Proceedings of the World Congress on Engineering 2010 Vol I

WCE 2010, June 30 - July 2, 2010, London, U.K.

Experimental Evaluation of the Concentration

Zone Widths in Cane Sugar Crystallization using
Data and Image Acquisition
O. Velazquez-Camilo, E. Bolaños-Reynoso*, L. Lopez-Zamora and J. Alvarez-Ramirez.

 to obtain a specific CSD the supersaturation control plays an

Abstract—The crystallization process consists in the important role since it is a prerequisite for nucleation and
solid-liquid separation of organic and inorganic chemicals growth. In turn, this is achieved through changes
involving mass transfer of a solute dissolved in a liquid phase to programmed in the cooling temperature, vacuum pressure,
a solid phase. The concentration zone widths let define the
equilibrium or saturation line, metastable zone (first and
supersaturation, agitation rate and seeded crystal, among
second) and unstable or labile zone, and they are of prime others [2]–[7]. One of the most important attributes in the
importance for the design of optimal operation of cane sugar crystallization processes is the presence of a continuous and a
processes. This work has the goal to present a novel method to dispersed phase. By the effects of transport and
determine experimentally the concentration zone widths for physiochemical phenomena, the crystallization is realized
commercial cane sugar (refined) using data and image through several steps, including nucleation, growth,
acquisition approach. Crystal size distribution (CSD) analysis
and micrograph sequences were used for determining the
occlusion and crystal attrition, leading to a distributed
stability limits in terms of density. As a main result, we found characterization of the physical and chemical properties of
that the width of the concentration zones (metastable and labile) the product as the crystal size, forms, morphology, porosity,
increases nonlinearly whereas the saturation temperature etc. [8], [9].
(cooling) decreases in a range from 70 to 40 °C. The results are
commented in terms of process operation conditions according The operation of crystallizer should be oriented to meeting
to the required information by the cane sugar crystallization
specified product quality measured as product purity and
industry, in order to have an appropriate control of the
supersaturation inside the process. CSD [10]. In the literature, there are a lot of studies that apply
the first-principle approach starting by mathematical models
Index Terms—Cane sugar crystallization, concentration zone based on material, energy and population balances, with the
widths, image and data acquisition, CSD. aim of optimizing some variables of the process (CSD,
crystal mass, density, etc.) to obtain better profit as much by
I. INTRODUCTION the producer as by the client [11]-[13]. On the other hand, in
The crystallization process consists in the solid-liquid the crystallization industry the direct design approach is
separation of organic and inorganic chemicals involving based on the study of the metastable zones to the
mass transfer of a solute dissolved in a liquid phase to a solid identification of an operation region allows to favor the
phase. At industrial conditions, the crystalline products crystal growth (seeded) and to avoid the spontaneous
require to have specific purity and crystal size distribution nucleación. Nevertheless, the study or application of the
(CSD) instead of random distributions. The crystallization by direct design approach has been less studied than the
cooling procedures is used when the solubility of the first-principle approach, because of the difficulty of
substance is an increasing function of the temperature. This disposing of laboratories with sophisticated equipments or
operation is widely used in the industry for producing due to the high cost of realizing experiments in plant. For the
crystalline solids with a high purity at a cost relatively lower cane sugar, industrial process design and operation is still
than other separation/purification operations [1]. In this form, based on the usage of empirical concentration zone widths.
To the best of our knowledge, a quantitative description of
Manuscript received March 12, 2010. This work was supported in part by
these concentration zone widths oriented for industrial
FOMIX CONACYT (National Council of Science and Technology) – applications is still lacking in the open scientific literature.
Veracruz, Mex. under Project key: 37571.
E. Bolaños-Reynoso* is research-professor (PhD) with the Instituto Our aim is to present a novel method for determining the
Tecnologico de Orizaba. Oriente 9 No. 852. Col. E. Zapata. 94320 Orizaba,
Ver. Mex. (corresponding author. Phone/fax: 52-272-725-70-56; e-mail: crystallization stability zones for industrial sugar cane using
eusebio@itorizaba.edu.mx) data and image acquisition. The approach uses both
O. Velazquez-Camilo is CONACYT’s PhD. scholarship with experimentation and modeling to obtain the saturation line
Universidad Autonoma Metropolitana-Iztapalapa, 09340 Mexico, D.F.
(e-mail: ovc@xanum.uam.mx). and metastable and labile zone widths in terms of the solution
L. Lopez-Zamora is research-professor (PhD) with the Instituto density from measurements with a high-precision digital
Tecnologico de Orizaba. 94320 Orizaba, Ver. Mex. (e-mail: llopezz02@ densimeter. We found that the width of the zones
yahoo.com.mx).
J. Alvarez-Ramirez is research-professor (PhD) with the Universidad
concentration increases nonlinearly as the saturation
Autonoma Metropolitana-Iztapalapa, 09340 Mexico, D.F. (e-mail: temperature decreases in a range from 70 to 40 °C.
jjar@xanum.uam.mx).

ISBN: 978-988-17012-9-9 WCE 2010

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2010 Vol I
WCE 2010, June 30 - July 2, 2010, London, U.K.

II. METHODOLOGY analysis, such as microscopy (electronic and handle),

captured image by camera, electrozone sensing, and low
A. Experimental Equipment angle laser light scattering (LALLS). Every technique can
A glass batch crystallizer with isolation, type stirred tank generate different measures of average diameter, as well as
with cooling-heating jacket was used by the experimental different properties of a particle. The suitable approach
development. The crystallizer was connected to a depends on the problem and on the available data [18].
programmable recirculation bath, variable agitation motor, Therefore, different approaches allow different ways to
concentration meter (density), data acquisition and a directly obtain average numbers: microscopy produces
microscopic imaging acquisition system in pseudo-line. Fig. D(1,0) (length), captured image by camera yields D(2,0)
1 exhibits the equipment configuration and Table 1 describes (superficial area), electrozone sensing gives D(3,0) (volume),
important information about the equipments, electronic and LALLS produces D(4,3) (equivalent volume).
devices and crystallizer instrumentation.
For this work, the program CSD Adq-Im [17] was
B. Image and Data Acquisition System
developed to make CSD complementary calculations to those
The experimental equipment was integrated by a data of the IMAQ Vision Builder system. Our software CSD
acquisition system (PCI-6025E, PCI-1407, SC-2345 and Adq-Im receives the crystal length in micrometers from
SCC-TC02 by National Instruments, Inc. (NI)), which was IMAQ system as input data. Then, CSD Adq-Im makes the
used to register the concentration (densimeter DMA-4500 by relationship between the direct measurement D(1,0),
Anton-Paar) in a host computer and to control the considering our results as the microscopy approach, and the
temperature of the system by means of a programmable derivate measurement D(2,1) produced by LALLS. Later on,
recirculation bath (Julabo F-34). The CSD was tracked in the derivative diameters D(3,2), D(4,3), and D(1,0) are
pseudo-line and registered by imaging acquisition system calculated from each log-normal distribution of relative
that included a monochrome camera (RS-170. Lens: 0.19 frequency from the LALLS approach. The latter approach
mm-pixel by NI) and microscope trinocular (48923-30 by (LALLS) obtains the derivative average diameter without
Cole Palmer). necessarily requiring the particles total number from the
slurry or solution at study. Finally, CSD Adq-Im carries out
For the pseudoline measurement at every sampling time of the calculations to obtain % number, % length, % surface, %
the experimental runs and its particles analysis (crystals) volume, and others statistical properties from log-normal
through captured images, the software IMAQ Vision Builder distributions of relative frequency [19]. The calculations
(NI) was used. This image approach is an alternative in were made following the mathematical formulism given by
measuring both length and area of particles in a direct way Marlven Instruments, Inc. [20] with its commercial
through IMAQ Vision’s software. The technique consists of equipment of particle analysis based on LALLS.
acquiring an image using a monochromatic camera with
video RS-170 and 60 Hz crisscross (8 bits of resolution) and C. Obtaining of the Metastable and Labile Zone Widths
handling the light beam from a microscope trinocular. The To obtain the metastable and labile zones widths (MSZW),
camera captures an image square that is to be processed and saturated solutions of commercial cane sugar (refined) at
cleaned. This avoids undesirable light variations. The latter is different equilibrium temperatures (40, 50, 60 and 70 °C)
achieved through the threshold technique that allows were prepared in a cooling batch crystallizer (Fig. 1). Here,
obtaining only an image in gray scale. Interesting areas are the solution was cooling down in intervals of 1°C. For each
isolated to be independently analyzed, and black pixels temperature stationary state a solution sample in pseudoline
(crystals) are counted. The black pixels are compared with was taken to measure the concentration (density) and the
acceptation limits to decide if the object is present or not CSD. 3 ml of filtered solution was sampled (phase continues)
according to binary images (background) [14]. Then, a with standard sugar paper (porosity of 19 µm) and 1 ml was
threshold technique approach, similar to that reported in introduced in the digital densimeter working to the
further multiscale segmentation image approach, was used to atmospheric pressure. Then, to measure the CSD, 5 ml of
compute the CSD features [15], [16]. solution without filtering was sampled and nuclei or crystals
(smalls) images were acquired with the support of an imaging
The measurements and analysis of particles were carry out acquisition system.
against a previous calibration through a Neubauer’s recount
camera (simple calibration) in order to get a direct conversion The saturated solutions preparation was realized following
from 1 pixel side to 200 μm (length). A pixel is defined as the a random design, being carried out four solutions with two
smallest homogeneous unit in color that is part of the digital replies, each one by different saturation temperatures. The
image. The pixels appear as small squares in white, black, or established weight of each solution was 4500 g (g sugar/ml
gray shades. In this work, a microscope with a 10x ocular water), so that the sampling was not an importance variable
lens with a 40x objective and an E square from Neubauer’s to consider and to be able to handle the system as a solution
camera from 50 μm away, were used. This is equivalent to constant volume. The proportions used to prepare the
20000 μm (10x40x50) per 100 pixels (length of pixel side). saturated solutions to its equilibrium temperature were
Thus, 1 μm is equal to 0.005 of the length of a pixel side [17]. obtained from Moncada’s equation [11].

There are different approaches for CSD measurements and 

Brixsat  0.0007T 2  0.264T  60.912 (1)

ISBN: 978-988-17012-9-9 WCE 2010

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2010 Vol I
WCE 2010, June 30 - July 2, 2010, London, U.K.

Fig. 1 Cooling batch crystallizer.

Table 1. Electronics and instrumentation devices of a cooling batch crystallizer.

Quantity Devices

6 L Glass crystallizer. Dimensions: 35 cm height and 14.4 cm internal diameter, 1.8 cm

1
inferior dome height and 5 cm upper dome height., 2.55 L cooling - heating jacket

Generic motor of variable velocity with direct transmission from 0 rpm to 1,500 rpm, 60
1 Hertz, 127 VCA , agitation arrow of 14 inches (length) and diameter of ¼ inch, in stainless
steel 316
Agitator/impeller of four rectangular ring with separation of 90° among each cross.
1
Crosses’ longitude of 2 inches x 1inch of length for largeness in stainless steel 316.
2 Thermocouple J type. From 0 °C to 760 °C, wire-rope: 3 m.
1 Thermo-well in copper of 14 inches (length) and diameter of ½ inch.
Thermal isolation for high temperature with glass fiber of thickness ½ inch and recovered
1
with paper aluminum foil.
Programmable recirculating bath (Julabo F-34), temperature range from -34 °C to 200 °C,
1
pump flow of 15 Lpm, bath volume from 14 L to 20 L and 120 VCA/60 Hz.

Digital densimeter (Anton-Paar DMA-4500), measurement range from 0 g/cm3to 3 g/cm3,

feed sample to the cell: 1 ml of solution, measurement error in the temperature 0.1 °C and
1
1x10-5 g/cm3 in density. Measurement time for sample: usually 30 seconds. Interface
COM1, COM2 for connection RS-232 to computer.

Digital tachometer ACT-3. Monarch Instrument. Measurement range from 5 rpm to 999
1 990 rpm with accuracy of 0.0015% +/ - 1 rpm, 4-20 mA or 0-5. V, sensitivity of 0.5 ms and
optic sensor of infrared ray with range from 1 rpm to 250 000 rpm.

ISBN: 978-988-17012-9-9 WCE 2010

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2010 Vol I
WCE 2010, June 30 - July 2, 2010, London, U.K.

the change of % volume (percentage in volume of specific

III. RESULTS size particles) and crystal size (average diameter D(4,3) in %
volume) in the CSD quantification, patterns were
A. Analysis of the Concentration Average in Function of established.
Cooling Temperatures
Fig. 2 presents the experimental data of the average density Fig. 3a shows the CSD for a saturated solution at 40 °C,
(3 runs by each saturation temperature) as a function of where a pattern of three zones of CSD for different
cooling down until reaching a stationary state for each temperature ranges is observed. From Fig. 4a, it is observed
saturated solution. We can observe that the densities for that from 40 to 37 °C the CSD has about 20-25 % volume,
every saturation temperature increases as the cooling and diameter D(4,3) ranging from 30.4 to 49.9 µm. This
temperature decreases. For each saturation solution, there is a region corresponds to the first metastable zone where neither
range of cooling temperature and concentration where nuclei formation nor crystals are formed. From 36 to 33 °C,
saturation can be found. In fact, for 40 °C the temperature the % volume increases suddenly from 50 to 95 %, while the
range was from 40 to 25 °C and the concentration from diameter D(4,3) from 50.9 to 130.2 µm. In turn, this region
1.34093 to 1.34921 g/cm3, for 50 °C the temperature range of corresponds to the second metastable zone where the crystal
cooling was from 50 to 40 °C and the concentration from growth dominates over the nucleation. When the cooling
1.34785 to 1.35351 g/cm3, for 60 °C was from 60 to 50 °C temperature decreases until to 32 °C, the % volume falls
and the concentration from 1.3542 to 1.3597 g/cm3 and for 70 down drastically to 22 % in average and the average diameter
°C was from 70 to 53 °C and the concentration from 1.35769 D(4,3) decreases to about 82.3 µm. In turn, it is considered
to 1.36592 g/cm3. This concentration and temperature ranges that this region represents the unstable or labile zone where
are the base to determine the concentration (critical points) of the nucleation dominates over the crystal growth. Under
MSZW, complemented with CSD measurements and the these conditions, the CSD standard deviation is increased.
acquired images, in order to quantify the CSD and to observe This pattern can also be observed qualitatively by means of
by means of micrographies the formation and growth of the micrographic sequences in Fig. 4.
crystal across the concentration zones.
Fig. 3b to Fig. 3d illustrates the CSD for a solution saturated
1.366
1.364 Equilibrium line
for 50, 60 and 70 °C, respectively. Table 2 resumes the CSD
1.362 Average at 40 蚓 data from patterns (critical points of density) of three
Average at 50 蚓
1.360
Average at 60 蚓 concentrations zones for each saturation temperature.
1.358 Average at 70 蚓
1.356
C. Metastable and Labile Zone Widths
Density (g/cm )
3

1.354
1.352 Fig. 5 shows the experimental density-temperature
1.350
1.348
relationship where the critical points of MSZW are located
1.346 by considering the minimum temperature for each
1.344
1.342
temperature range presented in the Table 2. The density
1.340 corresponding to every saturation temperature was located
1.338
25 30 35 40 45 50 55 60 65 70
considering the Fig. 2 that presents the density averages of
Temperature (蚓 ) the experimental runs. From Fig. 5, we can observe that the
Fig. 2 Average density in function of cooling down of 1 zones width (metastable and labile) increases of non-linear
°C. form as the saturation temperature (cooling) decrease in a
range from 70 to 40 °C. Meade and Chen [21] reported that
The saturation line (equilibrium) was obtained from (1) as the width for each zone for a cane sugar solution is constant
a function of density: and linear along the same cooling temperature range.
However, our results showed that this is not the case,
sat  1.33  8.89  10 5 T  6.91 10 6 T 2 becoming a contribution for understanding of the saturation
(2) line, metastable zone and labile zone.

where sat is the saturation density in g/cm3 for each specific A non-linear second order regression was applied to the
equilibrium temperature. The density interval for a experimental data presented in the Fig. 5. The modeling
temperature range from 70 to 40 °C is from 1.3594073 to equations describe the intermediate limit of the metastable
1.3392435 g/cm3, respectively. zone and the limit of starting of the labile or unstable zone.
B. CSD and Micrographs Analysis Specifically, the intermediate line with R2= 0.998 is given by:
Fig. 3 shows the experimental data of the CSD in % int ermediate  1.32  5.39  10 4 T  8.32  10 8 T 2
volume with a log-normal distribution for each saturated (3)
solution (40, 50, 60 and 70 °C), being this the most where intermediate is the density in the intermediate limit of the
representative with regard to the average of three metastable zone in g/cm3. The density interval of the model
experimental runs for every saturation temperature. The by a temperature range from 70 to 40 °C is from 1.36148 to
analysis of this figure is based on the quantification and 1.34502 g/cm3, respectively. The labile line can be describing
observation of patterns on the crystal population for both according to the fitted equation with R2= 0.998:
cooling temperature and density range. In accordance with

ISBN: 978-988-17012-9-9 WCE 2010

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2010 Vol I
WCE 2010, June 30 - July 2, 2010, London, U.K.

100 100

90 90

80 80

70 70

% Volume
60
% Volume

60
50 50
40 40
30 30
20 20
10 10
40 50
0 38 0
36 48
50 50
100 34 ) 100 46 )
150
32 (蚓 150 44 ( 蚓
Siz 30 re Siz re
e(
m
200 28 atu e(
m
200
42 ratu
250 26 er ) 250 e
)
mp mp
300 24 Te 300 40 Te
a b

100 100
90 90
80 80
70 70
% Volume

60 60
% Volume

50 50
40 40
30 30
20 20
10 10
60 70
0 0
50 58 68
100 100 66
56 ) 64
150 蚓 200 )
e(
200 54 62 (蚓
300
Siz 250 ur 60 re
e(
m 300 52 rat Siz
e (蚓 400 58 tu
e ra
) 350 mp ) 500 56
mp
e
400 50 Te 600 54 Te
c d
Fig. 3 CSD of saturated solutions at: a) 40 °C, b) 50 °C, c) 60 °C and d) 70 °C.

Fig. 4. Micrographic sequence of growth crystals in saturated solution to 40°C. a) first metastable zone (40-37 °C), b) second
metastable zone (36-33 °C) and c) labile zone (32 °C or smaller).

ISBN: 978-988-17012-9-9 WCE 2010

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2010 Vol I
WCE 2010, June 30 - July 2, 2010, London, U.K.

Table 2. Critical points identification to location of MSZW.

Saturated solution Saturated solution Saturated solution Saturated solution
70°C 60°C 50°C 40°C
Zones
Temp. Dens. Temp. Dens. Temp. Dens. Temp. Dens.
(°C) (g/cm3) (°C) (g/cm3) (°C) (g/cm3) (°C) (g/cm3)
70 1.3576 60 1.3542 50 1.3478 40 1.3409
First zone
67 1.3540 59 1.3537 48 1.3488 37 1.3407
66 1.3556 58 1.3551 47 1.3485 36 1.3429
Second zone
65 1.3552 56 1.3535 45 1.3511 33 1.3439
Unstable zone 64 1.3574 55 1.3560 44 1.3520 32 1.3453

[3] Sutradhar, B. C. (2004). Coping with Crystallization Problems.

1.3650
Critical points to 40蚓
Chemical Engineering. 46-52.
1.3625 Critical points to 50蚓
Unstable zone
[4] Ulrich J. (2003). Solution Crystallization-Developments and New
Critical points to 60蚓
1.3600 Critical points to 70蚓 Trends, Chem. Eng. Technol. 7. 921–927.
1.3575
Equilibrium line [5] Srinivasakannan C., Vasanthakumar R., Iyappan K. and Rao, P. G. A.
Intermediate line
(2002). Study on crystallization of oxalic acid in batch cooling
Density (g/cm )

Unstable line
3

1.3550
zo
ne crystallizer. Chem. Biochem Eng. Q 16 (3). 125-129.
1.3525 ble
sta
[6] Mersmann, A. Crystallization Technology Handbook; Marcel Dekker:
1.3500 eta New York. 1995.
nd M ne
2 zo
1.3475 ble [7] Velazquez-Camilo, O., Alvarez-Ramirez, J. J. and Bolaños-Reynoso,
sta
eta E. (2009). Comparative Analysis of the Crystallizer Dynamics Type
1.3450 st M
1.3425
1 Unsaturated zone Continuous Stirred Tank: Isothermic and Cooling Case. Rev. Mex. Ing.
Quim. (RMIQ). 8 (1). 127-133.
1.3400
[8] Salcedo-Estrada L. I., Quintana-Hernandez, P. A. and
1.3375 Bolaños-Reynoso E. (2002). Mathematical Modeling in Batch
30 35 40 45 50 55 60 65 70
Crystallization. Chem. Eng. Assoc. Chem. Eng. Uruguay 3(21). 3-11.
Temperature (蚓 )
[9] Christofides P. D., Shi D., El-Farra N. H., Li M. and Mhaskar P. (2006).
Fig. 5 Metastable and labile zone limits (MSZW) at the Predictive control of particle size distribution in particulate processes.
Chemical Engineering Science. 61. 266-280.
density – temperature diagram.
[10] Rawlings J. B. and Miller S.M. (1994). Model identification and
control strategies for batch cooling crystallizers. AIChe Journal. 40 (8).
labile  1.32  8.32 104 T  3.7 106 T 2 (4) 1312-1327.
[11] Bolaños-Reynoso Eusebio, Xaca-Xaca Omar, Alvarez-Ramirez Jose,
and Lopez-Zamora Leticia. (2008). Effect Analysis from Dynamic
Where labile is the density of starting limit of the labile zone Regulation of Vacuum Pressure in an Adiabatic Batch Crystallizer
Using Data and Image Acquisition. Ind. Eng. Chem. Res. 47 (23),
in g/cm3. The density interval of the model by a temperature 9426-9436.
range from 70 to 40 °C is from 1.36269 to 1.34992 g/cm3, [12] Fujiwara Mitsuko, Nagy Zoltan K., Chew Jie W. and Braatz Richard D.
respectively. Eqs. (3) and (4) shows clearly that the (2005). First-principles and direct design approaches for the control of
pharmaceutical crystallization. Journal of Process Control. 15.
concentration limits are non-linear functions of temperature. 493-504.
[13] Zhou George X., Fujiwara Mitsuko, Woo Xing Yi, Rusli Effendi, Tung
IV. CONCLUSION Hsien-Hsin, Starbuck Cindy, Davidson Omar, Ge Zhihong, and Braatz
Richard D. (2006). Direct Design of Pharmaceutical Antisolvent
The identification of the critical points of MSZW for Crystallization through Concentration Control. Crystal Growth &
commercial sugar cane was made in this work. A novel Design. 6 (4). 892-898.
experimental method, based on cooling down sugar cane [14] Hanks, J. Counting Particles of Cells using IMAQ Vision; Software is
the Instruments, Application Note 107; National Instruments, Inc:
solutions and micrographs evaluation was used, yielding a Austin, TX, 1997.
close description of the concentration limits for the saturation [15] Wang, X. Z.; Calderon-De-Anda, J.; Roberts, K. J. (2007). Real-Time
line, the first and second metastable zone, and labile zone in Measurement of the Growth Rates of Individual Crystal Facets using
Imaging and Image Analysis. A Feasibility Study on Needle-Shaped
density terms. In contrast to commercial practice, we found Crystals of L-Glutamic Acid. Trans. IChemE, Part A, 85, 921–927.
that the width of the zones increases in a non-linear form as [16] Calderon-De-Anda, J.; Wang, X. Z.; Roberts, K. J. (2005). Multi-scale
the cooling saturation temperature decreases from 70 to 40 Segmentation Image Analysis for the In-Process Monitoring of
Particles Shape with Batch Crystallizers. Chem. Eng. Sci. 60,
°C. The MSZW obtained experimentally should be useful for 1053–1065.
the design and operation of industrial crystallization [17] Cordova-Pestaña, N. M.; Bolaños-Reynoso, E.; Quintana-Hernandez,
equipment oriented to obtain specific products. P. A.; Briseño-Montiel, V. M. Developing of CSD Analysis Software
from Electronic Microscopy Measurement; XXV AMIDIQ’s
Memories: Mexico. 2004.
ACKNOWLEDGMENT [18] Rawle, A. Basic Principles of Particle Size Analysis; Technical Paper
We thank Amira Antonio Acatzihua (CONACYT’s MS Ref. WR141AT; Malvern Instruments: U.K., 1999.
[19] Quintana-Hernandez, P. A.; Moncada-Abaunza, D. A.;
scholarship) for her collaborations in this paper. Bolaños-Reynoso, E.; Salcedo-Estrada, L. I. (2005). Evaluation of
Sugar Crystal Growth and Determination of Surface Area Shape
REFERENCES Factor. Rev. Mex. Ing. Quim. 4, 123–129.
[20] MasterSizer S Long Beb’s User Manual; Malvern Instruments. Ltd.:
[1] Perry R. H. and D. Green W. Perry´s Chemical Engineers Handbook, Westborough, MA, 1997.
7a edition, McGraw-Hill. 2001. [21] Meade, G. P. and Chen, J. C. Cane Sugar Handbook: A Manual for
[2] Quintana-Hernandez, P., Bolaños-Reynoso, E., Miranda-Castro, B. and Cane Sugar Manufacturers and their Chemists. Wiley Publisher. 1977.
Salcedo-Estrada, L. (2004). Mathematical Modeling and Kinetic
Parameter Estimation in Batch Crystallization. AIChE Journal. 50 (7).
1407-1417.

ISBN: 978-988-17012-9-9 WCE 2010

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)