and W - - - .(19)
1-{- ac
transformer must be calibrated, but it
is a simple matter to calibrate the L V D T where W is the weight of solute adsorbed;
at the same time as the helix. c is the equilibrium solute concentration;
Although many workers have used Wo is the maximum weight of solute ad-
beam balances in adsorption studies, the sorbed (that is, the monolayer capacity) ;
majority of these are of the very high and a is a constant. In this case, it is
sensitivity--low total load type which are necessary to determine only a few points
not well suited for routine studies, such on the isotherm at low concentration and
as specific surface determinations, be- then calculate the monolayer capacity,
cause they are di~cult to construct and W o , from Eq t9.
are very fragile. Two very good articles The area occupied per solute molecule
on vacuum microbalances, with emphasis can be determined by the use of a solid
on the beam types, have recently ap- of known surface area to calibrate the
peared. The paper by Rhodin (z3) covers solute-solvent system, or by a study of
low-temperature applications while that the force-area relation in a film of the sol-
by Gulbransen (24) covers high-tempera- ute by means of a film balance (25).
ture applications. The reader is referred At first glance, adsorption from solu-
to these papers for details on this type tion appears to be a very attractive
of gravimetric apparatus. method for specific surface determina-
tions because it requires little skill to
SURFACE A R E A D E T E R M I N A T I O N S BY carry out and only simple apparatus. The
ADSORPTION FROM SOLUTION outgassed sample is immersed in a known
The determination of surface area by volume of solution of the desired concen-
adsorption of solutes from solution is tration, shaken until equilibrium is
quite similar in principle to gas adsorp- reached, and the supernatant liquid ana-
tion methods. I t is necessary first to de- lyzed. If a dye is used as the adsorbate,
termine the number of molecules of solute the solution concentration can be con-
required to completely cover the surface veniently determined colorimetrically.
with a monomolecular layer. A knowl- With some colorless solutes such as de-
edge of the area occupied by each solute tergents, an interferometer can be used to
molecule on the surface then enables the determine the solution concentration.
surface area to be calculated. However, considerable uncertainty can
The monolayer capacity is obtained by arise in assigning a value to the mono-
studying (at constant temperature) the layer capacity. Since the adsorbent is ex-
relationship between the amount of sol- posed to both solute and solvent mole-
ute adsorbed and the equilibrium solute cules, it is to be expected that there will
concentration. I t is found experimentally be some solvent adsorption. The latter
causes the apparent monolayer capacity or particle size determination is to be

to be too small since some unknown part used for control purposes for the produc-
of the surface is occupied by solvent mol- tion of a single material, the methods in-
ecules. This effect can be minimized by volving adsorption from solution can be
choosing solute-solvent combinations so developed into reliable and rapid tech-
that the solute is much more strongly ad- niques. However, when a large number
sorbed than the solvent. The system ste- of different materials are to be examined,
aric acid-benzene is often used, in which the liquid adsorption techniques should
case great care must be taken to keep the be relied on only for qualitative estimates
solution free from water, since the water of the specific surface, unless previous
competes with the stearic acid for oc- investigation has shown the method in
cupancy of the surface. The necessity of use to be reliable for the type of sample
excluding water can be eliminated by under investigation.
working with aqueous solutions, and
HEAT-oF-WETTING METHODS
some work has been done using water
solutions of various detergents (26). Gregg One further method of determining
(27) states that even in cases where the specific surface areas by means of ad-
solute is known to be preferentially adsorption is the heat-of-wetting or heat-of-
sorbed, great caution must be used in the immersion method. This method is based
interpretation of the value obtained for on the measurement of the heat evolved
the monolayer capacity. Gregg goes on to when a clean, outgassed solid powder is
say that the only case in which solvent immersed in and wet by a liquid. If the
adsorption may be safely neglected in the total heat evolved is H cal per g and the
absence of independent evidence is the heat evolved per square centimeter of
case where the solute is chemisorbed on surface is h, then the specific surface can
the surface. An example of this is the ad- be calculated from:
sorption of fatty acids on nickel and plat- H
inum catalysts (28). Z = --. . . . . . . . . . . . . . (20)
h
The value assigned to the area occu-
pied by each adsorbate molecule can also The value of H is determined experi-
give rise to considerable uncertainty in mentally using a calorimeter while h must
the calculated specific surface. The mole- be evaluated for the liquid-solid combi-
cules generally employed as solutes in nation employed by means of a sample
these studies are large and irregularly whose specific surface is known from in-
shaped so that the area occupied per mol- dependent measurements. Good discus-
ecule depends on the orientation of the sions of the apparatus and methods for
molecule with respect to the surface. heat-of-wetting measurements are given
Also, the large solute molecules will not by Gregg (see reference (27), p. 288).
have access to some of the smaller irregu- An absolute method for determining
larities and pores on the surface which the specific surface of nonporous solids
will lead to an error in the calculated spe- which is essentially a heat-of-wetting
cific surface. For particles with a large method has been developed by Harkins
surface roughness factor, this effect could and Jura (29). In this method, the pre-
be beneficial in that it should result in a viously cleaned solid is exposed to the
surface average diameter in better agree- vapor of a liquid which completely wets
ment with that obtained by other particle the surface (one which gives a 0 deg
size methods. contact angle with the surface) until
In applications where the surface area equilibrium is reached, at which time the
b~
TABLE I.--A COMPARISON OF THE ELECTRON MICROSCOPE AND NITROGEN ADSORPTION METHODS
OF SURFACE AREA AND PARTICLE SIZE DETERMINATION.
Material N2 Adsorption Surface Area Electron Microscope Surface Area Gas Permeability Surface Area Surface [
R o u g h nReference
e s s
Carbon blacks
Kosmos 20 ..................... 41 sq m per ml 47 sq m per ml 48 sq m per ml (30)
Kosmos 40 ..................... 78 sq rn per ml 72 sq m per ml 68 sq m per ml (30)
Statex B ....................... 99 sq rn per ml 72 sq rn per ml 103 sq m per rnl (30) N
Kosmobile S ................... 277 sq m per ml 162 sq rn per ml 176 sq m per ml (3o) 9
Mogul a ........................ 450 sqmper g 86.6 sq m per g (2)
Lampblack LBTT a .............. 208 sq In per g 28.5 sq rn per g (9)
Spheron G ..................... 120 sqmper g 106 sq m per g (31)
Sterling S ...................... 22 sqmper g 26 sq m per g (31) 9
Sterling MT ................... 6.6 sqrnper g 5.7 sq m per g (31)
Vulcan 3R .................... 77 sqrnper g 74 sq m per g (31)
Spheron C .................... 227 sqmper g 110 sq m per g (31)
Sterling VR ................... 25 sqmper g 43 sq rn per g (al)
Zinc oxides
F-1601 ....................... 56 sq m per ml 35 sq m per ml 45 sqmperrnl (3o) t~
I~-1602 ....................... 52 sq m per ml 27 sq rn per ml 35 sqmperml (3o)
G-1603 ....................... 23 sq m per ml 13 sq m per ml 16 sqrnperml (3o) N
Copper powder
15 X 2 0 . . . . . . . . . . . . . . . . . . . . . . 0.039 sqmper g 0.0365 sq m per g (39.)
10 X 15 . . . . . . . . . . . . . . . . . . . . . . 0,067 sqmper g 0.050 sq m per g (3~) N
Zinc powder
5X10 ....................... 0.233 sqmper g 0.125 sq m per g (39.)
10 X 15 . . . . . . . . . . . . . . . . . . . . . . 0.134sqmper g 0.084 sq m per g (32)
Glass spheres N
Fraction II .................... 0.55 sqmperg 0. 258 sq m per gb 0.287 sqmper gC (33)
Fraction IV ................... 0.37 sqmperg 0.151 sq m per gb 0.174 sqmper gC (33)
ColloidM silica
A ............................ 185 sqmper g 139 sq m per g (34)
B ............................ 125 sqmper g 111 sq rn per g (34)
C ............................ 68 sqmper g 43 s q In p e r g (3~.)
a Air or steam activated. Known to be porous.
b Photornicrographic count.
Poiseuille term only. 9
surface energy of the adsorbed film will so that the fifth column also indicates the
be the same as that in the bulk liquid. agreement between the surface average
The film-coated solid is then immersed particle sizes determined by the two
in the bulk liquid and the heat evolved methods.
from the destruction of the adsorbed film All of the materials listed in Table I
is measured. Knowledge of the surface are thought to be nonporous with the
energy of the liquid used then enables a exception of the glass spheres and the
calculation of the amount of surface de- two activated carbon blacks, Mogul and
stroyed which can be corrected for film Lampblack LBTT. The agreement be-
thickness to give an absolute value for tween adsorption and electron micros-
the specific surface of the powder. copy measurements for the remainder of
COMPARISON WITH OTHER METHODS the carbon blacks is within a factor of two
An examination of the literature re- in all cases and within 40 per cent for the
veals that most of the data available majority of the materials. The surface
compare the adsorption methods of par- roughness value of 0.58 for the furnace
ticle size determination with either gas black, Sterling VR, is probably a result
permeability or electron microscopy re- of nonrepresentative sampling.
suits. Since the permeability method es- The agreement between the two meth-
sentially measures the specific surface of ods is also satisfactory for inorganic ma-
the material in question, a comparison terials. The roughness factors are, in
of the results from it and those from ad- general, larger than those for the carbon
sorption is not very indicative of the blacks, but the carbons would be ex-
validity of particle sizes determined by pected to exhibit smoother surfaces be-
the adsorption method. In view of this cause of their method of preparation. Gas
fact, the results shown here will be con- permeability measurements on the two
fined to a comparison of gas adsorption samples of glass spheres (1) indicated a
and electron microscopy data, with re- porous structure, which would account
sults from gas permeability and other
for the rather large roughness factors
methods indicated when available.
found for these two samples.
A representative selection of the com-
The data presented in Table I are
parative data available is presented in
Table I. The gas adsorption data were all probably as good a measure of the ac-
obtained with nitrogen using the B E T curacy of the nitrogen adsorption method
equation (Eq 6) and 16.2 sq _~ as the for average particle size determination as
area of the adsorbed nitrogen molecule. is available, but they give no indication
The electron microscope data were com- of the reproducibility of the method. Ex-
puted from Eq 3 using the surface av- perience has shown that data obtained
erage diameter calculated from d3 = from a single precision apparatus (such
~__~dnd3/~_~and2. The results are presented as that illustrated in Fig. 4) are reproduc-
as specific surface areas in units of sq m ible to 1 per cent or better. Agreement
per g or sq m per ml. The surface rough- between different laboratories is gener-
ness factor is equal to the ratio of the ally at least within 5 per cent, provided
electron microscope diameter to the ad- that good sampling techniques are used
sorption diameter; that is, and that the same experimental proce-
Surface roughness = Z ~ = ~13EM. . (21)
dure is followed by the various labora-
~EM d,sh% tories.
276 SYMPOSIUIVI ON PARTICLE SIZE MEASUREMENT
REFERENCES
(1) G. Kraus and J. W. Ross, "Surface Area (1953); Vol. 56, p. 660 (1952); Journal of
Analysis by Means of Gas Flow Methods, Applied Physics, Vol. 22, p. 148 (1951).
II," Journal of Physical Chemistry, Vol. 57, (15) A. J. Rosenberg, "Rapid, Precise Measure-
p. 33 (1953). ment of Krypton Adsorption and the Sur-
(2) R. B. Anderson and P. H. Emmett, "Meas- face Area of Coarse Particles," Journal,
urement of Carbon Black Particles by the Am. Chemical Soc., Vol. 78, p. 2929 (1956).
Electron Microscope and Low Tempera- (16) R. A. Beebe, J. B. Beckwith, and J. M.
ture N trogen Adsorption Isotherms," Honig, "The Determination of Small Sur-
Journal of Applied Physics, Vol. 19, p. 367 face Areas by Krypton Adsorption at Low
(1948). Temperatures," Journal, Am. Chemical
(3) S. Brunauer, "The Adsorption of Gases and Soc., Vol. 67, p. 1554 (1945).
Vapors," Princeton University Press, (17) P. A. Faeth and C. B. Willingham, "Tech-
Princeton, N. J., Vol. 1, p. 4 (1953). nical Bulletin on the Assembly, Calibration,
(4) I. Langmuir, "The Adsorption of Gases on and Operation cf a Gas Adsorption Appa-
Plane Surfaces of Glass, Mica, and Plati- ratus for the Measurement of Surface Area,
num," Journal, Am. Chemical Soc., Vol. Pore Volume Distribution and Density of
40, p. 1361 (1918). Finely Divided Solids," Mellon Institute,
(5) J. W. MeBain, "The Sorption of Gases and Pittsburgh, Pa., Sept., 1955.
Vapors by Solids," G. Routledge and Sons, (18) F. M. Starkweather and D. T. Palumbo,
Ltd., London (England), p. 5 (1932). "A Simplified Procedure and Apparatus for
(6) J. H. deBoer and C. Zwikker, Zeitschrift Measuring Surface Area of Fine Powders
Physik und Chemie, Vol. B3, p. 407 (1929). by Gas Adsorption," Journal, Electrochem-
(7) S. Brunauer, P. H. Emmett, and E. Teller, ical Soc., Vol. 104, p. 287 (1957).
"Adsorption of Gases in Multimolecular (19) J. W. McBain and A. M. Bakr, "A New
Layers," Journal, Am. Chemical Soc., Sorption Balance," Journal, Am. Chemi-
Vol. 60, p. 309 (1938). cal Soc., Vol. 48, p. 690 (1926).
(8) P. H. Emmett, "Catalysis," Reinhold (20) F. M. Ernsberger, "Temperature Coeffi-
Publishing Co., New York, N. Y., Vol. 1, cient of the McBain Sorption Balance,"
p. 48 (1954). Review of Scientific Instruments, Vol. 24,
(9) A. S. Joy, "The Determination of Specific p. 998 (1953).
Surface by Gas Adsorption," Vacuum, Vol. (21) W. O. Milligan, W. C. Simpson, G. L.
3, p. 254 (1953). Bushey, H. H. Rachford, Jr., and A. L.
Draper, "Precision Multiple Sorption - De-
(10) H. K. Livingston, "The Cross-Sectional
sorption Apparatus," Analytical Chemistry,
Areas of Molecules Adsorbed on Solid Sur-
Vol. 23, p. 739 (1951).
faces," Journal of Colloid Science, Vol. 4, (22) H. B. Klevens, J. T. Carriel, R. J. Fries,
p. 447 (1949); Journal, Am. Chemical Soc., and A. It. Peterson, "The Proceedings of
Vol. 66, p. 569 (1944). the Second International Congress of Sur-
(11) P. H. Emmett, "A New Method for Meas- face Activity," Butterworths Scientific
uring the Surface Areas of Finely Divided Publications, London (England) (1957).
Materials and for Determining the Size of (23) T.N. Rhodin, Jr., "Advances in Catalysis,"
Particles," Symposium on New Methods Academic Press Inc., New York, N. Y.,
for Particle Size Determination in the Sub- Vol. 5, Chapter 2 (1953).
sieve Range, Am. Soc. Testing Mats., p. 98 (24) E.A. Gulbransen, "Advances in Catalysis,"
(I941). (Issued as separate publication Academic Press Inc., New York, N. Y.,
ASTM STP NO. 51.) Vol. 5, Chapter 3 (1953).
(12) P. H. Emmett, "Advances in Colloid Sci- (25) W. O. Harkins and D. M. Galls, "An Ad-
ence," Interscience, New York, N. Y., VoI. sorption Method for the Determination of
1, p. 4 (1942). the Area of A Powder," Journal, Am.
(13) F. W. Bloecher, "A New Surface Measure- Chemical Soc., Vol. 53, p. 2804 (1931).
ment Tool for Mineral Engineers," Trans- (26) W. W. Ewing and R. N. Rhoda, "Deter-
actions, Am. Inst. Mining Eng., Vol. 190, mination of Relative Specific Surface of
p. 255 (1951). Zinc Oxide Pigments," Analytical Chem-
(14) S. C. Liang, "On the Calculation of Ther- istry, Vol. 22, p. 1453 (1950).
mal Transpiration," Canadian Journal of (27) S. J. Gregg, "The Surface Chemistry of
Chemistry, Vol. 33, p. 279 (1955); Journal Solids," Reinhold Publishing Co., New
of Physical Chemistry, Vol. 57, p. 910 York, N. Y., Chapter 11 (1951).
DISCtYSSlON ON ADSORPTION METHODS 277
(28) H. A. Smith and J. F. Fuzek, "The Ad- Microscope," Godfrey L. Cabot, Inc.,
sorption of Fatty Acids on Nickel and Boston, Mass., 2nd Edition (1953).
Platinum Catalysts," Journal, Am. Chem- (32) P. H. Emmett and M. Cines, "Surface
ical Soc., Vol. 68, p. 229 (1946). Area Measurements on Metal Spheres and
(29) W. D. Harkins and G. Jura, "An Absolute on Carbon Blacks," Journal o] Physical and
Method for the Determination of the Area Colloid Chemistry, Vol. 51, p. 1329 (1947).
(33) G. S. Kraus, J. W. Ross, and L. A. Giri-
of a Finely Divided Crystalline Solid,"
falco, "Surface Area Analysis by Means of
Journal, Am. Chemical Soc., Vol. 66, p. Gas Flow Methods, I," Journal of Physical
1362 (1944). Chemistry, Vol. 57, p. 330 (1953).
(30) J. C. Arnell, Chemistry in Canada, Vol. 3, (34) R. K. Iler, "The Colloidal Chemistry of
p. 21 (1951). Silica and Silicates," Cornell University
(31) "Cabot Carbon Blacks Under the Electron Press, Ithaca, N. Y., p. 106 (1955).
DISCUSSION
MR. E. S. PALIK)--I was extremely discrepancies can arise, however, when
interested in this work because we at the solid under investigation is porous,
General Electric are carrying out a num- particularly if a large fraction of the pores
ber of surface area studies by a very simi- are not continuous (that is, blind). This
lar technique. But the comment I wanted is not too surprising when one realizes
to make is that in using k r y p t o n gas we that these two measurements are actually
employ a thermistor gage to measure quite different. The permeability method
these pressures and that we think this is measures the dynamics of gas flow
a refinement over the McLeod gage. I t is through a packed bed, while the adsorp-
faster to use and we can measure sur- tion method measures the number of
face areas down to 100 sq cm per g with molecules that can be fitted onto the par-
the thermistor gage arrangement. ticle surface.
The other comment is a question. Do MR. S. S. OBER.2----How did you ob-
you have any explanation as to why the tain the gas permeability data.
gas permeability surface areas were so MI~. FRIES.--The gas permeability
much lower than the adsorption surface data presented here were taken from pa-
areas when both methods measure sur- pers by J. C. Arnell (see reference (30)
face area? in the paper) and by Kraus, Ross and
MR. R. J. FRIES (author).--In answer Girifalco (see reference (33) in the pa-
to your first comment, in the paper as per). Arnell employed a steady-state flow
written there was a reference to a paper method to obtain his data as did Kraus,
by A. J. Rosenberg (reference (IS) in the Ross and Girifalco.
paper) concerning the use of a thermistor MR. OBER.--Kraus and Ross 3 doing
pressure gage in a k r y p t o n adsorption permeability measurements by means
system. This modification was not dis- of the Barrer and Grove 4 time-lag method
cussed here because of time limitations. show very ably how this transient tech-
Your second comment can be answered
2Abbott Laboratories, Physical Chemistry
by stating that for nonporous materials Research, N. Chicago, Ill.
the agreement between nitrogen adsorp- 3 G. Kraus and J. W. Ross, "Surface Area
Analysis by Means of Gas Flow Methods, II,"
tion and gas permeability surface areas Journal of Physical Chemistry, Vol. 57, p. 334
is generally quite satisfactory. Serious (1953).
4 R. M. Barrer and D. M. Grove, "Flow of
Gases and Vapors in a Porous Medium and
1 Chemist, General Electric Co., Cleveland, Its Bearing on Adsorption Problems," 'Transac-
Ohio. tions, Faraday Soe., Vol. 47, p. 826 (1951).
nique is affected by blind pores. In their steady-state method of Rigden 6 is not

preceding paper 5 they show that the
affected by the particulate blind pores.
5 G. Kraus, J. W. Ross, and L. A. Girifaleo,
"Surface Area Analysis by Means of Gas Flow Hence, it is important to know which air
Methods, I," Journal of Physical Chemistry,
Vol. 57, p. 330 (1953). permeability technique is being used as
6p. j. Rigden, "The Specific Surface of
Powders. A Modification of the Theory of the well as what corrective measures were
Air Permeability Method," Journal, Soc. Chem-
ical Industry (London), Vol. 66, p. 130 (1947). adopted in presenting the surface data.
A S T U D Y OF T H E B L A I N E F I N E N E S S T E S T E R A N D A
D E T E R M I N A T I O N OF S U R F A C E A R E A F R O M A I R
PERMEABILITY DATA
BY STEPHEN S. 0BER I AND KENNETH J. FREDERICK I
SYNOPSIS
The Blaine fineness tester is a simple and inexpensive instrument for the
measurement of specific surface by air permeability. This paper deals with the
variables met in the use of this instrument and their effect on the precision and
accuracy of the calculated surface areas. Modifications of the Kozeny-Carmen
equation which have appeared in the literature are recited. A porosity function,
based on a single correction factor, is proposed which makes surface area data
from the Blaine fineness tester fully independent of test conditions. It is shown
that this same factor can be used to bring these data into agreement with
nitrogen adsorption values.
The permeability method for measur- physical characteristics of the instru-

ing the specific surface of a powder has ment, the relationship of the time meas-
the virtue of simplicity. This is particu- urement to the powder surface area is
larly true when the Blaine fineness tester quite complex.
(1)~ is considered. This inexpensive in- A brief description of the Blaine fine-
strument has long been used as a stand- ness tester follows. The Kozeny-Carmen
ard A S T M method 3 for the determina- equation is cited and introduces a discus-
tion of surface areas of cements and clays. sion of the variables which control the
While this unit actually measures the time-of-flow values. Previous attempts to
time for a set volume of air to flow correlate mathematical theory with ex-
through a packed bed of powder parti- perimental results are discussed briefly.
cles, it has been used to indicate relative A simple, empirical correction factor for
degrees of fineness of the powders tested. the Kozeny-Carmen equation is pro-
Since the time-of-flow data depend upon posed. While the correction factor sug-
both the nature of the powder and the gested is not new, the method outlined
to obtain and utilize it is novel. Illustra-
1 Abbott Laboratories, Physical Chemistry tive data are given to show its usefulness.
Department, Research Division, North Chicago,
Ill. BLAINE FINENESS TESTER
to the list of references appended to this paper. The essential parts of the Blaine fine-
3 Method of Test for Fineness of Portland ness tester are illustrated in Fig. 1. I n
Cement by Air Permeability Apparatus (C 204 -
55), 1958 Book of ASTM Standards, Part 4, p. this schematic diagram the unit is shown
140. to consist of a stainless steel sample con-
279
tainer, R, with tapered outside walls and space, F, below the bed out through a
a carefully machined inside cylinder, S. stopcock, G, to a draw bulb, H. The top
A perforated steel disk, T, fits in snugly of the cylinder, I, is corked to permit
at the bottom of the cylinder. A filter withdrawal of the air from the closed end
paper wafer, U, cut to fit the inside of the manometer tube, F. Air is with-
diameter of the cylinder goes on top of drawn to the point where the manometer
the steel disk. A weighed portion of the fluid level is at the top line, A. The cork
powder sample, P, is placed next on top in the top of the cylinder is then re-
of the paper wafer. A second paper wafer, moved, and the time for the manometer
U, is placed on top of the powder sample, fluid to flow from line B to line C is
measured.
KOZENY-CARMEN EQUATION
Following publication of the papers on
[-- u p the flow of fluids through porous beds by
/ ~
Kozeny (2) and Blake (3), m a n y workers
(1, 4-9) contributed to the development
of the technique for the purpose of meas-
uring powder surface areas. Carmen (4)
adapted and modified the Kozeny per-
A
meability expression to allow specific
BI-
surface to be calculated from steady-
state fluid flow measurements through
prepared powder beds. Lea and Nurse
CI- (5) suggested the use of air as the per-
DV meating fluid. Blaine (I) suggested the
use of a constant volume air permeability
apparatus and modified the Kozeny-
Carmen equation to include the time-of-
flow measurement. This equation is the
one which is recommended for use with
the Blaine fineness tester:
Keal~TX/2
Fro. 1.--Schematic Drawing of Blaine Fine- S = (1)
ness Tester. palt~(1 - e) . . . . . . . . . . .
where:
and a stainless steel ramrod, V, machined
to fit within the cylinder and designed S = specific surface, sq cm per g,
to penetrate the cylinder to a fixed K = constant,
depth, is used to compress the wafer- T = time for the air to pass through
powder-wafer sandwich within the known the sample bed, sec,
volume remaining in the cylinder. p = powder density, g per cc,
The ramrod is removed, and the n = viscosity of air, poises,
cylinder with its compact bed is placed e = 1 -- W / p Vc = fractional void
in the ground-glass, tapered joint, E, at space,
the top of the manometer. Off to the W = weight of powder sample, g
right and immediately below the steel Vo = volume of cylinder to which bed
cylinder, a glass tube leads from the is confined, cc.
OBER AND FREDERICK ON BLAINE FINENESS TESTER 281
For a given instrument and a given significant source of error has been shown
material, Eq 1 reduces to: to be pore structure. By pore structure
is meant the behavior of fluid flow within
S = K t eSll2 T '12 . . . . . . . . . (2) very narrow confines regardless of
whether these confines are within or
without the particles proper. Rose (10),
DISCUSSION OF VARIABLES Rigden (11), Barrer and Grove (12),
Sample variables: Kraus, Ross and Girifalco (13), Coulson
(14) have all treated this flow problem
Equation 2 implies that the surface under the headings of "wall slippage,"
area of a given powder is independent of "Knudsen capillary flow," "molecular
sample weight. In practice this is not streaming." By means of modified
true. There must be at least enough porosity functions, e~/(1 -- e) for steady
sample to fill the cylinder volume, and state measurements, and e/(1 -- e) for
there must not be so much sample that time-lag, decreasing pressure head meas-
the particles cannot be compacted with- urements, the shortcomings of the
out alteration. For finely divided pow- Kozeny-Carmen equation have been
ders, however, this still leaves a con- minimized.
siderable range of sample weights and of It should be pointed out that no cor-
corresponding porosities. Unfortunately, rection will ever account fully for blind
even within this operable range, it has pores or occlusions within particles. This
been found that the value of specific means that air permeability cannot be
surface calculated from Eq 2 depends used to measure total surface area of
upon the particular porosity chosen for such powders.
the measurement. Actually, when T 1/2 The treatment by Coulson (14) of
was plotted against (1 - e)/e 8/2 for a specific surface measurements is excellent
finely divided procaine penicillin G pow- and most pertinent to the present discus-
der, the curve obtained not only was sion. He shows that when all the particle
nonlinear, in contradiction of the physical properties are taken into ac-
Kozeny-Carmen equation, but the curve, count, excellent results can be obtained
when extrapolated, failed to pass through over a very wide range of surface areas
the origin, as the equation requires. and quite a surprising range of particle
Many factors contribute to these dis- shapes. The method fails for powders
crepancies. Surface area is the variable where the shape is a very fiat plate or
to be measured. Differences in particle where the particle is a large agglomerate
size distribution are presumably taken with far more internal than external
into account by the porosity function, surface. The solutions proposed by Coul-
e~/2/(1 -- e). Evidently this is not the son mean that either the formula be-
case, and so herein lies one source of comes complex by the addition of all
error. Particle shape and particle shape the necessary correction factors or the
distribution also are sources of error. method becomes more involved, such
The greater the deviation from smooth as for time-lag studies.
spherical particles, the greater will be There is still need for a simple empir-
the error, since the derivation of the ical correction to the Kozeny-Carmen
Kozeny-Carmen equation assumes spher- equation which will retain the simplicity
ical particles. of the air permeability method and the
While shape and distribution factors ease with which such flow data can be
can and have been applied, the most used to calculate surface areas.
282 SYMPOSIUM ON P A R T I C L E S I Z E M E A S U R E M E N T
INSTRUMENT VARIABLES an appreciable effect upon the time-of-

In the Blaine fineness tester the flow measurement. Only if calibration is
variables of major importance are the carried out for each relatively narrow
sample cylinder, manometer and manom- region of surface area (and corresponding
eter fluid. The influences of instrument time-of-flow) can this error be neglected.
design factors are eliminated usually To check this point repeat determina-
through the Use of a constant which tions were made on a single powder plug.
either accounts theoretically or corrects First, times-of-flow were taken imme-
diately after the manometer fluid was
TABLE I.--EFFECT OF MANOMETER raised to line A. Time-of-flow data were
DRAINAGE TIME. obtained next for runs where the fluid
V a r i a t i o n of T i m e - o f - F l o w for a
Single I n s t r u m e n t .
was held at line A for 1 min before flow
I was started. In all cases the times re-
Run Dr ~age Time-of- corded were those required for the
Tin min Flow, min
manometer fluid meniscus to pass from
P r o c a i n e penicillin G line B to line C. Typical results are listed
s a m p l e No. 5 in Table I.
No. 1 . . . . . . . . . . . . . . . . . 1.658
No. 2 . . . . . . . . . . . . . . . . . 1.650
Observation of the manometer fluid
No. 3 . . . . . . . . . . . . . . . . . 1.657 height differential indicated that in-
No. 4 . . . . . . . . . . . . . . . . . 1.655 creased drainage time resulted in a
NO. 5 ................. 1.660 decreased pressure head at the time of
No. 6 . . . . . . . . . . . . . . . . . 1.660 initial flow. This is reflected in the longer
No. 7 . . . . . . . . . . . . . . . . . 1.661
flow times. Extensive data show that
No. 8 . . . . . . . . . . . . . . . . . 1.660
time-of-flow measurements taken with a
drainage time of 1 min before start of
TABLE II.---EFFECT OF MANOMETER
DRAINAGE TIME.
flow are far more precise and reproducible
V a r i a t i o n of Specific S u r f a c e in than are measurements taken imme-
Calibrated Instruments. diately after manometer adjustment.
The method used to gather all subse-
Specific
Tester Surface, sq c m quent data in this paper allowed this
per g
1 rain for drainage.
P r o c a i n e penicillin G
This drainage error shows up in an-
sample No. 5 other way when the same sample is run
D-12 . . . . . . . . . . . . . . . . . . . . . . . . . 22 500 at the same porosity on different instru-
F-10 . . . . . . . . . . . . . . . . . . . . . . . . . 23 450
ments which have been calibrated against
the same cement standard (Table II).
empirically for these factors. In the case One method of overcoming this trouble
of the Blaine fineness tester, however, a is to extend the calibration program to
single constant will never compensate include a number of standard samples
adequately for all of the instrumental which will effectively cover the full
variables. The farther removed the un- range of specific surface to be measured.
known sample is in specific surface from CORRECTION FACTOR
the calibration standard, the more pro-
Blaine (1) has suggested that Eq 1 can
nounced will be the error.
be written as follows:
The ma~or difficulty lies in the manom-
Kaeal2TX/2
eter fluid and its properties of viscosity s - (3)
and surface tension. The fluid's draining p~12(a- e)'"
properties in the manometer tube exert where a = constant = 0.850.
OBER AND FREDERICK ON B L A I N E FINENESS TESTER 283
T h e addition of this constant was said I l I I I I
to m a k e S independent of porosity. W i t h
12
x as the reciprocal of a, the equation
reads as follows:
S Ke~/2T1/2 . (4) I0
Correcte//C.
d
p@/2(1 -Xe)-
Extensive testing of E q 4 over a range

of materials and surface areas was car-
ried out to s t u d y its validity. I t was
8
// :,
found t h a t x did not equal 1.177 (the m e l IO
reciprocal of Blaine's value, 0.850). F u r - /
t
ther, it was found t h a t x did not remain -I- I
I
constant for either instrument tested t

I
I
over the wide range of surface values I
I
measured, namely 3000 to 64,000 sq cm i
per g. The d a t a suggested, however, t h a t / Ke3/2 T 1/2

l / S--
Eq 4 could be used to achieve calculated I p~Ua (,-xe)
/I
surface values relatively independent of /
porosity if an a p p r o p r i a t e way of han- t
dling the variation of x with surface
/
area could be found. I
I n pursuing the s t u d y of the Blaine 0.2 0.4 0.~
l-xe
fineness tester and the problem of in- 3/2
e
s t r u m e n t and porosity dependency, an
experimental m e t h o d was evolved for FIG. 2.--Relationship of Time-of-Flow to
calculating the x factor. This method en- Porosity for Air Permeability Data. Use of Cor-
rection Factor x.
tailed the following analytical geometry
t r e a t m e n t of the experimental data.
A graph was m a d e for T 1/2 versus
TABLE III.--VALUES OF (1 - - e)/e ~/2 for four or five different
CORRECTION FACTOR.
porosities, e, for each sample. F r o m these
Correction d a t a values of x were selected b y trial
Specific Factor, x
Sample Surface, and error which would give corrected
sq cm porosity functions. These corrected func-
per g Tester, Tester,
D-12 F-10 tions gave the necessary linearity to the
plots of T 1/2 versus (1 -- x e ) / d / 2 . I t was
Procaine Penicillin
G gratifying to find t h a t the latter lines,
No. 1. 5 250 1.102 1.058 when extrapolated, passed through the
No. 2. 8 960 1. 075 1. 063 origin.
No. 3. 9 890 1. 075 1. 062
No. 4 (blend of 1 This procedure is illustrated in Fig. 2.
and 5).. 18 000 1.078 1.073 Curve CD represents experimental d a t a
No. 5. 22 960 1.058 1.062
No. 6. 64 300 1.042 1.064 p l o t t e d against the s t a n d a r d porosity
function from E q 1. Line A B results
Portland C e m e n t when the modified porosity function is
l14g. 3 070 1.084 1.065
l14h. 2 950 1,084 1.067 used with x having a value of 1.058.
Some indication of how the correction
factor, x, varies with marked differences about excellent agreement between the
in surface area and with different instru- nitrogen adsorption and the air permea-
ments will be seen in Table I I I . I t will bility values for other penicillin samples
be observed that for instrument D-12, x of varying degrees of fineness. For exam-
changes with specific surface and with ple, the new calibration applied to sam-
particle size distribution. For instrument ple No. 3 (whose specific surface by the
F-10, on the other hand, x is essentially regular calibration technique is 8960 sq
constant except for a drastic change in cm per g) brings the reported surface
particle size distribution. area up to 15,050 sq cm per g. The ni-
The full value of the correction factor trogen adsorption figure for this same
is apparent when calibration of two in- sample was reported as 15,100 sq cm per g.
struments is carried out using the NBS
portland cement standard, 114 g. If the CONCLUSION
Surface area data calculated from air

TABLE IV.--USE OF CORRECTION
FACTOR. permeability measurements obtained by
Agreement of Surface Area Data from the Blaine fineness tester may be in con-
Different Testers. siderable error when the calculations are
Specific Surface, sq cm carried out using the equation given in
Sample
per g ASTM Standard Method C 2 0 4 - 5 5 . 3
The two major sources of error are: (a)
Tester D-12 Tester F-10
failure of the porosity function, e3/2/(1 --
Procaine Penicillin G e), to describe adequately experimental
No. 1 . . . . . . . . . . . . . . . 5 210 5 270 permeability of a powder bed, and (b)
No. 2 ................ 8 950 8 970
9 860 9 920
failure of the method to take into account
No. 3 ...............
No. 4 ............... 18 000 18 040 manometer fluid drainage.
No. 5 ............... 22 960 22 960 A modified porosity function is pro-
64 300 64 350
No. 6 ...............
posed, e3/2/(1 -- xe), which overcomes
these difficulties. Limited data on sam-
NBS value of 3070 sq cm per g is taken ples of procaine penicillin G powders,
along with the appropriate x factor, the which were measured for surface area by
specific surface data on all procaine peni- both techniques, indicate that use of the
cillin powders encountered show no error correction factor x makes it possible to
other than random, no variation due to obtain surface area data with the Blaine
porosity and no differences between in- fineness tester which agree with corre-
struments (Table IV). Thus, while the x sponding nitrogen adsorption values.
factor turned out to be dependent upon
instrument and specific surface, the cal- Acknowledgment:
culation of x as proposed solved all the The authors wish to express their sin-
error problems simultaneously. cere thanks to Robert Waters of the
If the Brunauer, Emmett and Teller Standard Oil Co. of Indiana for the
(BET) value of 38,800 sq cm per g for nitrogen adsorption data cited in this
procaine penicillin G sample No. 5 is paper. The authors also wish to acknowl-
taken as the standard, the new increased edge the help of Robert W. Rinehart of
value of the constant, K, in Eq 4 brings the Upjohn Co. in initiating this study.
OBER AND FREDERICK ON BLAINE FINENESS TESTER 285
REFERENCES
(1) R. L. Blaine, "A Simplified Air Per- of Surface Areas of Fine Powders," Journal
meability Fineness Apparatus," ASTM of Chemical Education, Vol. 31, pp. 354-
BULLETIN, No. 123, Aug., 1943, pp. 51-55. 356 (1954).
(2) J. Kozeny, "Uber kapillare Leitung des (9) F. J. Spillane, "An Automatic Direct-
Wassers in Boden," Sitzungsberichte, Reading Apparatus for Determining the
Akademie Wissenschaften Wien, Vol. 136a, Surface Area of Powders," Analyst, Vol.
p. 271 (1927). 82, pp. 712-715 (1957).
(3) F. C. Blake, "The Resistance of Packing (I0) H. E. Rose, "The Permeability Method of
to Fluid Flow," Transactions, Am. Inst. Specific Surface: A Correction Factor,"
Chemical Engrs., Vol. 14, pp. 415-421 Journal of Applied Chemistry, Vol. 2, pp.
(1922). 511-520 (1952).
(4) P. C. Carmen, "Determination of the (11) P. J. Rigden, "The Specific Surface of
Specific Surface of Powders.--Part II," Powders, A Modification of the Theory of
Journal Soc. Chemical Industry (London), the Air Permeability Method," Journal
Vol. 58, pp. 1-7 (1939). Soc. Chemical Industry (London), Vol. 66,
(5) F. M. Lea and R. W. Nurse, "The Specific pp. 130-136 (1947).
Surface of Fine Powders," Journal. Soc. (12) R. M. Barrer and D. M. Grove, "Flow of
Chemical Industry (London), Vol. 58, pp. Gases and Vapors in a Porous Medium and
277-283 (1939). Its Bearing on Adsorption Problems,"
(6) A. Guyer, E. Graf, and A. Guyer, Jr., Transactions, Faraday Soc., Vol. 47, pp.
"Untersuchungen an Schutt-und Wirbel- 826-837 (1951).
schichten," Hdvetica Chimica Acta, Vol. 38, (13) G. Krauss, J. W. Ross, and L. A. Girifalco,
pp. 473-484 (1955). "Surface Area Analysis by Means of Gas
(7) E. L. Gooden and C. M. Smith, "Measur- Flow Methods," Journal o[ Physical Chem-
ing Average Particle Diameter of Powders," istry, Vol. 57, pp. 330-326 (1953).
Industrial and Engineering Chemistry (14) J. M. Coulson, "The Flow of Fluids
(Analytical Edition), Vol. 12, pp. 479-482 Through Granular Beds: Effect of Particle
(1940). Shape and Voids in Streamline Flow,"
(8) J. A. Allen and C. J. Haigh, "The Per- Transactions, Inst. Chemical Engrs., Vol.
meability Method for the Measurement 27, pp. 237-257 (1949).
DISCUSSION
MR. MORTON W. S c o T x . l - - W o u l d t h e special errors inherent in each technique.

authors care to make any remarks com- MR. DONALD PASTOR.a--Is this appa-
paring the Blaine fineness tester with the ratus applicable to measuring silica in
Fisher sub-sieve sizer? the size range from 1 to 60 it? If so, what
MR. STEPHEN S. OBER (author).--The density is required?
Blaine fineness tester is based upon a MR. OBER.--With control of the rela-
transient state whereas the Fisher sub- tive humidity of the air or gas passing
sieve sizer is based upon a steady state through your silica sample, you should
air permeability method. Consequently, be able to measure the surface area by
some of the sources of error mentioned means of the Blaine unit. The density re-
in this paper do not apply to the Fisher quired is that of the solid or crystal den-
unit. Beyond the general comment we sity.
care to say nothing, for we have had no MR. PASTOR.--The density of the solid
opportunity to compare the units di- is 2.6. However, by density I meant how
rectly. many grams do you pack into the stain-
M~. CHA~L~S HUNT3--We have made less steel cylinder?
a few comparisons of the Fisher sub-sieve MR. OBER.--The packing density is
sizer and the Blaine tester which show governed by the formula for e, the frac-
they are in reasonable agreement, and tional void space. By definition, there-
one would expect them to be, because fore,
they are both based on the Carmen equa- W
tion. The Fisher apparatus, of course, e=l----
pV
gives the answer directly in surface mean
partide diameter, which is quite an ad- where:
vantage, whereas the Blaine tester is
simpler and easier to check for instru- W = the sample weight, g,
mental errors. O = the solid or crystal density, g per
M~. OBER.--I would like to underscore cu cm, and
the last statement by Mr. Hunt. The V = the cylinder volume when com-
essence of our contribution is that the pacted, cu cm.
Blaine tester is simple and can be made The cylinder volume is usually just short
extremely precise by proper accounting of 2 cu cm. The sample weight taken is
of the instrumental errors. We would governed by the degree of fineness of the
not, however, expect data from the sample. There must be sufficient sample
Fisher and Blaine units to agree to this to achieve some packing. On the other
limit of precision unless both techniques hand there must not be more sample than
accounted equally for the respective and can be compacted without alteration. As
1 Senior Scientist, Pharmaceutical Engineer, the fineness of this sample increases, this
Smith, Kline, and French, Philadelphia, Pa.
2 Chemist, NationM Bureau of Standards, a Supervisor, Applied ~esearch, Fram Corp.,
Washington, D. C. Providencej R. I.
286
:DIscussION ON BLAINE FINENESS TESTER 287
practical operating range increases. As a To be specific in reply to your query,

very approximate rule, when the surface this variation is due to (1) varying
area of the material to be measured ap- amounts of space between the exit end
proaches 3000 sq cm per g, this range of the powder bed and the top of the
narrows until the technique can no longer closed end of the manometer tube, (2) to
be applied. varying diameters of manometer tubes,
MR. R. J. F R I E S . ~ W h a t was the (3) to nonconstancy of diameter of these
difference between the two instruments tubes, (4) to varying amounts of manom-
which led to a variation of the factor x eter fluids, and (5) to varying purity of
for one of them and a reasonable con- manometer fluid, particularly with re-
stancy of x for the other? spect to the contamination by surface
MR. OBER.--Any property which active agents. There are obviously other
affects the flow characteristics of the factors also.
manometer fluid affects the final result. We turned to the mathematical ex-
The instrument constant, K, of the modi- pediency of the x factor (so that the equa-
fied Kozeny-Carmen equation sup- tion had two constants instead of one) to
posedly takes into account such varia- remove this instrument variation. The
tion. That it does not can be glibly use of such a factor illustrates and em-
ascribed to the dynamic nature of the phasizes that the principle of the Blaine
technique. We are not dealing with a unit can be greatly extended in practical
steady-state measurement. Rather it is application. I t also shows that use could
a rate of deacceleration which is inte- be even more practical if manufacturers
grated to give a period of time which, in of these instruments could adhere to
turn, is related to specific surface. Con- rigid physical specifications. Unlike the
sequently, differences in rates of flow do constant K, however, x will never be
show up as instrument-to-instrument universally applicable, for x also depends
variation. upon particle size distribution and prob-
4 Research Associate, Mellon Institute, Pitts- ably upon pore size and particle shape
burgh, Pa. distribution as well.
S T P 2 3 4 - E B / A u g . 1959
A DISCUSSION OF T H E ASTM R E C O M M E N D E D P R A C T I C E
FOR R E P O R T I N G P A R T I C L E SIZE C H A R A C T E R I S T I C S
OF P I G M E N T S (D 1366) 1
137 JO~N H. CALBECK2
The ASTM Tentative Recommended fined as the diameter in microns below

Practice for Reporting Particle Size which 99.5 per cent by weight of the
Characteristics of Pigments (D 1366- pigment falls.
55 T) I was published in 1955 after Group The dispersion parameter (DP) is de-
13 for Fineness Characteristics of Pig- fined as the micron size within which 50
ments of fubcommittee XV of ASTM per cent of the pigment lies divided by
Committee D-1 cn Paint, Varnish, Lac- the specific surface diameter.
quer, and Related Products had strug- These three parameters appear to be
gled with this problem for 5 years. This all that is presently required by the users
paper deals with the development cf of particulate materials and they can be
that recommended practice, the reasons calculated from the data obtained by
for it, and discusses some technological most methods now in use. More elabo-
phases of particle size measurement and rate parameters were proposed during
reporting that were brought up in the the work of the committee which will be
committee. of interest and may be of value when
This recommended practice is designed this recommended practice is revised.
to apply in most cases where well-known The committee was instructed to de-
methods for determining particle size in velop a method of "expressing particle
the subsieve range are employed and is size and particle size distribution" that
intended to standardize the reporting of would be independent of the methods
such data and to make comparison pos- used in obtaining the data. In other
sible when pigments are examined by words, the group was to divorce itself
different methods. from consideration of the many methods
I t specifies that fineness characteristics of particle size determination and devote
should be reported by three parameters: its efforts to the development of methods
(1) Particle size parameter, (2) coarse- for reporting particle size data. At first,
ness parameter, and (3) dispersion pa- this appeared to be an impossible assign-
rameters. m e n t - - a case of "putting the cart before
The particle size parameter is defined the horse," but as the work progressed it
as the specific surface diameter (SSD), became more evident that this was the
that is, the diameter of a sphere having proper approach because the wide variety
the specific surface characteristic of the of methods being used was causing end-
pigment. less confusion and because the funda-
The coarseness parameter (CP) is de- mental data obtained by this wide vari-
1 1958 Book of ASTM Standards, Part 8, p. ety of methods could, for the most part,
223. be expressed in the same terms. Further-
Director of Research, Pigment Division,
American Zinc Oxide Co., Columbus, Ohio. more, the committee felt that if all work-
288
68g
, .~ + :+...~1..+., ,++.~
/'xi. O~ ' ~ o m 00. ,
~ ~ . . . . ~'~ t~+'+- . . . . . :--+~
.... ~:r',-~ ~ ~ . . . . . . ~-,,1
t~
9 , . . . . . . . . . , 9 . . . . . . .
I
C3
;Z
. . . . . . . . . . . . . . . . . . . . Specific G r a v ity
r t~ ~ Pigmen t Number
~ ~ ~ ~ o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ t~ c~ Average Diameter by Surface Mean, P~
(SSD)
a;
9 + . .~.~. . . oc~ooc~oooc~c~oc~ Median Average
~D
~=~ ~=~
Median by Volume or Weight (from
~ : : : : ~ 0 o : q ~ O o ~ : ~1 distribution curve or histogram)
I
C~...,t~~c.~toC.~c~twC~ 6Xd~f
. . . . ~ Specific Surface, s q m per ml., ~
9
~ 6Zd~-f 9
.~ .~ .~ .~ .~ .~ .'a .~ .~ ~ ~ ~ ,~ ~ .~ ~ ~1 0 .~ .~ Specific Surface, sq m per g, p ~ f
--I~o . . . . . ~ ~ ~ ~ 0 Mode, per cent q
s
9
9
i
Particle Size Range,
i
tS
A
~ O ~ Percentage in Range,
. . . . . . . o~8 " " 8' ~8~ Tt~
0 ~ -- Q1
x
Quartile Deviation,
~o ~ c~ . . ~ Percentage in Range ~- to 2D
~ N
9 ~ Ratio Diameter to Difference 1-3
.... ~ ~ ~ ~ ~ Qo ~ ~ :-,1 ~ ~ Quartile Diameters
~ : : : : o o ~ o o ~ , ~ t*Size, below g0 per cent
.... V
~00 .... 0 o N c~~ r ~ t~o'q~C~O~ ~ t*Size, b e l o w 9 9 p . . . . . t
~r . . . . . . r162 ~ ~ ] 9 l Arbitrary Cla~s Size Group
I
ers in this field were given standard Table I. Study of these data suggested
methods of reporting their findings more the use of a particle size parameter as
rapid progress in the development of new indicated in Column A, referred to as
methods would result, and a more gen- "average diameter by surface mean."
eral appreciation of particle size statis- Later, the simpler designation, specific
tics would be promoted. surface diameter (SSD) was adopted. A
The problem that confronted the com- coarseness parameter and a scatter pa-
mittee was whether it was possible to rameter were considered but not adopted.
write a set of recommendations for re- A draft of the recommended practice
porting particle size data, for which the was reviewed by the Technical Division
methods of test were of such a contro- of the NPVLA and the comments re-
versial nature. To write a method of received were favorable from the viewpoint
porting the results for one pigment by of its publication by the ASTM as tenta-
one method presented no problem, but tive. A number of criticisms made at
to write one for a wide variety of pig- that time are of interest. There was the
ments tested with a variety of apparatus fear on the part of manufacturers and
seemed impossible. suppliers that these parameters might be
Work on this project was stimulated written into specifications. This has not
by a request from the Technical Division happened in the past three years and will
of the National Paint, Varnish, and Lac- not happen until more satisfactory test
quer Assn. In collecting data on pigments methods are developed and approved.
for publication in its Pigment Index, 3 the The matter of shape factor and agglom-
Technical Division of the NPVLA ob- erates was frequently brought up. Some
tained such a variety of data on particle preferred that the complete particle size
size from manufacturers of pigments that distribution curve be written into the
publication of the data in tabular form recommended practice and that standard
was very difficult, if not impossible. deviation be used in place of dispersion
Further consideration developed the parameter. Coefficient of uniformity,
idea that the particle size characteristics standard deviation divided by SSD, was
of all particulate material could be ex- also suggested. The use of the expression
pressed by one parameter at least, that "dispersion parameter" was not favored
is, average particle size, and might be because in the coatings industry "dis-
more completely expressed if additional persion" does not have the statistical
parameters were employed, for example, meanir~g but refers to the ease with which
distribution curves or factors calculated a pigment may be incorporated in a
from the data of distribution curves, liquid. However, the expression is re-
shape factors, and coarseness factors, tained in the recommended practice for
either taken from the distribution curves want of a more descriptive one.
or from independent data such as screen-
DISCUSSION OF COOPERATIVE D A T A
ing.
All of the data received from the co- Table I shows the particle size of 20
operators was tabulated as shown in pigments furnished by the cooperators
which were calculated to 14 parameters.
8 T h e Pigment Index is a division of the Raw These parameters were divided into two
Material Index published by the National Paint,
Varnish, and Lacquer Assn., Inc. and contains groups under the headings "Particle
t h e chemical and physical properties of over Size Parameters," and "Scatter Param-
3500 pigments used in t h e coatings industries
and is used as a handbook by all formulators in
eters."
t h e coatings industries. Particle Size Parameters.--In Table I,
CALBECK ON PARTICLE SIZE CHARACTERISTICS OF PIGMENTS 291
column A gives the average diameter by each particle size divided by that size is
surface mean (later adopted as the par- plotted against the particle size. The high
tide size parameter of the recommended point or "mode" of the curve indicates
practice and called specific surface di- the particle size that is characteristic of
ameter (SSD)) of the 20 pigments stud- the performance of the material. Column
ied, while column B shows the median H simply lists the particle size range of
average diameters (frequently called the pigment in microns. Columns I and
average particle size). K indicate the percentage by weight of
The parameters in column D were not the material that falls between certain
calculated but were taken from the dis- particle size limits. Column I shows the
tribution curves or histograms that were range is from one half to twice the spe-
available for 15 pigments studied. The
median particle size, in microns (~), that
is, that particle size that divides the
cific surface diameter
(2)to 2A , and
column K shows the range is from one
array in half, was taken from these half to twice the median particle size
curves.
Columns E and F list the specific sur- -~ to 2D , as shown by the distribution
face figures for 20 pigments on a volume table or curve.
basis and on the basis of weight. Many Column J is a device frequently used
other particle size parameters could have by statisticians and known as the quartile
been prepared from the data submitted, deviation. The difference in microns be-
but these five seemed to convince the tween the first and third quartile is di-
committee that only one was needed, and vided by the sum of the micron sizes at
the choice of the specific surface diam-
eter was unanimous. the first and third quartiles Qaa ~ Qll "
Scatter Parameters: Column L is the ratio of the average
The eight scatter parameters, more diameter to the difference between the
properly called dispersion parameters, as first and third quartiles. This accentuates
shown in Table I, are obviously an at- the skewness of the distribution. Note
tempt to display the particle size dis- that the dispersion parameter adopted
tribution of a particulate material by was similar to this but used SSD instead
shortcuts. Until the mathematics re- of average diameter.
quired to convert the data in a distribu- Columns M and N are the basis of the
tion curve into the physical properties coarseness parameter written into the
and performance characteristics of the recommended practice, the size below
particulate material are greatly simpli- 99 per cent having been chosen by the
fied, these shortcuts should suffice, al- committee because it would take the
though the committee felt that the ulti- place of the screen size specification in
mate was the distribution curve or the the pigment index. However, the impor-
histogram. 4 tance of a coarseness parameter should
In column G the mode per cent per be emphasized. The coarseness param-
micron is shown for 15 materials. A curve eter, in the sense that it is a measure of
is drawn in which the weight per cent of subsieve coarseness, frequently provides
4 There will always be the necessity of inter- the user of pigments and particulate ma-
preting the histogram or distribution curve, and terials more pertinent information than
two parameters, one for dispersion and one for
eoarseness or "skewness," appeared to be a
either the particle size or the dispersion
realistic answer to the problem. parameters. The material in the range of
particle sizes comprising the fourth Neither should the coarseness parameter
quartile, or perhaps the last decile, has a be combined with the dispersion param-
profound effect on the physical properties eter because the data for both are taken
of the product into which it goes. For from a distribution curve or histogram.
example, in paints, texture, fineness of The calculation of the two parameters is
grind, and package stability are influ- no more work, and the results are more
enced by this relatively small per cent of meaningful.
9f-
%
~q
3
O~
7=
t~
o*
O.
0.2 0.5 I 2 3 4 5 6 8 I0.0 20.0

Diameler,/x
FIo. 1.--Curves for Obtaining Coarseness and Dispersion Parameters.
the pigment. Where a material is to be Class Size Group Classification:

dissolved or is a part of a chemical re-
In column O are listed the class size
actiGn, the subsieve coarseness is often an
groups into which the 20 pigments would
important factor, especially in cases
fall if classified according to an arbitrary
where undesirable side reactions may
rule suggested early in the work. Such
occur. The coarseness parameter chosen
classifications appeared to have no prac-
may not be the best for many uses and
tical value in predicting the performance
a different one may have to be considered
of the material, and this plan was aban-
for each particular use. However, the
doned early in the discussions.
point that was emphasized by the com-
mittee was that a separate coarseness DISTRIBUTION CURVES
parameter should be chosen for each par-
ticular use rather than trying to incor- Particle size determinations usually
porate it in the particle size parameter. provide data from which distribution
tables or curves may be prepared. There or as weight percentages. Examples of

are some exceptions, notably the gas ab- each are given in Tables I and II of the
sorption methods. These data should Recommended Practice D 1366. Cumu-
80
~st Ouorh/e-- .. -Med/on
70 r
Speclflc Surfoce 0.152 sq m per g 3rd Ouarh/e

/
6O Speclflc Surface Diameter 5.57ff
(SSD)
Coerseness Porometer (CP) 8.7ff,
50 Dispersion Porometer (DP)I 2.6
Medlon 5.54ff
Ist Ouorhle 5.5p-
oo40 3rd Quortl[e 6.2 ,u,
$ Mode 5.55ff-
o_
3O
20
I0
D /
/
D2
~ - -/x_ .
1of
4 5 9 I0 [2
Microns
Fie. 2.--Histogram Zinc Dust--Microscopic Method (D 1366- 55 T Section 4(a)).
. . . . . . . . . . :12 o -
i I ] / Coarseness Porameter (CP) 17.0,o,
~50 i 1 l I O,sp . . . . . . P. . . . . for (DP) 348.0
[" i I M~ ] I Median 2,7H-
4o - ~ - - - I ---~--1--- _ 3rd Quart,le 5,30/z

II ] [ / Mode o.,~5~
2_ 30 [--4, I [ ~~---~--- ] ~ I
, ...-/st Ouorh/e I I I I I I
-/ ', I I I o, I / i_J3~ o~o.,/o I / I
-~1~--~ o3
~o / 2- .... -r . . . . . ~ .......... 6 7
-~-- .... (- .....................
8 9 I0 iI 12
Microns
Fzo. &--Histogram Zinc Dust--Sedimentation Method (D 1366- 55 T, Section 4(b)).
consist of a series of class intervals, usu- lative weight distribution curves are
ally expressed as diameters in microns, drawn from the weight percentages and
and the corresponding frequencies for the upper class size units. If data from
each class interval expressed as numbers sedimentation determinations is used, the
weight distribution per class interval is and from Table II which gives the sedi-
given and provides the 2;d~f function. mentation data from a very nonuniform
The d~f function is obtained then by di- zinc dust.
viding each item by the corresponding Figure 1 shows three dotted curves
size in microns and adding the quotients that do not appear in Fig. 1 of the recom-
to obtain the i~d~/function. The former, mended practice. Curves 1, 2 and 4 il-
divided by the latter, gives the SSD. On lustrate the types of curves obtained
the other hand, if the data are obtained with the per cent df and per cent d2f
by the microscope method, the class size functions when compared with the
diameter and the frequency are provided weight distribution curves 3 and 5 which
and the latter must be multiplied by the are based on the per cent d3f function. 5
diameter squared and the diameter cubed It is important to note the wide varia-
to obtain the 2:d2f and 2d~f functions. tions in parameters in the case of one
The recommended practice recommends zinc dust as compared with the other.
that the weight distribution be plotted The uniform zinc dust with the low dis-
TABLE I I . - - M E T t t O D OF CALCULATION.
d2]
Parameter
f df
( Particle size, # . . . . . . . . . . . . . . . 4.34 5.24 5.57 5.74
Uniform Zinc Dust t Coarseness, ]z . . . . . . . . . . . . . . . . 8.0 8.70
Dispersion . . . . . . . . . . . . . . . . . . . 14.3 12.6
k Mode . . . . . . . . . . . . . . . . . . . . . . . 5.25
Particle size, # . . . . . . . . . . . . . . . 0.28 0.40 1. 182 3.84

NonuniformDustZinc { Coarseness,/z . . . . . . . . . . . . . . . . 3.0 10.0 17.0
Dispersion . . . . . . . . . . . . . . . . . . . 110.0 300.0 348.0
Mode . . . . . . . . . . . . . . . . . . . . . . . 0.125 o. 125 O. 125
d = mean class size in microns, and

f = frequency.
on 3-phase semi-log paper and this is persion parameter shows similar param-
illustrated by Fig. 1 which is derived eters no matter how calculated, whereas
from data of Fig. 1 of the recommended the one with the high dispersion param-
practice. However, the data may be eter and the excessive skewness shows a
taken from the tables or other types of wide variety of parameters when calcu-
distribution curves or histograms. lated by different formulas. These param-
To illustrate the importance of always eters taken from Fig. 1 are tabulated in
using a weight basis in calculating these Table II.
dispersion and coarseness parameters, Histograms show more vividly these
there are shown in Figs. 1 to 3 some differences in parameters obtained when
curves and histograms that have been the particle size characteristics are not
obtained from Table I of the recom- reported on a weight basis. Figures 2 and
mended practice ~ which gives micro- 3 are the families of histograms that
scopic data on a very uniform zinc dust may be obtained if the data as reported
The data in Tables I and I I are expanded
in Tables I and II of Recommended
to include the dr, d2f, daf, and d r functions, and Practice D 1366 are presented on a d, d 2,
cumulative columns are added to include per and d 3 basis. Figure 2 is a rectangular
cent (if, per cent d2f, and per cent d'~f. d = mean
class size in microns; f = frequency. histogram calculated three ways from
the data of Table I. The abcissa is the acteristics of pigments is being used in
upper class size limit in microns and thethe pigment field. I t is the author's hope
ordinate is per cent df or per cent d2f or
that the three-parameter system, com-
per cent d3f divided by the particle sizeprising a particle size, a dispersion, and
interval, which in this case is 0.5 u in all
a coarseness or skewness parameter, will
cases. This method of preparing histo- become the basis cf the reporting meth-
grams is especially adapted to compari- ods in all fields. The assumption that any
sons because the area in each particle size
one class of pigments follows the gaussian
interval is the per cent of that size in the
law of distribution is misleading in most
array. This gives a family of three histo-
cases and dispersion and skewness can
grams so similar that one can hardly dis-
tinguish one from the other. As in Table best be represented by two separate pa-
II, all the characteristics are very muchrameters taken from a complete distribu-
alike, as always occurs when the degree tion curve. Some changes in nomencla-
ture and methods may be advisable to
of skewness is small. Similarly, Fig. 3 is
prepared from the data of Table I I of make the recommended practice accept-
the recommended practice, but the re- able in all fields, and this can easily be
sults are strikingly different. As in Table
done. One phase of the work of the com-
II, all the particle size characteristics are
mittee was never completed, and that
different, illustrating the necessity of was the publication of a glossary of terms
using one method of reporting if depend- covering the reporting of particle size
able comparisons are to be made. analysis. This should be done at an early
CONCLUSIONS date and would eliminate one of the
The ASTM Recommended Practice principal causes for confusion in the re-
D 1366 for reporting particle size char- porting of particle size data.
THE STANFORD RESEARCH INSTITUTE PARTICLE BANK
BY R. D. CADLEI AND W. THUMAN1
SYNOPSIS
Research workers in the fine particle field often spend weeks or months pre-
paring samples of particulate material for their research. The material may
have special characteristics with respect to particle size, size distribution,
density, and other properties. A large part of the sample preparation involves
determining the properties of the sample. When a particular investigation is
concluded, the samples may be of no further use to the man who prepared them
but may be of considerable use to others working in the free particle field. Early
in 1956 the Institute established a particle bank to serve as a depository for
such samples and to make them available to any investigator who might need
them.
This paper describes the response to the original questionnaires that were
sent out prior to the establishment of the bank, types of samples which have
been submitted, and numbers and types of requests for samples that have been
received. A number of the samples for the particle bank have been analyzed for
particle size or particle size distribution by different methods, and the com-
parative data are supplied.
Judging from the activity of the bank, it is filling a real need in the fine
particle field and it is expected that its usefulness will increase as it becomes
better known and as a larger supply of samples is accumulated through future
years.
Numerous research, development, and Research Institute considered the advis-

testing programs involve the use of ability of establishing a clearing house,
specially prepared and thoroughly char- or bank, for samples of fine particles, in
acterized samples of particulate materi- the hope that it would fulfill the follow-
als. Examples of such samples are those ing objectives:
used to calibrate equipment for deter- 1. To prevent duplication of effort in
mining particle size distributions. They sample preparation,
are often prepared in much larger quan- 2. To provide a much greater variety
tities than are required, and at the end
of samples for an investigator than would
of a program are discarded or stored
otherwise be possible,
indefinitely. The preparation and char-
3. To develop an increasing body of
acterization of these materials is usually
very tedious. Therefore in 1956 Stanford information concerning the samples as
a result of their use by various investi-
I Chemistry Department, Stanford Research
Institute, Menlo Park, Calif. gators, and
296
CADLE AND THUMAN ON THE STANFORD PARTICLE BANK 297
4. To stimulate fine particle research in a source of particles having certain

and technology. known properties such as shape, tensile
Information on the need for a particle strength, hardness, radioactivity, and
bank and the participation which could crystalline structure. This favorable
be expected Was obtained by mailing a response led to the establishment of the
questionnaire to 150 organizations repre- bank in July, 1956.
senting a cross section of industrial con- The purpose of this paper is to describe
TABLE I.--SUMMARY OF AVAILABLE MATERIALS.
Number of Samples Approximate Total

Composition of Differing Particle Diameter-Range of Maximum Sample
Size Distribution All Samples, ~ Size, g
Carbonyl iron ......................... 5 1.5 t o 30 25

Carbon black .......................... 24 0 . 0 0 2 to 2 100
Clay ................................. 20 0.1 to 40
Polystyrene latex (emulsion) . . . . . . . . . . . . 11 0 . 0 8 8 to 1 . 1 7 1 '5"
Lycopodium powder .................... 1 ,-~32 5
Puff bail spores . . . . . . . . . . . . . . . . . . . . . . . . 3 4 . 8 to 8 . 6 0.2
Glass beads ........................... 15 36 to 470 10
C h r o m i t e ore . . . . . . . . . . . . . . . . . . . . . . . . . . 1 <4 30
C h r o m i t e ore r o a s t . . . . . . . . . . . . . . . . . . . . . 1 <4 30
Coffee r o a s t s o o t . . . . . . . . . . . . . . . . . . . . . . . 1 <4 30
Silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 0 . 0 1 to 0 . 0 3 40
Cocoanut charcoal ..................... 1 N0.004 10
Z i n c oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 . 1 1 to 1 . 6 50
F l y ash. 1 1 to 80 50
Talc ...................... ........... 2 0 . 1 to 80 50
Ilmenite .............................. 1 0 . 5 to 30 50
Fluorspar ............................. 1 0 . 5 to 30 50
T i t a n i u m dioxide . . . . . . . . . . . . . . . . . . . . . . 4 0 . 2 to 1 40
A l u m i n u m oxide . . . . . . . . . . . . . . . . . . . . . . . 1 0 . 0 1 to 0 . 0 4 40
Calcium metasilicate .................... 2 ~30 40
Tungsten ............................. 5 1 to 4 . 5 20
Molybdenum .......................... 1 4.4 20
Uranium doxide. 1 --~1.2 5
Zirconium dioxide . . . . . . . . . . . . . . . . . . . . . . 1 N O . 28 5
T h o r i u m dioxide . . . . . . . . . . . . . . . . . . . . . . . 1 ~-~0.03 5
North Carolina pyrophyllite ............. 1 I to 70 25
Feldspar .............................. 1 1 to 35 25
cerns, governmental laboratories, and the operation of the bank, to describe

academic institutions. The response was the experience obtained to date with
67 per cent of the total mailing. The re- respect to both samples and clients, and
plies showed that 60 per cent favored the to present comparative data for certain
establishment of such a bank and that samples.
23 per cent could provide samples of
standardized material at that time. M E T H O D OF OPERATION
Ninety-seven per cent of those who fa- Industrial, governmental, and uni-
vored the establishment of a particle versity laboratories which can donate
bank expressed a need for powders samples of standardized materials are
classified according to size. About half invited to furnish the particle bank with
expressed a need for powders of known as much information as possible concern-
chemical analysis, and about half showed ing the nature of the materials and the
an interest in powders of known specific methods used for analysis, and to wait
surface. About 5 per cent were interested for a response from the bank before sub-
mitring the materials. This procedure EXPERIENCE

helps to maintain a high average quality Approximately 115 different samples
of information and materials and pre- are available in the bank at the time of
vents unnecessary duplication. Samples writing (February, 1958), and these
are accepted with the understanding have been supplied by many organiza-
that they become the property of the tions. The different chemical composi-
bank. tions represented and the number of
Sample quantities vary from fractions samples of differing particle size distribu-
of a gram to a few pounds. In cases where tion of each composition are indicated
samples are available in quantities over in Table I.
10 lb, storage facilities require some About thirty investigators or organi-
limitation. This limitation is determined zations have been supplied with 120
in early correspondence, and is partially samples during the twenty months of
dependent upon the nature of the mate- operation; 73 per cent of these were
rial involved. industrial, 20 per cent governmental,
The bank maintains a catalogue of and 7 per cent educational. The largest
available samples which is furnished on number of requests (23 per cent) has been
request. Inquiries are invited from in- for carbonyl iron. Next are various clays
vestigators interested in samples with (20 per cent), followed by carbon black
particular characteristics. If a particular (16 per cent), glass beads (14 per cent),
sample is not available at the bank, and tungsten (7 per cent). Approximately
information is sent concerning available 200 letters have been received requesting
materials which most closely represent either general information, information
the sample requested. The bank also concerning specific samples, or samples
informs the requestor as to whether the themselves. Fifteen per cent of the letters
material is available through commercial were from outside the United States,
sources. including Holland, Denmark, Great
Usually the quantity of a sample made Britain, Canada, France, Italy, Africa,
available to a requestor is limited to 20 Australia, and Sweden.
per cent of the quantity of that sample Only very incomplete information is
in the bank. This limit was established available concerning the application of
so that each material could receive the the samples, since this information need
broadest possible use. The request is not be supplied by the requestor.
usually for less than this amount, and SIZE DETERMINATION METHODS
more is furnished in special cases. As would be expected, many different
The recipient of a sample receives all methods were used to obtain the size
of the information on that sample made distribution data. For example, those for
available to the particle bank by the the carbonyl iron were obtained by
donor. Of course, neither the particle sedimentation. Much of the information
bank nor the donor can guarantee the for the carbon blacks was obtained by
accuracy of the information available electron microscopy and for the glass
or the applicability of the sample for a beads by sieves. Data for many of the
particular purpose. clays were obtained by the ASTM soils
A service charge of $5 is made to the colloids hydrometer3
recipient for each sample to cover hand- 2 Tentative Method for Grain-Size Analysis
ling costs and to ensure that only samples of Soils (D 4 2 2 - 5 4 T), 1955 Book of ASTM
Standards, Part 3, p. 1756. See also p. 89 of
actually needed are requested. this Symposium.
CADLE AND THIYh~AN ON THE STANFORD PARTICLE B A N K 299
TABLE II.--PARTICLE SIZE DATA FOR ZINC OXIDE PIGMENTS.
Permeability
Light Elec- L ~ ! d Sedi- Gas Ultra- Infra-

tron menta- Air Ad- micro- Tur- red
Micro- Micro- sorption sorp scope bidi- Trans-
scope scope tion Liquid tion Count meter mis-
Kozeny Arnell sion
Equation Equa-
i tion
KADOX BLACK LABEL-15
F-16Ol
da ................. 0.15 0.10 .o. .~ .o.

d~? . . . . . . . . . . . . . . . . o:i4 o:h
S, c sq m p e r g . . . . . .
0.28
3.8
0.18
6.0 iii o iii o i!i 0.26
4.1 7.8 9.5
dw d ................ 0.21 0.14 o:i4
N ~ X 101~ . . . . . . . . . 2042 7257
d~j ............... 0.37 0.27
0.34
XX RED-72
K-1602
0.19] 0 . 1 2
dr8 ................ o. 34] o.23 o:37 o~ o:b
S, sq m p e r g . . . . . . . . 3.1 4.6 4.3 2.9 7.2 3.3 6.2
dw .................. 0.25 0.15 ~
N X I 0 I~ . . . . . . . . . . 1139 ... 4200
dwtn ................ 0.42 0.44
XX RED-78
G-1603
0.3C 0.25 0.36

dv s ................. 0.79 0.48 5:~6 o:§ o:25 o.~ o:27
0.62
S, sq m p e r g . . . . . . . . 1.3 2.2 4.3 NBS a 1.7 2.8 3.9
NJZ h 1.7
dw .................. 0.49 0.35
N X 10 l~ . . . . . . . . . . . 153
dwm ................ I.I o:h
REHEATED SUPERFINE
i1111!
KH-1604
1.0
dvs ................. 1.9 1.63
S, sq m p e r g . . . . . . . . 0.6 9 0.5 0.65
dw .................. 1.4
hr • 101~ . . . . . . . . . . . 6.6
dwm ............... 2.2
a~ = a r i t h m e t i c m e a n d i a m e t e r (Y,d/Y,n), ~.
b d~8 = s u r f a c e m e a n d i a m e t e r (Y,da/Zd2), ~.
cS = s u r f a c e a r e a , sq m p e r g.
a d~ = mean weight diameter ( ~ ) , ~.
e hr = n u m b e r of p a r t i c l e s p e r g a n d is g i v e n b y N" = 1/pD ~, w h e r e p = d e n s i t y .
f dwm = w e i g h t m e a n d i a m e t e r (Znd4/Y~nd3), ~.
a NBS = N a t i o n a l B u r e a u of S t a n d a r d s .
NJZ = N e w J e r s e y Zinc.
300 SYMPOSIUM ON PARTICLE SIZE ~EASUREMENT
The set of four samples of zinc oxide, by hydrogen reduction of the purified
furnished by the New Jersey Zinc Co., oxides. Particle size data were obtained
has been studied by several investigators by two commercial devices, namely,
using about ten different methods. The the Fisher Sub-Sieve Sizer and the Cenco
results obtained have been summarized Photelometer. The former device ob-
by Arnell 3 and are reproduced in Table tains the specific surface by the air
II because they emphasize the impor-
T A B L E I I I . - - S I Z E DATA F O R T U N G S T E N
tance of proper interpretation of particle AND MOLYBDENUM POWDERS.
size data. The order arithmetic mean
diameter, less than the surface mean Surface I Mean
Material Mean I Weight
diameter, less than the weight mean Diameter,a # Diameter,b #
diameter is to be expected since this is
the order of increasing statistical weight Tungsten . . . . . . . . . . . . 1.05 I 0.75
given to the larger particles. Similarly, Tungsten . . . . . . . . . . . .
Tungsten . . . . . . . . . . . . 1.65
2.30 I 1.5
1.8
the arithmetic mean diameter was less Tungsten . . . . . . . . . . . . 4.50 3.1
than the mean weight diameter. Mean Tungsten . . . . . . . . . . . . 3.80 2.8
Molybdenum . . . . . . . . 4.40 3.7
diameters obtained with the optical
microscope were somewhat larger than Obtained with Fisher sub-sieve sizer.
those obtained with the electron micro- b Obtained with Cenco photelometer.
scope. This is to be expected for mixtures
of particles having mean diameters close permeability method 4. The surface mean
to the limit of resolution of the light diameter is then calculated, using the
microscope, for two reasons. The first is equation
that the particles smaller than the limit 6 X 104
d~8
of resolution may be overlooked and the pSw
second is that the sizes of the individual
particles observed with a microscope where:
appear to be larger than they are by an d** = surface mean diameter,
amount approximately equal to the 2;da
resolving power. The ultramicroscope ~3d-~,v,
count, which involves determining the p = density of the particles,
number of particles per unit weight of g per cu cm, and
powder, gave results which agree well Sw -- specific surface, sq cm
with those obtained with the electron per g.
microscope. This is not surprising, since The latter device is a modification of the
much smaller particles can be detected L. A. Wagner sedimentation-turbidi-
with the ultramicroscope than can be metric apparatus3 The data were re-
resolved with the optical microscope. ported as per cent of weight v e r s u s size
The gas adsorption technique yielded
smaller diameters than those obtained range. Mean weight diameters, ~ / ~ n n '
with the electron microscope, which is
were estimated graphically. The results
to be expected if the particles are highly
obtained by the two methods (Table III)
irregular.
agree quite well considering the differ-
The samples of tungsten and molyb-
denum powder, supplied by Sylvania * E. L. Gooden and C. M. Smith, Industrial
Electric Products, Inc., were prepared and Engineering Chemiatry (Analytical Edition),
Vol. 12, pp. 479-482.
3j. C. Arnell, "Permeability Studies-IV. L. A. Wagner, "A Rapid Method for the
Surface Area Measurements of Zinc Oxide and Determination of the Specific Surface of Port-
Potassium Chloride Powders," Canadian Jour- land Cement," Proceedings, Am. Soc. Testing
nal of Research, Vol. 27A, pp. 207-212 (1949). Mats., Vol. 33, Part II, p. 553 (1933).
DISCUSSION ON THE STANFORD PARTICLE BANK 301
ences in the experimental techniques requests for samples, the particle bank
and in the methods for estimating repre- has made a reasonable start toward
sentative diameters. fulfilling the objectives set for it. Hope-
CONCLUSIONS fully, it will become even more useful
Judging from both the number of as more samples are deposited and it
samples deposited and the number of becomes better known.
DISCUSSION
MR. FRANCIS J. LICATA.I--This idea creases with time, and it would be in-
of the particle size bank seems to be a teresting if possibly some analogous phe-
very good one. In investigating some par- nomenon might take place with the
ticles we encountered a phenomenon that larger particles that you are measuring.
may be of interest. We have observed MR. ALLAN I. MICI~AELS.3--In re-
that small particles on storage seem to gard to the data on tungsten powders,
increase in size for no apparent reason. work has been done in attempting to
This occurs with particles which go check the correlation between the Fisher
through completely a No. 200 or a No. subsieve sizer and the Cenco Photelom-
325 mesh screen. After several months, eter, especially by Mr. Bernard Kopel-
there may be about 10 per cent increase man of the Sylvania Physics Labora-
in particle size. tories. He did show that if you work
MR. R. D. CADLE (author).--I do not tungsten powder to a proper degree it is
know of any data that we have to prove possible to obtain agreement between a
or disprove this concept of particle subsieve size measurement and a pho-
growth with time. The size distributions telometer measurement to within a few
for the zinc oxide samples described in tenths of a micron very consistently. He
our paper had been determined over a also obtained good agreement by these
large number of years. The different in- two techniques on various other refrac-
vestigators who studied them used dif- tory metal and inorganic powders.
ferent techniques, so a direct comparison MR. K. T. W m T B Y . L I happen to
is not possible. However, the variations remember one instance several years ago
are small compared with the usual un- where the apparent sedimentation par-
certainties that exist between different ticle size of the talc changed after ship-
methods for size distributions. I should ment.
like to point out that sampling errors This was brought to light when the
may be extremely important in trying particle size of finely ground talc ap-
to compare samples over quite a period peared to increase after shipment. Subse-
of time. quent ir~vestigation indicated that the
MR. CHARLES M . H U N T . ~ I wouId vibration during shipment was causing
like to comment on that last point. Cer- the plate-like talc particles to stick to-
tainly it is very easily demonstrated gether strongly enough to resist the dis-
that many colloidal gels change with age. persing agents being used.
If one is measuring surface area it de- 3Sylvania Electric Products, Inc., Metal-
lurgical Laboratory, Towanda, Pa.
1 Metasap Chemical Co., Harrison, N. J. 4Assistant Professor of Mechanical EngL
2 Chemist, National Bureau of Standards, neering, Mechanical Engineering Department,
Washington, D. C. University of Minnesota, Minneapolis, Minn.
STP234-EB/Aug. 1959
LIST OF ASTM STANDARDS FOR PARTICLE SIZE

MEASUREMENT
T h e following list c o n t a i n s the titles and designations of those s t a n d a r d s

p u b l i s h e d b y t h e A S T M t h a t are considered to be of i n t e r e s t in t h e field of
p a r t i c l e size d e t e r m i n a t i o n . T h e f o o t n o t e s i d e n t i f y t h e v o l u m e s of t h e
A S T M B o o k of S t a n d a r d s c o n t a i n i n g these publications. T h e y are also
a v a i l a b l e separately.
Methods of Test for:

Sieve Analysis of Granular Metal Powders (B 214) 1
Subsieve Analysis of Granular Metal Powders by Air Classification (B 293) 1
Average Particle Size Refractory Metals and Compounds by Fisher Subsieve Sizer (B 330) x
Sieve Analysis and Water Content of Refractory Materials (C 92) ~
Fineness of Portland Cement by the Turbidimeter (C 115)3
Amount of Material Finer than No. 200 Sieve in Aggregate (C 117)3
Sieve Analysis of Fine and Coarse Aggregates (C 136) 3
Clay Lumps in Natural Aggregates (C 142)3
Fineness of Hydraulic Cement by the No. 200 Sieve (C 184) 3
Fineness of Portland Cement by Air Permeability Apparatus (C 204) 3
Sieve Analysis of Plastic Calcined Magnesia (C 239) 8
Sieve Analysis of Wet Milled and Dry Milled Porcelain Enamel (C 285) 2
Wet Sieve Analysis of Ceramic Whiteware Clays (C 325) 2
Sieve Analysis of Nonplastic Pulverized Ceramic Materials (C 371) 2
Fineness of Hydraulic Cement by the No. 325 Sieve (C 430) 4
Coarse Particles in Pigments, Pastes, and Paints (D 185)s
Sampling and Fineness Test of Powdered Coal (D 197) n
Sieve Analysis of Coke (D 293) s
Size of Anthracite (D 310) ~
Sieve Analysis of Crushed Bituminous Coal (D 311) 5
Coarse Particles in Mixtures of Asphalt and Mineral Matter (D 313) 3
Molding Powders Used in Manufacturing Molded Electrical Insulators (D 392) 6
Screen Analysis of Coal (D 410) ~
Grain-Size Analysis of Soils (D 422) 3
Designating the Size of Coal from Its Screen Analysis (D 431) 5
Sieve AnMysis of Granular Mineral Surfacing for Asphalt Roofing and Shingles (D 451) 3
Sieve Analysis of Nongranular Mineral Surfacing for Asphalt Roofing and Shingles (D 452) 3
Sampling and Testing Aluminum Powder and Paste (D 480) ~
z 1958 Book of ASTM Standards, Part 3.

2 1958 Book of ASTM Standards, Part 5.
4 1959 Supplement to Book of ASTM Standards, Part 4.
302
Copyrights 1959 by A S T M International www.astm.org

A S T M STANDARDS FOR PARTICLX SIZE MEASUREMENT 303
Particle Size of Soaps and Other Detergents (D 502) 7

Sieve Analysis of Mineral Filler (D 546) 3
Analysis of Barium Sulfate Pigments (D 715) 5
Analysis of Magnesium Silicate Pigment (D 717) 5
Analysis of Aluminum Silicate Pigment (D 718) 5
Amount of Material in Soils Finer Than the No. 200 Sieve (D 1140) 5
Fineness of Dispersion of Pigment-Vehicle Systems (D 1210) 5
Sieve Analysis of Glass Spheres (D 1214) 5
Fineness of Grind of Printing Inks by the Production Grindometer (D 1316) 5
Attrition of Pelleted Carbon Black (D 1507) 8
Fines Content of Pelleted Carbon Black (D 1508) 3
Pellet Size Distribution of Carbon B]ack (D 1511) 3
Sieve Residue from Carbon Black (D 1514) 3
Specifications for:
Sieves for Testing Purposes (Wire Cloth Sieves, Round-Hole and Square-Hole Screens or
Sieves) (E 11) 1, 2, 5.5, 5, ~, 3
Recommended Practices for:
Reporting Particle Size Characteristics of Pigments (D 1366) ~
Analysis by Microscopical Methods for Particle Size Distribution of Particulate Substances
of Subsieve Sizes (E 20) 3' 5
s 1958 Book of ASTM Standards, Part 7.
THIS PUBLICATION is one of many
issued by the American Society for Testing Materials in
connection with its work of promoting knowledge of
the properties of materials and developing standard
specifications and tests for materials. Much of the data
result from the voluntary contributions of many of the
country's leading technical authorities from industry,
scientific agencies, and government.
Over the years the Society has published many tech-
nical symposiums, reports, and special books. These may
consist of a series of technical papers, reports by the
ASTM technical committees, or compilations of data
developed in special Society groups with many organiza-
tions cooperating. A list of ASTM publications and
information on the work of the Society will be furnished
on request.
@
pplication for Membership
The undersigned hereby applies for t( sustaining
company
individual ~
associate ~ m e m ~
. ..
in the American Society for Testing Materials including subscription

to ASTM BULLETIN. If this application be duly approved, he agrees
to be governed by the Charter and By-laws of the Society and to further
its objects as laid down therein.
N A M E ....................................................................................................................
(Firm, Organization or Individual Appliean!)
ADDRESS FOR M A I L ............................................................................................

(If other than below)
................................................................ ZONE....................
N A T U R E OF B U S I N E S S ........................................................................................
N A M E .................................................... T I T L E ......................................................
I f company membership, indicate above the name and title of individual who will
exercise membership privileges.
N A M E OF ORGANIZATION ....................................................................................
If individual membership, indicate above the name of organization with which applicant is a~liated.
ADDRESS OF ORGANIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPLICANT'S T I T L E OR OCCUPATION ................................................................
D A T E OF B I R T H ....................................................................................................
GRADUATE OF, OR ATTENDED ............................................................................

Name of College or University
Y E A R .................... D E G R E E , OR COURSE ................................................
R e c o m m e n d e d b y $ ......................................................................................
(Two M~MB~RS) (
Application for membership should be mailed t o

I~IATERIALS--1916RACE ST., PHILADELPHIA3, PA.
AMER1CAN S C O T T Y EOIr T E S T I N G
-" ~ i r
307
P 41-59
EXTRACT FROM CHARTER

1. T h e name of the proposed corporation is the " A m e r i c a n Society for Test-
ing M a t e r i a l s . "
2. T h e corporation is formed for the promotion of knowledge of t h e m a t e r i a l s
of engineering, and the s t a n d a r d i z a t i o n of specifications and t h e m e t h o d s
of testing.
EXTRACT FROM BY-LAWS

ARTICLE I. Members and Their Election
SECTION 1. T h e Society shall consist of I n d i v i d u a l Members, C o m p a n y Mem-
bers, Sustaining Members, Associate Members, S t u d e n t Members a n d Honor-
ary Members.
SEc. 2. An I n d i v i d u a l M e m b e r shall be a person, technical or scientific
society, college or u n i v e r s i t y or d e p a r t m e n t thereof, library, g o v e r n m e n t
bureau or d e p a r t m e n t , or such other organizations as the Board of Directors
m a y deem as a p p r o p r i a t e l y coming u n d e r this classification.
SEc. 3. A C o m p a n y M e m b e r shall be a company, corporation, firm, indus-
trial or trade association, or such o t h e r organizations as the B o a r d of Directors
m a y deem as appropriately coming u n d e r this classification.
SEC. 4. A Sustaining M e m b e r shall be an I n d i v i d u a l Member o r C o m p a n y
M e m b e r who wishes to s u p p o r t and p a r t i c i p a t e in the work of the Society
t h r o u g h the p a y m e n t of larger dues.
SEC. 5. An Associate M e m b e r shall be a person less t h a n t h i r t y years of age.
An Associate M e m b e r shall have the same rights a n d privileges as an I n d i v i d u a l
Member, except t h a t he shall not be eligible for office. His s t a t u s shall be
changed from Associate M e m b e r to I n d i v i d u a l M e m b e r at the beginning of t h e
fiscal year next succeeding his t h i r t i e t h b i r t h d a y .
ARTICLE V. Meetings
S~CTION 1. T h e Society shall meet annually, for the t r a n s a c t i o n of its busi-
ness, including actions on s t a n d a r d s , at a time and place fixed b y t h e B o a r d of
Directors. Twenty-five members shall c o n s t i t u t e a quorum.
SEC. 2. Special meetings may be called whenever t h e Board of Directors shall
deem it necessary, or upon the w r i t t e n request of 25 members to t h e President.
ARTICLE V I I I . Dues
SECTIOtq 1. T h e fiscal year shall commence on the first day of J a n u a r y , T h e
a n n u a l dues*, payable in advance, shall be as follows: For I n d i v i d u a l Members,
$18; for C o m p a n y Members, $75; for Sustaining Members, $200; for Associate
Members, $10; for S t u d e n t Members, $2. H o n o r a r y Members shall not be
subject to dues.
SEC. 2. T h e e n t r a n c e fees, payable on admission to the Society, shall be $10
for I n d i v i d u a l Members, C o m p a n y Members and Sustaining Members, and $5
for Associate Members. S t u d e n t Members shall pay no e n t r a n c e fee. T h e fee
payable upon t r a n s f e r from one class of m e m b e r s h i p to a n o t h e r , shall be t h e
difference between the corresponding e n t r a n c e fees.
SEe. 5. Any person elected after six m o n t h s of any fiscal year shall h a v e
expired, m a y pay only one-half of the a m o u n t of dues for t h a t fiscal year; b u t
in t h a t case he shall not be e n t i t l e d to a copy of t h e Proceedings for t h e c u r r e n t
year.
* NoTe--Of the annual dues $3.50 is for subscript;on to ASTI~IBULLETIN.
308
P 41-61
flpplitation for ' lemtJership

The undersigned hereby applies for t sustaining
( company
individual
assocmte }
l membership
in the American Society for Testing Materials including subscription
to ASTM BULLETIN. If this application be duly approved, he agrees
to be governed by the Charter and By-laws of the Society and to further
its objects as laid down therein.
NAME ....................................................................................................................
(Firm, Organization or Individual Applicant)
A D D R E S S F O R MAIL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(if other than below)
................................................................ ZONE....................
NATURE OF BUSINESS ........................................................................................
NAME .................................................... TITLE ......................................................

If company membership, indicate above the name and title of individual who will
exercise membership privileges.
~TAME O F O R G A N I Z A T I O N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I f individual membership, indicate above the name of organizalion with which applicant is a~llaled.
ADDRESS OF ORGANIZATION ................................................................................
APPLICANT'S TITLE OR OCCUPATION ................................................................
DATE Or BIRTIt....................................................................................................
GRADUATE OF~ O R A T T E N D E D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Name of College or University
YEAR .................... DEGI~EE, OR COURSE ................................................
R e c o m m e n d e d b y ~ ......................................................................................
(TWOM~ra~EES) ~ ......................................................................................
Application for membership should be mailed to

A~ERlC.4/q SOCIETYFOE TEST]I'~GtVIATI:EI.~LS--1916RACE ST., PHILADELPFIIA3, PA.
3O9
EXTRACT FROM CHARTER

1. T h e name of the proposed corporation is t h e " A m e r i c a n Society for Test-
ing M a t e r i a l s . "
2. T h e corporation is formed for the p r o m o t i o n of knowledge of the materials
of engineering, and the s t a n d a r d i z a t i o n of specifications and the methods
of testing.
EXTRACT FROM BY-LAWS

ARTICLE I. Members and Their Election
SECTION 1. T h e Society shall consist of I n d i v i d u a l Members, C o m p a n y Mem-
bers, Sustaining Members, Associate Members, S t u d e n t Members and Honor-
a r y Members.
SEC. 2. An I n d i v i d u a l M e m b e r shall be a person, technical or scientific
society, college or u n i v e r s i t y or d e p a r t m e n t thereof, library, g o v e r n m e n t
b u r e a u or d e p a r t m e n t , or such o t h e r organizations as the Board of Directors
m a y deem as a p p r o p r i a t e l y coming u n d e r this classification.
SEC. 3. A C o m p a n y M e m b e r shall be a company, corporation, firm, indus-
trial or t r a d e association, or such other organizations as the Board of Directors
m a y deem as appropriately coming under this classification.
SEc. 4. A Sustaining M e m b e r shall be an I n d i v i d u a l M e m b e r or C o m p a n y
M e m b e r who wishes to s u p p o r t and p a r t i c i p a t e in the work of the Society
t h r o u g h the p a y m e n t of larger dues.
S~c. 5. An Associate M e m b e r shall be a person less t h a n t h i r t y years of age.
An Associate M e m b e r shall have the same rights a n d privileges as an Individual
Member, except t h a t he shall n o t be eligible for office. His s t a t u s shall be
changed from Associate M e m b e r to I n d i v i d u a l M e m b e r at the b e g i n n i n g of the
fiscal year next succeeding his t h i r t i e t h b i r t h d a y .
ARTICLE V . Meetings
SECTION 1. T h e Society shall meet annually, for the t r a n s a c t i o n of its busi-
ness, including actions on s t a n d a r d s , a t a time a n d place fixed b y t h e B o a r d of
Directors. Twenty-five members shall c o n s t i t u t e a quorum.
SEc. 2. Special meetings m a y be called whenever t h e Board of Directors shall
deem it necessary, or upon the w r i t t e n request of 25 members to the President.
ARTICLE V I I I . Dues
SECTION 1. T h e fiscal year shall commence on the first day of J a n u a r y . T h e
a n n u a l dues*, payable in advance, shall be as follows : For Individual Members,
$18; for C o m p a n y Members, $75; for Sustaining Members, $200; for Associate
Members, $10; for S t u d e n t Members, $2. H o n o r a r y Members shall n o t be
subject to dues.
SEc. 2. T h e e n t r a n c e fees, payable on admission to the Society, shall be $10
for Individual Members, C o m p a n y Members and Sustaining Members, a n d $5
for Associate Members. S t u d e n t Members shall pay no e n t r a n c e fee. T h e fee
payable upon t r a n s f e r from one class of m e m b e r s h i p to a n o t h e r , shall be t h e
difference between the corresponding e n t r a n c e fees.
SEC. 5, Any person elected after six m o n t h s of any fiscal year shall h a v e
expired, m a y pay only one-half of the a m o u n t of dues for t h a t fiscal year; b u t
in t h a t case he shall not be e n t i t l e d to a copy of the Proceedings for t h e c u r r e n t
year.
* NOTE--Of the annual dues $3.50 is for subscription to ASTM BULLETIN.
310
P 41-61

ASTM - STP 234 - Symposium On Particle Size Measurement

Uploaded by

Copyright:

Available Formats

ASTM - STP 234 - Symposium On Particle Size Measurement

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

ASTM - STP 234 - Symposium On Particle Size Measurement

Uploaded by

Copyright:

Available Formats

SYMPOSIUM ON

AMERICAN SOCIETY FOR TESTING MATERIALS

.~IS T M Special Technical Publication No. 234

Price $6.25; to Members $5.oo

The papers and discussions in this 1958 Symposium on Particle Size

Copyright* 1959 by ASTM International www.astm.org

connection with sieves, it might be particle. The Coulter counter reported

I n spite of the importance of sieving countered in most industrial processes.

Copyright* 1959 by ASTM International www.astm.org

FIG. 1 . - - T y p i c a l Per Cent Passing - Ti me Curve.

t = sieving time, only two dimensions, a will be a function

Detailed descriptions of apparatus and quartz is irregular with smooth surfaces,

Fro. 2.--Photomicrographs of Particle Types Used in This Study.

oSAo S . . . . . . . . . . . (4) sieve opening, the differences were not

1; ' I , ' I1• 0

99.8 W h e n such plots were m a d e for the

TABLE L--HIGH-LOAD SIEVING CONSTANTS.

Material Weight Relative CI Particle Shape

Medium ............................. 500 0.51

ST, PETER SAND

Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 2.45 1

Original No. 1 . . . . . . . . . . . . . . . . . . . . . . . . 500 2.64

comes: plots similar to Fig. 5 and n from plots

cient of 0.932 was obtained which is Characteristics of Region 1 (High Load)

100 IOOO too Io0o

FIG. 7.--Region 1 Sieving Constant as a Function of Sieve Load,

Under the general regularity condi-

Typical Weight-rime Data

that remain, attention may be focused dN

I. (log d - - log d ) 2 1 7.5 ..... 50.36

Beads St. Peter Sand

Fit of the Log-Normal Law to Region 2 of Relation of Particle Size Distribution to

TABLE III,--COEFFICIENTS FOR THE cept should be zero. T h o u g h this was

sand, the intercepts for the flint a n d

Hard Wheat Middlings /

PerCentP a s s i n g - - o l ' - ~ . / ~ -100

distributions on each of the four mate- P~ no doubt depends on the distribution

smaller opening if oriented in a certain theory and these experiments indicate

Effect of Load on Region 2

and the region 2 sieving constants deter-

Beads St. Peter Sand Flint Hard Wheat Middlings

149 143 158

4.47 2.64 2.22 2.25

lish a proper end point. From this study dt log ~rgptV/~

Even if it is assumed that sieving is Where qS(Zm) - ~ and

to 5 rain is actually not a sieving error dC(W, x) aW

Therefore for region 1 = Wc-R~pBpX.. (33)

Cle region 1 sieving constant at critical sieve loading,

= geometric n u m b e r m e a n particle size,

oz r = normal probability integral

BY H. W. DAESCHNER, 1 E. E. SEIBERT, 1 AND E. D. PETERS~

Woven-wire sieves present a variety of problems to the petroleum refiner

Fro. 1.--Typical Precision Micromesh Sieves. Nominal Size (X55).

Fro. 2.--Cross-Sectionof Micromesh Mounted on Supporting Grid. 45 ~ mesh size (;4100).

TABLE I.--CALIBRATED VALUES OF Difference Be-

90. .. 85.8 1.7 86.6 2.1

FIG. 3.--Typical Woven-Wire Sieves (X 55).

TABLE IV.--RETENTION EFFICIENCY OF MICROMESH COMPARED