2003 Ullmann Crystallization and Precipitation (2003)

Article No : b02_03
published online 15 JAN 2003
Crystallization and Precipitation

JOHN W. MULLIN, University College London, Torrington Place, London,
United Kingdom WC1E 7JE
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . 582 5.7. Comparison of Batch and Continuous

2. System Properties . . . . . . . . . . . . . . . . . . . 583 Crystallization . . . . . . . . . . . . . . . . . . . . . . 607
2.1. Solutions and Solubility . . . . . . . . . . . . . . . 583 5.8. Crystallizer Modeling and Design . . . . . . . 608
2.2. Saturation and Supersaturation. . . . . . . . . 583 5.8.1. Population Balance . . . . . . . . . . . . . . . . . . . 608
2.3. Crystal Size and Solubility. . . . . . . . . . . . . 585 5.8.2. Design and Scaleup Problems . . . . . . . . . . . 609
2.4. Effect of Impurities . . . . . . . . . . . . . . . . . . 585 6. Crystallization from Melts . . . . . . . . . . . . . 610
3. Phase Equilibria . . . . . . . . . . . . . . . . . . . . 585 6.1. Single Stage Processes . . . . . . . . . . . . . . . . 610
3.1. One-Component Systems . . . . . . . . . . . . . . 585 6.2. Multistage Processes . . . . . . . . . . . . . . . . . 612
3.2. Two-Component Systems. . . . . . . . . . . . . . 586 6.3. Column Crystallizers . . . . . . . . . . . . . . . . . 612
3.2.1. Eutectics . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 6.4. High-Pressure Crystallization . . . . . . . . . . 614
3.2.2. Solid Solutions . . . . . . . . . . . . . . . . . . . . . . 587 6.5. Prilling and Granulation . . . . . . . . . . . . . . 615
3.2.3. Compound Formation . . . . . . . . . . . . . . . . . 587 7. Crystallization from Vapors . . . . . . . . . . . 615
3.3. Three-Component Systems . . . . . . . . . . . . 588 8. Precipitation . . . . . . . . . . . . . . . . . . . . . . . 615
3.4. Multicomponent Systems . . . . . . . . . . . . . . 590 8.1. Solubility Products. . . . . . . . . . . . . . . . . . . 615
3.5. Phase Transformations . . . . . . . . . . . . . . . 590 8.2. Ostwald’s Rule of Stages . . . . . . . . . . . . . . 616
4. Kinetics and Mechanisms of Crystallization 592 8.3. Development of Precipitates . . . . . . . . . . . 616
4.1. Crystal Nucleation . . . . . . . . . . . . . . . . . . . 592 8.3.1. Ripening . . . . . . . . . . . . . . . . . . . . . . . . . . . 616
4.1.1. Primary Nucleation . . . . . . . . . . . . . . . . . . . 592 8.3.2. Agglomeration . . . . . . . . . . . . . . . . . . . . . . 617
4.1.2. Secondary Nucleation . . . . . . . . . . . . . . . . . 594 8.3.3. Precipitate Morphology . . . . . . . . . . . . . . . . 617
4.1.3. Nucleation Measurements . . . . . . . . . . . . . . 594 8.3.4. Coprecipitation . . . . . . . . . . . . . . . . . . . . . . 618
4.1.4. Induction Periods. . . . . . . . . . . . . . . . . . . . . 595 8.4. Precipitation Techniques . . . . . . . . . . . . . . 619
4.2. Crystal Growth . . . . . . . . . . . . . . . . . . . . . 595 8.4.1. Reaction Precipitation . . . . . . . . . . . . . . . . . 619
4.2.1. Measurement of Growth Rate. . . . . . . . . . . . 597 8.4.2. Salting Out . . . . . . . . . . . . . . . . . . . . . . . . . 620
4.2.2. Expression of Growth Rate . . . . . . . . . . . . . 598 8.5. Precipitation Methods and Equipment . . . 621
4.2.3. Dependence of Growth Rate on 9. Fractional Crystallization . . . . . . . . . . . . . 622
Crystal Size. . . . . . . . . . . . . . . . . . . . . . . . . 598 9.1. Recrystallization from Solutions . . . . . . . . 622
4.3. Growth – Nucleation Interactions . . . . . . . 599 9.2. Recrystallization from Melts . . . . . . . . . . . 622
4.4. Crystal Habit Modification . . . . . . . . . . . . 599 9.3. Recrystallization Schemes . . . . . . . . . . . . . 623
4.5. Inclusions in Crystals. . . . . . . . . . . . . . . . . 601 9.4. Recrystallization from Supercritical Fluids 624
4.6. Caking of Crystals . . . . . . . . . . . . . . . . . . . 601 9.5. Separation of Enantiomers and Racemates 625
5. Crystallization from Solutions . . . . . . . . . . 602 10. Miscellaneous Crystallization Techniques . 625
5.1. Cooling Crystallizers . . . . . . . . . . . . . . . . . 602 10.1. Salting-Out Crystallization . . . . . . . . . . . . 625
5.1.1. Nonagitated Vessels. . . . . . . . . . . . . . . . . . . 602 10.2. Reaction Crystallization. . . . . . . . . . . . . . . 625
5.1.2. Agitated Vessels . . . . . . . . . . . . . . . . . . . . . 602 10.3. Adductive and Extractive Crystallization . 625
5.1.3. Direct-Contact Cooling . . . . . . . . . . . . . . . . 603 10.4. Spray Crystallization . . . . . . . . . . . . . . . . . 626
5.2. Evaporating Crystallizers . . . . . . . . . . . . . 603 10.5. Spherical Crystallization . . . . . . . . . . . . . . 626
5.3. Vacuum (Adiabatic Cooling) Crystallizers. 603 10.6. Freeze Crystallization . . . . . . . . . . . . . . . . 626
5.4. Continuous Crystallizers . . . . . . . . . . . . . . 604 References . . . . . . . . . . . . . . . . . . . . . . . . . 628
5.5. Crystal Yield . . . . . . . . . . . . . . . . . . . . . . . 605
5.6. Controlled Crystallization . . . . . . . . . . . . . 606
2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

DOI: 10.1002/14356007.b02_03
582 Crystallization and Precipitation Vol. 10
Symbols N: impeller rotational speed, Hz

q: heat of crystallization, J/kg
a: activity
r c: size of critical nucleus, m
a*: activity of a saturated solution
R: ratio of molecular masses, mass depo-
a : mean ionic activity
sition rate
A: particle surface area, preexponential
S: supersaturation ratio (¼ c/c*)
factor, m2
S0 : activity supersaturation
b: kinetic order of secondary nucleation
v: molar volume, m3/mol
B: secondary nucleation rate, m3 s1
v: mean linear growth velocity, m/s
c: solution concentration
V: water lost by evaporation, kg/kg
c*: equilibrium saturation concentration
W: initial mass of water, kg
C: specific heat capacity
x: mole fraction
D: diffusivity, m2/s
Y: crystal yield, kg
D: homogeneous distribution coefficient
z: valence
g: kinetic order of growth
a: surface roughness factor, volume shape
G: crystal growth rate, m/s
factor
i: relative kinetic order (¼ b/g)
b: surface shape factor
J: nucleation rate, m3 s1
g: interfacial tension, J/m2
k: Boltzmann constant
g : mean ionic activity coefficient
K: rate constant, solubility product
l: latent heat, heterogeneous distribution
L: crystal size, m
coefficient
M: relative molecular mass
n: number of moles of ions
M T: total magma density, kg/m3
s: relative supersaturation, ¼ (S 1)
n: kinetic order of primary nucleation
t: induction period, residence time, batch
n 0: population density of nuclei (¼ B/G),
time, s
m4
1. Introduction zation is increasingly employed in the production

of materials for the electronics industry; applica-
Few branches of the chemical and process indus- tions of precipitation have been extended to
tries do not, at some stage, employ crystallization biotechnology, e.g., for processing proteins.
or precipitation for production or separation pur- The unit operation of crystallization is gov-
poses. Vast quantities of crystalline substances erned by very complex, interacting variables. It is
are manufactured commercially: sodium chlo- a simultaneous heat- and mass-transfer process
ride and sucrose, for example, have worldwide with a strong dependence on fluid and particle
production rates exceeding 108 t/a, while annual mechanics. Crystallization occurs in a multi-
rates for fertilizer chemicals such as ammonium phase, multicomponent system and involves par-
nitrate, potassium chloride, ammonium phos- ticulate solids whose size and size distribution
phates, and urea exceed 106 t. Although crystal- are incapable of definition and vary with time.
line products of the pharmaceutical, organic fine The solids are suspended in a solution which can
chemical, and dye industries are produced in fluctuate between a so-called metastable equilib-
relatively low tonnages, they still represent a rium and a labile state that is unstable and prone
valuable and important industrial sector. Crys- to change; the solution composition can also vary
tallization is also a key operation in, for example, with time. Nucleation and growth kinetics, the
the desalination of seawater, the concentration of key processes in this operation, are often influ-
fruit juices, and the removal of unwanted materi- enced profoundly by traces of impurities: a few
als or recovery of valuable constituents in many parts per million may alter the product beyond
industrial processes (e.g., sodium sulfate remov- recognition.
al from viscose spin-bath liquors, recovery of Five main types of information are generally
metal salts from electroplating baths). Crystalli- required to design a crystallization process:
Vol. 10 Crystallization and Precipitation 583
1. Solubility and phase relationships substances from solution. It is also used when-
2. Metastability limits ever possible for the crystallization of organic
3. Nucleation characteristics compounds, but in this particular field for a
4. Crystal growth characteristics variety of reasons some other solvent must often
5. Hydrodynamics of crystal suspensions be employed. A guide to the selection of the
‘‘best’’ solvent for a given crystallization opera-
Solubility and phase relationships influence the tion is given in [7] and an algorithm for the
choice of crystallizer and method of operation. prediction of an optimal solvent or solvent mix-
These data must be obtained by using the materials ture for cooling crystallizers is proposed in [9].
to be encountered in the plant because traces of Compilations of solid – liquid solubility data are
impurity often have a considerable effect on phase available in [5], [7], [10–12].
relationships. Metastable limits define acceptable
operating conditions for the minimization of un-
controlled nucleation and encrustation of heat- 2.2. Saturation and Supersaturation
exchange surfaces. The processes of nucleation
and growth are both exceedingly complex; they are A saturated solution is a solution that is in
influenced greatly by temperature, supersaturation, thermodynamic equilibrium with the solid phase
and impurities. A knowledge of these system of its solute at a specified temperature. However,
characteristics is essential in design. Crystal sus- solutions frequently contain more dissolved sol-
pension velocities must also be known so that ute than that given by the equilibrium saturation
liquor circulation rates in fluidized-bed crystal- value and are then said to be supersaturated. The
lizers and agitation rates in stirred vessels can be degree of supersaturation can be expressed by the
specified. Because the crystals are present in large concentration difference Dc:
quantities, settling is hindered; further complica-
Dc ¼ cc ð1Þ
tions can arise if their shapes are irregular.
Many different methods are available for crys- where c is the actual solution concentration and
tallization. Crystals can be grown from the liquid c* the equilibrium saturation value. Other com-
(solution or melt) or vapor phase (desublimation, mon expressions are the supersaturation ratio S
see ! Sublimation), but in all cases the state of and the relative supersaturation s which are both
supersaturation must first be achieved. The meth- dimensionless:
od used to obtain supersaturation depends on the
S ¼ c=c ð2Þ
characteristics of the crystallizing system: some
solutes are readily deposited from solution when
cooled, whereas others may crystallize only after s ¼ Dc=c ¼ S1 ð3Þ
some solvent has been removed. The addition
of another substance to the system to alter Solution concentration may be expressed in a
the equilibrium conditions is used frequently in variety of units, but for general mass balance
precipitation processes. Supersaturation is some- calculations, units such as kilograms of anhy-
times achieved as a result of a chemical reaction drate per kilogram of solvent or kilograms of
between two or more substances and one of the hydrate per kilogram of free solvent are most
reaction products is precipitated. convenient. The former avoids complications if
Comprehensive accounts of industrial crystal- different phases (e.g., anhydrates and hydrates)
lization theory and practice have been presented can crystallize over the temperature range con-
in several books [1–8]. sidered. The latter simplifies yield calculations
when a single hydrate phase crystallizes.
Although the terms S and s are dimensionless,
2. System Properties their magnitudes depend on the units used to
express solution concentration. For example, a
2.1. Solutions and Solubility supersaturated solution of sucrose at 20 C con-
tains 2.45 kg of sucrose per kilogram of water,
Water is almost exclusively used as the solvent and the corresponding value for c* is 2.04;
for the industrial crystallization of inorganic therefore, the value of S (¼ c/c*) is 1.20.
However, if the composition is expressed as In practice, however, supersaturation is generally

kilograms of sucrose per kilogram of solution expressed directly in terms of solution concen-
(c ¼ 0.710, c* ¼ 0.671), the value of S becomes tration (Eqs. 1 – 3). The relationship between
1.06 [7]. concentration-based supersaturation and funda-
None of the above expressions represents mental (activity-based) supersaturation can be
exactly the true thermodynamic supersaturation. expressed by means of the relevant concentra-
The fundamental driving force for crystallization tion-dependent activity coefficient ratios; for
is the difference between the chemical potential details see [13].
of a given substance in the transferring and the
transferred state, i.e., in solution (state 1) and in Metastability. The state of supersaturation
the crystal (state 2). For an unsolvated solute is an essential feature of all crystallization opera-
crystallizing from a binary solution, this may be tions. OSTWALD [14] introduced the terms labile
written as and metastable supersaturation to describe su-
persaturated solutions in which spontaneous (pri-
Dm ¼ m1 m2 ð4Þ
mary) nucleation (see Section 4.1) would or
The chemical potential m is defined in terms of would not occur, respectively. MIERS and ISAAC
the standard potential m0 and the activity a by [15] proposed a representation of the metastable
zone by means of a solubility – supersolubility
m ¼ m0 þRTlna ð5Þ
diagram (Fig. 1). The lower, continuous, equi-
The fundamental dimensionless driving force for librium solubility curve can be determined accu-
crystallization may, therefore, be expressed as rately, but the position of the upper, broken,
0
supersolubility curve is less certain because it is
Dm=RT ¼ lnða=a Þ ¼ lnS ð6Þ influenced considerably by factors such as the
where a* is the activity of a saturated solution, S0 rate at which supersaturation is generated, the
the activity supersaturation, R the gas constant, intensity of agitation, and the presence of crystals
and T the absolute temperature; i.e., or impurities. The width of the metastable zone is
usually expressed as a temperature difference Dq,
0
S ¼ expðDm=RTÞ ð7Þ which is related to the corresponding concen-
tration difference Dc by the local slope of the
For electrolyte solutions, use of the mean ionic solubility curve, dc*/dq:
activity a is more appropriate; this is defined by
Dc ¼ ðdc =dqÞDq ð14Þ
a ¼ an ð8Þ
The measurement of metastable zone width is
where n is the number of moles of positive and discussed in Section 4.1.3.
negative ions in one mole of solute (n ¼ nþ þ
n). Therefore
Dm=RT ¼ nlnSa ð9Þ
where
Sa ¼ a =a ð10Þ
Alternatively, supersaturation can be expressed

as
sa ¼ Sa 1 ð11Þ
and Equation (9) becomes

Dm=RT ¼ nlnð1þsa Þ ð12Þ
For low supersaturations (sa < 0.1), the follow-

ing approximation is valid:
Dm=RT ’ nsa ð13Þ Figure 1. Solubility – supersolubility diagram
Supersaturation Measurement. The su- n represents the number of moles of ions formed
persaturation of a solution can be calculated from one mole of electrolyte. For a nonelectro-
simply from Equations (1) – (3) if the actual lyte, n ¼ 1.
solution concentration and the corresponding For most inorganic salts in water, the solubili-
equilibrium saturation concentration at a given ty increase becomes significant only for particle
temperature are known. sizes smaller than ca. 1 mm. For example, for
Many ways exist for measuring supersatura- barium sulfate at 25 C: T ¼ 298 K, M ¼
tion (i.e., concentration), but all of these are not 0.233 kg/mol, n ¼ 2, r ¼ 4500 kg/m3, g ¼
readily applicable to industrial crystallization. If 0.13 J/m2, R ¼ 8.3 J mol1 K1. Thus for a 1-
chemical analysis is difficult, measurement of a mm crystal (r ¼ 5107 m), c/c* ¼ 1.005 (i.e.,
concentration-dependent property of the system 0.5 % increase); for 0.1 mm, c/c* ¼ 1.06 (i.e.,
(e.g., density or refractive index) may be possi- 6 % increase); and for 0.01 mm, c/c* ¼ 1.72
ble. Both of these properties can usually be (i.e., 72 % increase). All such calculated values
measured with high precision on a sample trans- should be treated with caution, however, not only
ferred under controlled laboratory conditions. because of the potential unreliability of g values,
On the other hand, an in situ, preferably con- but also because the Gibbs – Thomson effect
tinuous method of concentration measurement is may cease to be influential at extremely small
usually required for a crystallizer operating under crystal sizes [7].
laboratory or pilot-plant conditions. Although
the above properties are temperature-dependent,
they can often be measured with sufficient accu- 2.4. Effect of Impurities
racy for supersaturation determination. In indus-
trial crystallization, temperature and feedstock Industrial solutions invariably contain dissolved
concentration can fluctuate and thus make the impurities which can increase or decrease the
assessment of supersaturation difficult. Under solubility of the prime solute considerably [7].
these conditions, a crude method based on a mass Therefore, the solubility data used to design
balance coupled with feedstock and exit-liquor crystallization processes must relate to the
concentrations and crystal production rates aver- actual system used. Impurities can also have
aged over several hours may be adequate. profound effects on other crystallization char-
acteristics such as nucleation and growth (cf.
Chap. 4).
2.3. Crystal Size and Solubility
If the solute particles dispersed in a solution are 3. Phase Equilibria

small enough, the solute concentration may
greatly exceed the normal equilibrium saturation 3.1. One-Component Systems
value. The relationship between particle size
and solubility, first derived for liquid – vapor Temperature and pressure are the two variables
systems by THOMSON (1870), utilized by GIBBS that can affect the phase equilibria in a one-
(1890), and applied to solid – liquid systems by component system. The phase diagram in Fig-
OSTWALD (1900) and FREUNDLICH (1909), may be ure 2 depicts equilibria between the solid, liquid,
expressed in the form and vapor states of water: ice, water, and steam,
respectively. At the triple point B (0.6 kPa,
c ðrÞ 2Mg
ln
¼ ð15Þ 0.01 C), all three phases are in equilibrium.
c n RTrr
The sublimation curve AB records the vapor
where c(r) is the solubility of particles with radius pressure of ice, the vaporization curve BC re-
r, c* the normal equilibrium solubility of the cords the vapor pressure of liquid water, and the
substance, R the gas constant, T the absolute fusion curve BD records the effect of pressure on
temperature, r the density of the solid, M the the melting point of ice. The fusion curve for ice
relative molecular mass of the solute in solution, is very unusual because an increase of pressure
and g the interfacial tension of the crystallization increases the melting point of most other one-
surface in contact with its solution. The quantity component systems.
point. Polymorphic transformations are further

discussed in Section 3.5.
3.2. Two-Component Systems
Three variables (temperature, pressure, and con-

centration) can affect the phase equilibria in a
two-component (binary) system. The effect of
pressure, which is usually negligible, is generally
ignored so that the relevant data can be shown on
a two-dimensional temperature – concentration
plot.
Figure 2. Phase diagram for water Three important basic types of binary sys-
tem – eutectics, solid solutions, and systems with
Polymorphs. A single substance can crys- compound formation – are discussed. They are
tallize in more than one of seven crystal systems, also referred to in the discussion of melt crystal-
32 classes, or 230 point groups. Because these lization (Chap. 6). Although the terminology
crystalline forms differ in their lattice arrange- used is specific to melt systems, the types of
ment, they can exhibit not only different basic behavior described may also be exhibited by
shapes but also different physical properties. A aqueous solutions of salts, for example. In fact,
substance capable of crystallizing in more than no fundamental difference exists between a melt
one different crystalline form is said to exhibit and a solution [7].
polymorphism. Carbon, for example, has three
polymorphs: graphite (hexagonal) and diamond
(regular), and fullerenes. Calcium carbonate has 3.2.1. Eutectics
three: calcite (rhombohedral), aragonite (ortho-
rhombic), and vaterite (trigonal). An example of a binary eutectic system AB is
Each polymorph is composed of a common shown schematically in Figure 3. A eutectic
component but constitutes a separate phase. (Greek: eu tektos ¼ easily melted) is the mixture
Since only one polymorph is thermodynamically of components that has the lowest crystallization
stable at a specified temperature and pressure, all temperature in the system. The concentration of
the other polymorphs are potentially capable of
being transformed into the stable polymorph.
Some polymorphic transformations are rapid and
reversible, others are not.
Polymorphs may be enantiotropic (intercon-
vertible) or monotropic (incapable of transfor-
mation). Graphite and carbon, for example, are
monotropic at ambient temperature and pressure,
whereas ammonium nitrate has five enantiotro-
pic polymorphs over the temperature range 18
to 125 C:
At a given temperature, the more stable phase

will always have the lower solubility in any given
solvent. Similarly, at a given pressure, the more Figure 3. Phase diagram for a binary eutectic system AB
stable phase will always have the higher melting For explanation of symbols, see text.
component B in system AB is plotted as the

abscissa and temperature as the ordinate. Point
A is the crystallization temperature (freezing
point) of pure component A, and point B that
of component B. Curves AE and EB represent the
crystallization temperatures of all mixtures of the
two components A and B. Above the two curves,
all mixtures of A and B exist only in the liquid
state, i.e., as a melt. If a melt represented by point
X is cooled along the vertical line XZ, crystals
will start to be deposited at point Y (with proper
initiation); theoretically, these crystals should be
pure component B. On further cooling, more
crystals of pure component B will be deposited
until, at the eutectic point E, the system solidifies
completely. The horizontal line passing through
point E is called the solidus. The liquid-phase
composition during cooling changes continu- Figure 4. Phase diagram for a binary system AB composed
ously along curve BE, which is called the liqui- of a continuous series of solid solutions
dus. For example, if mixture X is cooled to point For explanation of symbols, see text.
Z, the crystals C will be pure component B and
the liquid L will be a mixture of A and B. The temperatures (freezing points) of pure compo-
mass proportion of solid phase (crystal) to liquid nents A and B, respectively. The upper curve (the
phase (residual melt) at temperature Z is quanti- liquidus) represents the temperature at which
fied by the ratio of the lengths LZ to CZ. This mixtures of A and B begin to crystallize on
relationship is known by various names such as cooling. The lower curve (the solidus) represents
the mixture rule or the lever rule. Similar reason- temperatures at which mixtures begin to melt on
ing can be applied to mixtures located in the heating. A melt of composition X begins to
region of curve AE, in which case the crystals crystallize on reaching temperature Y. At tem-
would be pure component A. perature Z, the system consists of a mixture of
The eutectic point E is common to both crystals with composition C and a liquid with
curves. A liquid of this composition cooled to composition L. The ratio of crystals to liquid is
the eutectic temperature crystallizes with un- again given by the mixture rule (see Section
changed composition, and continues to deposit 3.2.1). However, the crystals do not consist of
such crystals until the whole system solidifies. a single pure component (as in a simple eutectic
Although a eutectic in a given system has a fixed system) but are an intimate mixture (a solid
composition, it is not a chemical compound but solution) of components A and B. To purify the
simply a physical mixture of the individual crystals further, they must first be melted; the
components. The component crystals are often resulting melt must then be cooled and recrys-
clearly visible under a low-power microscope. tallized. This sequence may have to be repeated
many times to achieve the desired purity.
In brief, a simple eutectic system may be
3.2.2. Solid Solutions purified in a single-stage crystallization opera-
tion, whereas a solid-solution system always
The second common type of binary system is the needs a multistage operation.
continuous series of solid solutions. The term
solid solution or mixed crystal refers to an inti-
mate mixture, on the molecular scale, of two or 3.2.3. Compound Formation
more components. The components of a solid-
solution system cannot be separated as easily as The solute and solvent of a binary system can
those of a eutectic system, as shown in Figure 4. combine to form one or more different com-
Points A and B represent the crystallization pounds, for example, hydrates in aqueous
melting and crystallization occur without any

change of composition. In Figure 6, however,
compound D decomposes at a temperature T1
below its theoretical melting point T2. Thus, if
compound D is heated, melting begins at tem-
perature T1, but it is not complete. At temperature
T1, the system of overall composition D contains
crystals of pure component B in a melt of com-
position C. If this mixture is then cooled, a solid
mixture of B and C is obtained. Subsequent
heating and cooling cycles result in further
decomposition of compound D.
Inorganic salt hydrates are of interestas heat-
storage materials, particularly for storage of solar
heat in domestic and industrial space heating.
(! Heat Storage Media) Ideally, the hydrate
should have a congruent melting point so that
Figure 5. Phase diagram of a binary system AB that forms a sequences of crystallization – melting – crys-
compound D with a congruent melting point
Symbols indicate the phases coexisting in equilibrium: L ¼
tallization can be repeated indefinitely. Incon-
liquid; E, E0 ¼ eutectics. gruently melting hydrate systems tend to stratify
on repeated temperature cycling, with a conse-
solutions. If the compound can coexist in stable quent loss of efficiency. This occurs because
equilibrium with a liquid phase of the same melting yields a liquid phase that contains crys-
composition, it is said to have a congruent melt- tals of a lower hydrate or the anhydrous salt,
ing point; i.e., melting occurs without change in which settle to the bottom of the container and
composition (Fig. 5). If it cannot, the melting fail to redissolve on subsequent heating.
point is said to be incongruent (Fig. 6). Calcium chloride hexahydrate, although not a
In Figure 5, the heating – cooling cycle fol- true congruently melting hydrate, appears to be
lows the vertical line through point D; i.e., one of the most promising materials [16], [17].
Sodium sulfate decahydrate, sodium acetate tri-
hydrate, and sodium thiosulfate pentahydrate,
which have incongruent melting points, are also
worthy of mention [18], [19].
3.3. Three-Component Systems
The phase equilibria in three-component (tern-

ary) systems can be affected by four variables:
temperature, pressure, and the compositions of
any two of the three components. The effect of
pressure (usually negligible in normal ranges) is
generally ignored, and the phase equilibria are
plotted on an isothermal triangular diagram.
Equilibrium relationships in three-component
systems can be represented on a temperature –
concentration space model as shown in Fig-
ure 7 A. The ternary system 2-, 3-, and 4-nitro-
Figure 6. Phase diagram of a binary system AB that forms a phenol (o -, m-, and p-nitrophenol), in which
compound D with an incongruent melting point
Symbols indicate the phases coexisting in equilibrium: L ¼
compound formation does not occur, has been
liquid; E ¼ eutectic; T1 ¼ decomposition temperature of D; chosen for illustrative purposes. The three
T2 ¼ theoretical melting point of D. components are referred to as O, M, and P,
M binary eutectic A. Similarly, curves BD and

CD denote the lowering of freezing points of the
binary eutectics B and C, respectively, upon
addition of the third component. Point D, indi-
cating the lowest temperature at which solid and
liquid phases can coexist in equilibrium in this
system, is a ternary eutectic point (21.5 C;
57.7 % O, 23.2 % M, 19.1 % P). At this tempera-
ture and concentration, the liquid freezes to form
a solid mixture of the three components. The
section of the space model above the freezing
point surfaces formed by the liquidus curves
represents the homogeneous liquid phase. The
section below these surfaces down to a tempera-
ture represented by point D denotes solid and
liquid phases in equilibrium. The section of the
model below this temperature represents a
completely solidified system.
Figure 7 B is the projection of the curves AD,
BD, and CD in Figure 7 A onto the triangular
base of the prism. The apexes of the triangle
represent pure components O, M, and P, and their
melting points are indicated in parentheses.
Points A, B, and C on the sides of the triangle
indicate the three binary eutectic points; point D
is the ternary eutectic point. The projection dia-
gram is divided by curves AD, BD, and CD into
three regions which denote the three liquidus
surfaces in the space model. The temperature
falls from the apexes and sides of the triangle
toward the eutectic point D; several isotherms
showing points on the liquidus surfaces are also
drawn. The phase reactions occurring when a
Figure 7. Eutectic formation in the ternary system o-, m-, and given ternary mixture is cooled can be traced. A
p-nitrophenol A) Temperature – concentration space model; molten mixture with a composition X starts to
B) Projection on a triangular diagram solidify when the temperature is reduced to
Numerical values represent temperatures in C. 80 C. Point X lies in the region ADCM, so pure
m-nitrophenol is deposited when the temperature
is decreased. The composition of the remaining
respectively. Points O0 , M0 , and P0 on the vertical melt changes along line MX0 in the direction
edges of the model represent the melting points away from point M which represents the depos-
of the pure components o- (45 C), m- (97 C), ited solid phase (the mixture rule). At X0 , where
and p-nitrophenol (114 C). The vertical faces of line MX0 intersects curve CD, the temperature is
the prism represent temperature – concentration about 50 C and p-nitrophenol also starts to
diagrams for the three binary eutectic systems crystallize. On further cooling, both m- and p-
O – M, O – P, and M – P, which are all similar nitrophenol are deposited, and the composition
to that shown in Figure 3. of the liquid phase changes in the direction X0 D.
The binary eutectics are represented by points When the melt composition and temperature
A (31.5 C; 72.5 % O, 27.5 % M), B (33.5 C; reach point D, the third component (o-nitrophe-
75.5 % O, 24.5 % P), and C (61.5 C; 54.8 % M, nol) also crystallizes, and the system solidifies
45.2 % P). Curve AD within the prism represents without further change in composition. Similar
the effect of addition of component P to the O – reasoning can be applied to the cooling or
eutonic point or drying-up point of the system.

After complete evaporation of water, the com-
position of the solid residue is indicated by point
X5 on the base line. Similarly, if an unsaturated
solution, represented by a point located to the
right of B in the diagram, is evaporated isother-
mally, only NaNO3 is deposited until the solution
composition reaches point B. The salt KNO3 is
then also deposited, and the solution composition
remains constant until evaporation is complete.
If water is removed isothermally from a solution
of composition B, the composition of deposited
solid is given by point X6 on the base line, and it
remains unchanged throughout the evaporation
Figure 8. Phase diagram for the ternary system KNO3 –
NaNO3 – H2O at 50 C process.
melting of systems represented by points in other 3.4. Multicomponent Systems

regions of the diagram.
Many different types of phase behavior are The more components a system contains, the
encountered in ternary systems that consist of more complex are the phase equilibria and the
water and two solid solutes. One simple case is more difficult it is to represent phase reactions
considered here: the system KNO3 – NaNO3 – graphically. Specific descriptions of multicom-
H2O at 50 C (Fig. 8). The salts do not form ponent solid – liquid diagrams and their uses are
hydrates nor do they combine chemically. Point dealt with comprehensively in several books and
A represents the solubility of KNO3 in water at monographs [7], [20–23]. Techniques for pre-
50 C (46.2 g per 100 g of solution) and point C dicting multicomponent solid – liquid phase
the solubility of NaNO3 (53.2 g per 100 g of equilibria have also been described [22–26].
solution). Curve AB indicates the composition of
saturated ternary solutions in equilibrium with
solid KNO3 and curve BC those in equilibrium 3.5. Phase Transformations
with solid NaNO3. The upper area enclosed by
ABC represents the region of unsaturated homo- Metastable crystalline phases frequently crystal-
geneous solutions. Three other triangular areas lize prior to an expected, more stable phase, in
are constructed by drawing straight lines from accordance with Ostwald’s rule of stages (cf.
point B to the two remaining apexes of the Section 8.2). The more common types of phase
triangle; the compositions of the phases within transformation that occur in crystallizing and
these regions are marked on the diagram. At point precipitating systems include those between
B, the solution is saturated with both KNO3 and polymorphs (Section 3.1) and solvates. Trans-
NaNO3. formations can occur in the solid state, particu-
If water is evaporated isothermally from an larly at temperatures near the melting point of the
unsaturated solution represented by point X1, the crystalline solid, or due to the intervention of a
solution concentration increases along the line solvent.
X1X2. Pure KNO3 is deposited when the concen- A stable phase has a lower solubility than a
tration reaches point X2. If more water is evapo- metastable phase, as indicated by the solubility
rated to give a system of composition X3, the curves in Figures 9 A and 9 B for enantiotropic
solution composition is represented by point X0 3 (reversible) and monotropic (irreversible) sys-
on the saturation curve AB, and by point B when tems, respectively. Transformation cannot occur
composition X4 is reached; further removal of between the metastable (I) and stable (II) phases
water causes deposition of NaNO3. All solutions in the monotropic system in the temperature
in contact with solid will thereafter have a con- range shown, but it is possible above the transi-
stant composition B, which is referred to as the tion temperature in an enantiotropic system.
may also crystallize in the form of different

solvates, e.g., hydrates. These are not strictly
speaking polymorphs, since they are not chemi-
cally identical, but like polymorphs they are
capable of transforming from one form to anoth-
er and hence can conveniently be included in the
following general considerations.
As described in Section 3.1 (One-Component
Systems), all polymorphs of a given substance,
although chemically identical, exhibit different
physical properties that can considerably affect
the end-use of the material. For example, one
polymorph of a pharmaceutical compound may
have quite significant differences in solubility,
bioavailability and pharmacological action from
another. It is essential, therefore, when investi-
gating a new chemical substance with a view to
eventual industrial production, to investigate at
an early stage the possibility of the existence of
different polymorphs or solvates and how they
may be isolated. Without such an investigation,
new phases may make a sudden appearance years
after the development of the first form and this
can often be very inconvenient. However, the
existence of different polymorphs or solvates
need not always be considered as a problem.
Indeed, if discovered early enough, they may
Figure 9. Solubility curves for substances with two poly- have potential commercial advantages in al-
morphs I and II A) Enantiotropic polymorphs; B) Monotropic lowing increased patent coverage and greater
polymorphs
Broken lines in A indicate the metastable solubility curves of
flexibility in, for example, the formulation of
the two enantiomorphs. pharmaceuticals.
For monotropic polymorphs (Figure 9 B) on-
ly one form is thermodynamically stable at all
Below the transition temperature metastable (I) temperatures in the range considered. All other
can transform to stable (II). Above the transition forms are metastable and potentially capable of
temperature (II) can transform to (I). transforming into the stable form. For enantio-
Transformation is not inevitable even though tropic polymorphs (Figure 9 A) two or more
a system may have entered a condition that would forms are thermodynamically stable over differ-
theoretically allow it. Transformation can only ent temperature ranges. In these cases it is essen-
be ensured if crystals of a more stable solid phase tial to identify the transition temperatures as
are present, e.g., by deliberate seeding or by accurately as possible since they mark bound-
spontaneous nucleation. Theoretical analyses of aries that should be avoided when planning
both solid-state and solvent-mediated transfor- processing operations. Furthermore, compounds
mations are presented in [27], [28]. with transition temperatures within the ambient
range are likely to cause problems in subsequent
Polymorphs and Solvates. The ability of a storage and use.
single compound to crystallize in more than one Laboratory procedures that can be adopted in
crystallographic form (polymorphism) is en- the preliminary search for possible polymorphs
countered in a wide range of industries including or solvates include: crystallizing from a wide
pharmaceuticals, dyestuffs, agrochemicals, range of solvents (polar, non-polar, hydrophilic,
photochemicals, and other specialty compounds, and hydrophobic) at different temperatures;
both organic and inorganic. Many compounds chilling saturated solutions rapidly; precipitation
by rapid quenching with a liquid non-solvent; the metastable form and cooled rapidly to avoid
heating excess solid with a high boiling solvent; any solvent-mediated transition. As noted above,
crystallization from the melt or by sublimation, the drying conditions for metastable polymorphs
and so on. The identity and purity of all product must be chosen carefully to avoid any solvent-
crystals should then be checked by appropriate mediated transformation occurring.
analytical techniques.
Once different polymorphs or solvates have
been isolated and identified, samples can be used 4. Kinetics and Mechanisms of
as seed crystals in subsequent crystallization Crystallization
operations to promote the production of a specific
form. It is important to identify any process 4.1. Crystal Nucleation
conditions that could result in polymorphic trans-
formation, e.g., the initiation of a solvent- Nucleation, i.e., the creation of crystalline bodies
mediated transformation in monotropic systems within a supersaturated fluid, is a complex, often
during a drying operation. Solid phase transfor- ill-defined event, and nuclei may be generated by
mations can be temperature dependent, but they many different mechanisms. Numerous nucle-
can also occur during energetic processes such as ation classification schemes have been proposed;
grinding or tabletting. most distinguish between two basic modes:
The process implications of polymorphism in
organic compounds and some general recom- 1. Primary nucleation – in the absence of
mendations for the batch cooling crystallization crystals
of a desired polymorph may be summarized as 2. Secondary nucleation – in the presence of
follows [28]. First, it is necessary to isolate and crystals
identify each polymorph and to generate solubil-
ity data in more than one solvent in order to Several comprehensive reviews of general
determine if the system is monotropic or enan- nucleation phenomena are given in [5], [7],
tiotropic. This information will help in the selec- [29], [30].
tion of a solvent for the industrial process,
although the ultimate choice will have to include
considerations of process yield, solvent recovery 4.1.1. Primary Nucleation
costs, hazards, etc.
For enantiotropic systems the temperature Classical theories of primary nucleation are
range of the crystallization process will be deter- based on sequences of bimolecular collisions and
mined by the particular polymorph required. If it interactions in a supersaturated fluid, which re-
is metastable below the transition temperature, sult in the buildup of lattice-structured bodies
crystallization should begin just above transition that may or may not achieve thermodynamic
temperature, where the kinetics are relatively stability. This type of primary nucleation is re-
slow. Seeding with the desired polymorph at this ferred to as homogeneous, although the terms
point recommended. If the required polymorph is spontaneous and classical have also been used.
stable below the transition temperature, seeding Ample experimental evidence demonstrates
should be commenced just below the transition that ordered solute clustering can occur in super-
temperature. saturated solutions prior to the onset of homoge-
Seeding is also recommended for monotropic neous nucleation [6], [31–34]. Concentration
systems. For the stable polymorph, the tempera- gradients develop readily in supersaturated solu-
ture after seeding should be held constant for a tions of citric acid [33] under the influence of
predetermined time to allow the solution to de- gravity; theoretical analysis of this phenomenon
supersaturate, after which an appropriate cooling estimates the size of the clusters at 4 – 10 nm
profile (see Section 5.6) should be adopted to [34].
maintain a constant controlled supersaturation. If Primary nucleation may also be initiated by
the metastable polymorph is required, and the suspended particles of foreign substances (e.g.,
solution is supersaturated with respect to the dust or other debris). This mechanism is gener-
stable form, the solution should be seeded with ally referred to as heterogeneous nucleation.
Most primary nucleation in industrial crystal- nucleus size rc is unstable and will tend to
lization is almost certainly heterogeneous rather dissolve. Any crystal larger than rc is stable and
than homogeneous; i.e., it is induced by the will tend to grow.
foreign solid particles that are invariably present Combination of Equations (15) and (16) and
in working solutions. The mechanism of hetero- expression of the rate of nucleation J in the form
geneous nucleation is not well understood, but it of an Arrhenius reaction rate equation give
probably begins with adsorption of the crystal- " #
lizing species on the surface of solid particles, 16pg 3 v2
J ¼ Aexp ð17Þ
thus creating apparently crystalline bodies larger 3k3 T 3 ðlnSÞ2
than the critical nucleus size. These stable par-
where A is a preexponential factor, g is interfacial
ticles then grow into macrocrystals.
tension, v is molar volume, k is the Boltzmann
constant, T is absolute temperature, and S is the
Homogeneous Nucleation. Consideration
supersaturation ratio. Equation (17) not only de-
of the energy involved in solid-phase formation
monstrates the powerful effect of supersaturation
and in creation of the surface of an arbitrary
on homogeneous nucleation, predicting an ex-
spherical crystal of radius r in a supersaturated
plosive increase in the nucleation rate beyond
fluid leads to the relationship
some so-called critical value of S, but also in-
DG ¼ 4pr2 gþð4p=3Þr 3 DGv ð16Þ dicates the possibility of nucleation at any level
where DG is the overall excess free energy of supersaturation.
associated with the formation of the crystalline
body, g is the interfacial tension between the Heterogeneous Nucleation. The presence
crystal and its surrounding supersaturated fluid, of foreign particles (heteronuclei) enhances the
and DGv is the free energy change associated with nucleation rate of a given solution. Equations
the phase change. The first term on the right-hand similar to that for homogeneous nucleation
side of Equation (16), representing the surface (Eq. 17) have been proposed to express this
contribution, is positive and proportional to r2. enhancement. However, the result is simply a
The second term, representing the volume con- displacement of the nucleation rate vs. supersat-
tribution, is negative and proportional to r3. uration curve as shown in Figure 11, indicating
The overall dependence of DG on r is shown in that heterogeneous nucleation occurs more read-
Figure 10. Any crystal smaller than the critical ily, i.e., at lower supersaturation.
For primary nucleation in industrial crystalli-
zation, classical relationships like those based on
Equation (18) have little practical use. All that
Figure 10. Free energy diagram for homogeneous nucle- Figure 11. Effect of supersaturation on the rates of homoge-
ation demonstrating the critical nucleus size neous and heterogeneous nucleation
can be justified is a simple empirical relationship

such as
J ¼ Kn Dcn ð18Þ
which relates the primary nucleation rate J to

the supersaturation Dc (Eq. 1). The primary
nucleation rate constant Kn and the order of the
nucleation process n depend on the physical
properties and hydrodynamics of the system.
Values of n are usually greater than 2.
4.1.2. Secondary Nucleation
Secondary nucleation, by definition, can take

place only if crystals of the species under con-
sideration are already present. Since this is main-
ly the case in working crystallizers, secondary
nucleation has a profound influence on virtually
all industrial crystallization processes.
Apart from deliberate or accidental introduc-
tion of tiny seed crystals to the system, and Figure 12. Simple apparatus for measuring metastable zone
productive interactions between existing crystals widths [35] a) Control unit; b) Hot – cold air blower;
c) Rotating magnet; d) Contact thermometer; e) Water bath
and quasicrystalline embryos or clusters in solu- stirrer; f) Magnetic stirrer
tion, the most influential mode of new crystal
generation in an industrial crystallizer is contact based on the measurement of metastable zone
secondary nucleation. The contact in this case widths (Section 2.2) by using a simple apparatus
can be between the existing crystals themselves, (Fig. 12) that consists of a 50 mL flask fitted with
between crystals and the walls or other internal a thermometer and a magnetic stirrer, located in
parts of the crystallizer, or between crystals and an external cooling bath. A solution of known
the mechanical agitator. composition is heated to about 5 C above its
Secondary nucleation rates in industrial crys- saturation temperature and then cooled at a slow
tallizers are most commonly correlated by em- steady rate. The temperature at which nuclei
pirical relationships such as appear is recorded. The difference between the
B ¼ Kb MTj N l Dcb ð19Þ saturation and nucleation temperatures is the
maximum allowable undercooling (the metasta-
where B is the rate of secondary nucleation ble zone width) corresponding to the particular
(birthrate), Kb is the birthrate constant, MT is the cooling rate used. Both primary and secondary
slurry concentration (magma density), N is a term nucleation can be studied this way.
that gives some measure of the intensity of The typical results [7] shown in Figure 13
agitation in the system (e.g., the rotational speed demonstrate that seeding has a considerable in-
of an impeller), and Dc is the supersaturation. fluence on the nucleation process. The difference
The exponents j, l, and b vary according to the between the slopes of the two lines indicates that
operating conditions. primary and secondary nucleation occur by dif-
ferent mechanisms.
Solution turbulence also affects nucleation. In
4.1.3. Nucleation Measurements general, agitation reduces the metastable zone
width. For example, the metastable zone width
One of the earliest attempts to derive meaningful for gently agitated potassium sulfate solutions is
nucleation kinetics for solution crystallization about 12 C; vigorous agitation reduces this to
was proposed by NÝVLT [35]. The method is ca. 8 C. The presence of crystals also induces
data truly represent homogeneous nucleation,

will allow calculation of the interfacial tension
g. The effect of temperature on g can also be
evaluated.
An attempt has been made to derive a general
correlation between interfacial tension and the
solubility of inorganic salts (Fig. 14) [37]. The
link between interfacial tension and solubility
can be substantiated on the basis of regular
solution theory [9]. However, the success of this
method for evaluating interfacial tension de-
pends on precise measurement of the induction
period t, which presents problems if t is less than
a few seconds.
Short induction periods can be determined by
a stopped-flow technique that detects rapid
changes in the conductivity of a supersaturated
solution [39] (e.g., during a precipitation reac-
Figure 13. Metastable zone width of aqueous ammonium tion). Typical results for CaCO3, SrCO3, and
sulfate solutions as a function of cooling rate [7] a) Seeded BaCO3, produced by mixing an aqueous solution
solution; b) Unseeded solution of Na2CO3 with a solution of the appropriate
chloride, are shown in Figure 15. The slopes of
secondary nucleation at supercooling around the linear (high-supersaturation) regions are
4 C. The relation between supercooling Dq and used to calculate the interfacial tensions (80 –
supersaturation Dc is given by Equation (14). 120 mJ/m2), which compare reasonably well
Useful information on secondary nucleation with the values predicted from the interfacial
kinetics for crystallizer operation and design can tension – solubility relationship in Figure 13.
best be determined from model experiments that
employ techniques such as those developed for
MSMPR (mixed-suspension mixed-product re- 4.2. Crystal Growth
moval) crystallizers (see Section 5.8). In a real
crystallizer, however, both nucleation and (For a detailed discussion of crystal growth, see
growth proceed together and interact with other ! Crystal Growth.)
system parameters in a complex manner [7], [35], Once a stable nucleus has been created in a
[36]. solution, it is capable of growing into a crystal.
In its simplest form, crystal growth may be
considered a two-step process involving (1)
4.1.4. Induction Periods mass transport, either by diffusion or convection
from the bulk solution to the crystal face, fol-
A delay occurs between achievement of super- lowed by (2) a surface reaction in which the
saturation and detection of the first newly created growth units are integrated into the crystal lat-
crystals in a solution. This so-called induction tice. Either step may control the overall growth
period t is a complex quantity that involves both process, although convective mass transport is
nucleation and growth components. However, if unimportant for crystals smaller than ca. 10 mm
the assumption is made that t is essentially because these crystals are scarcely affected by
concerned with nucleation (i.e., t is inversely turbulent eddies and diffusional mass transport
proportional to J), then from the classical nucle- predominates.
ation equation (Eq. 6) it follows that [7] For diffusion-controlled growth, the theoreti-
cal linear crystal growth rate G for a nonionic
logt / g 3 =T 3 ðlogSÞ2 ð20Þ
species may be calculated from
Thus, for a given temperature T, a plot of log t vs.
G ¼ DvDc=L ð21Þ
(log S)2 should yield a straight line which, if the
Figure 14. Interfacial tension as a function of solubility [37]
where D is the diffusion coefficient, v the molar

volume, Dc the supersaturation, and L the crystal
size; i.e., the diffusion-controlled growth rate is
directly proportional to the degree of supersatu-
ration [7].
However, most crystal growth processes are
not simply diffusion-controlled because the sur-
face reaction (integration) step generally plays a
contributing role. The two most common surface
processes are referred to as spiral and polynucle-
ar growth. Spiral growth (also known as BCF
growth because it was first postulated by BURTON,
CABRERA, and FRANK [40]) stems from the emer-
gence of screw dislocations on a crystal face,
as illustrated in Figure 16. Growth proceeds at
relatively low supersaturation at a rate propor-
tional to the square of the supersaturation.
Polynuclear growth develops from surface
(monolayer) nucleation on the edges, corners,
and faces of a crystal. These surface nuclei
spread across the crystal face, and further nuclei
Figure 15. Induction period as a function of initial supersat- develop on them. This mechanism, illustrated in
uration [39] Figure 17, is sometimes referred to as the B þ S
Figure 16. Spiral (BCF) crystal growth beginning at a screw dislocation
(birth and spread) model. Polynuclear growth is Face Growth Rates. Different crystal faces
related to supersaturation by a complex exponen- grow at different rates. In general, high-index
tial relationship [41]. faces grow faster than low-index faces. Changes
At first sight, therefore, identifying the mech- in growth environment (temperature, supersatu-
anism of growth by examining the relationship ration, pH, impurities, etc.) can also have a
between the experimentally determined growth profound effect on growth. Differences in indi-
rate and supersaturation might appear to be pos- vidual face growth rates give rise to habit (shape)
sible. In practice, however, this is not easy be- changes in crystals (see Section 4.4).
cause of the many errors inherent in growth rate Equipment for precise measurement of indi-
measurement and, consequently, the relatively vidual crystal face growth rates is depicted in
poor reproducibility of the data. Figure 18. A fixed crystal in a glass cell is
Several comprehensive reviews of modern observed with a traveling microscope. Solution
theories of crystal growth are available [5], temperature, supersaturation, and velocity are
[7], [41–43] (see also ! Crystal Growth). precisely controlled [7].
The solution velocity past the fixed crystal
is frequently an important growth-determining
4.2.1. Measurement of Growth Rate parameter. It is sometimes responsible for the
so-called size-dependent growth effect often
A variety of methods have been used to measure
crystal growth rate; they are divided into two
main categories: (1) direct measurement of the
linear growth rate of a chosen crystal face and (2)
indirect estimation of an overall linear growth
rate from mass deposition rates measured either
on individual crystals or on groups of freely
suspended crystals [4], [7], [35], [44], [45].
Figure 18. Equipment for measuring the growth of a single

Figure 17. Polynuclear (B þ S) crystal growth initiated by crystal a) Pump; b) Saturator; c) Single crystal fixed on a wire;
surface nucleation d) Glass cell; e) Rotameter; f) Thermometer
observed in agitated vessel and fluidized-bed reasonably uniform fluidized state in the growth
crystallizers. Large crystals have higher settling zone. The crystals are allowed to grow at a
velocities than small crystals and, if their growth constant temperature until their total mass is ca.
is diffusion-controlled, they tend to grow faster. 10 g. They are then removed from the crystalliz-
Other reasons for size-dependent growth rates er, washed, dried, and weighed. The final solution
are discussed in Section 4.2.3. Examples of salts concentration is measured, and the mean of the
that exhibit solution-velocity-dependent growth initial and final supersaturations is taken as the
rates include the alums, nickel ammonium sul- average for the run. This assumption does not
fate, and potassium sulfate. However, salts such involve any significant error because the solution
as ammonium sulfate and ammonium or potassi- concentration is usually not allowed to change by
um dihydrogen phosphate are not affected by more than about 1 % during a run. The overall
solution velocity. crystal growth rate is then calculated in terms of
mass deposited per unit area per unit time at a
Overall Growth Rates. In the laboratory, specified supersaturation.
growth rate data for crystallizer design can be
measured in fluidized beds or agitated vessels. A
typical laboratory fluidized-bed crystallizer is 4.2.2. Expression of Growth Rate
shown in Figure 19. Crystal growth rates are
measured by growing large numbers of carefully Crystal growth rates are commonly expressed in
sized seeds in fluidized suspension under strictly three different ways:
controlled conditions. A warm undersaturated
solution of known concentration is circulated in 1. As mass deposition rate R, e.g., kg m2 s1
the crystallizer and supersaturated by cooling to 2. As mean linear growth velocity v (¼ dr/dt),
the working temperature. About 5 g of closely m/s
sized seed crystals with a narrow size distribution 3. As overall linear growth rate G (¼ dL/dt), m/s
and a mean size of ca. 500 mm is introduced into
the crystallizer, and the upward solution velocity The relationships between these quantities are
is adjusted so that the crystals are maintained in a
1 dm 3arG 6ar dr 6arv
R ¼ Kg Dcg ¼ ¼ ¼ ¼ ð22Þ
A dt b b dt b
where L is some characteristic dimension of the

crystal (e.g., the equivalent sieve aperture size),
r is the radius of the equivalent sphere, and r is
the density of the crystal. The order of the growth
process, g, is generally between 1 and 2. The
volume and surface shape factors (a and b,
respectively) are related to particle mass m and
surface area A, respectively, by
m ¼ arL3 ð23Þ
and
A ¼ bL2 ð24Þ
For spheres and cubes, 6 a/b ¼ 1.
4.2.3. Dependence of Growth Rate on

Crystal Size
A considerable amount of experimental evidence

Figure 19. Laboratory-scale fluidized-bed crystallizer indicates that crystal growth kinetics often de-
a) Pump; b) Heater; c) Cooler; d) Thermometer; e) Crystal bed pend on crystal size. Apart from cases of solution
velocity dependence (Section 4.2.1), this condi- other system parameters in a complex manner.
tion may result from the crystal size dependence These factors are summarized in Figure 20.
of the surface integration kinetics. Different For a complete description of the crystal size
crystals of the same size can also have different distribution of the product in a continuously
growth rates, for example, because of differences operated crystallizer, both the nucleation and
in surface structure or perfection. Furthermore, the growth processes must be quantified, and the
small crystals (< 50 mm) of many substances laws of conservation of mass, energy, and crystal
grow much more slowly than larger crystals, and population must be applied. The importance of
some do not grow at all [46]. population balance, in which all particles are
The behavior of very small crystals has con- accounted for, was first stressed in the pioneer-
siderable influence on the performance of ing work of RANDOLPH and LARSON [36] (cf.
continuously operated industrial crystallizers Section 5.8.1).
because new crystals with a size of 1 – 10 mm
are constantly generated by secondary nucle-
ation. These subsequently grow to populate 4.4. Crystal Habit Modification
the full crystal size distribution. Therefore, the
ability to predict the growth rates of small Changes in the face growth rates of crystals give
crystals is useful in assessing the performance rise to changes in their habit (shape). The growth
of crystallizers. kinetics of individual crystal faces usually de-
pend to various extents on supersaturation, so
that crystal habit can sometimes be controlled by
4.3. Growth – Nucleation Interactions adjusting operating conditions. The most com-
mon cause of habit modification, however, is the
Crystal nucleation and growth in an industrial presence of impurities. The crystallizing solution
crystallizer cannot be considered in isolation may already contain impurities (e.g., raffinose
because they interact with one another and with which induces crystallization of characteristic
Figure 20. Complex interactions in a continuous crystallization process

flat sucrose crystals from beet sugar feedstocks),

or they can be added deliberately.
In some cases, mere traces (ca. 1 mg/kg) of an
impurity can cause significant changes in the
crystal habit, as is the case for FeðCNÞ4 6 which
causes sodium chloride to crystallize in dendritic
form. On the other hand, habit modification
sometimes occurs only in the presence of large
quantities of impurity, e.g., > 5 wt % of biuret is
needed to change the shape of urea crystals from
needles to bricks. Transition-metal ion species,
such as complexes of Cr(III) and Fe(III), are
particularly active impurities at < 10 mg/kg for
a variety of inorganic salts in aqueous solution.
Surface-active agents can also change crystal
habit: anionic surfactants (e.g., alkyl sulfates;
alkyl and arylalkyl sulfonates) and cationic sur-
factants (e.g., quaternary ammonium salts) are
commonly used. Low molecular mass organic
phosphonates and high molecular mass polyelec-
trolytes, polyacrylamides, poly(vinyl alcohols),
etc., also find specific application. A change of Figure 21. Kossel model of crystal growth showing sites for
solvent frequently results in a change of crystal impurity adsorption on a crystal surface A) At a kink; B) At a
step; C) On a ledge (face)
habit because the solvent represents a massive
impurity in a crystallizing system.
In the simple Kossel model of crystal growth, surface flux of growth units to the step and, thus,
three basic sites may be considered for the ad- in the step velocity.
sorption of an impurity species: at a kink (Fig. 21 In addition to physical obstruction, the effects
A), at a step (layer front, Fig. 21 B), or on a ledge of impurity adsorption and change of solvent
(face) between steps (Fig. 21 C). Adsorption at on crystal growth may be explained in terms of
kinks, the key sites at which growth units are changes in crystal surface properties. These
incorporated into the lattice, effectively reduces changes can be quantified by the a factor,
both their number and the velocity at which the also called the surface entropy factor or surface
step advances. Consequent increases in interkink roughness factor, which is related to the inter-
distance diminish the importance of surface dif- facial tension g between the growing crystal and
fusion in the growth process and cause the step its solution [48].
velocity to depend on kink density; this results In brief, at low values of a, i.e., at low
in polygonization of the growth layers [47]. interfacial tension g, the crystal surface is inher-
Adsorption at a step also reduces both the number ently rough, on the molecular scale; under these
of sites available for growth and the step velocity. conditions, growth is controlled only by the rate
However, unless the adsorbed units are closer of diffusion of growth units to the crystal face. At
together than the diameter of a critical two- high values of a and g, the surface is inherently
dimensional nucleus, the advancing step can still smooth and growth cannot proceed at low super-
squeeze between impurity species and progress saturation unless growth centers (e.g., emergent
relatively unimpeded. Step adsorption, therefore, screw dislocations) exist on the face. Growth
implies a critical concentration of dissolved im- under these conditions may then proceed by the
purity, below which the step velocity is unaf- spiral (BCF) mechanism. At intermediate values
fected and above which it decreases rapidly. of a and g, growth may proceed by the polynu-
Adsorption of an impurity on a face is likely to clear (B þ S) mechanism (see Section 4.2).
be effective in cases where surface processes, The interfacial tension g can be changed by
particularly diffusion, play an important role in additives. Adsorption on a crystal face, for ex-
crystal growth. The result is a decrease in the ample, reduces g and could, therefore, change the
growth mechanism. The dependence of growth If the inclusion is a liquid, concentration stream-
rate on supersaturation thus changes, and if this lines will be seen as the two fluids meet; if it is a
occurs differently on different faces of the crys- vapor, a bubble will be released [7].
tal, the habit can consequently change. Similar Crystals produced industrially may contain
reasoning can be applied to the removal of a significant amounts of included mother liquor,
particular impurity from the crystallizing solu- in extreme cases up to 1 wt %, which can sig-
tion. Furthermore, since g is a solvent-dependent nificantly affect product purity. Stored crystals
property (it increases as solubility decreases), a may cake because of liquid seepage from inclu-
change of solvent can have the same effect on sions in broken crystals, which leads to subse-
crystal habit as an additive. quent recrystallization (see Section 4.6). To min-
Some form of habit modification is employed imize inclusions, the crystallizing system should
in a large proportion of all industrial crystalli- be free of dirt and other solid debris to prevent its
zation and precipitation operations to control incorporation into the crystals. Vigorous agita-
the type of crystal produced and to improve the tion or boiling should be avoided because it can
rheological properties of the slurry, downstream lead to the formation of air or vapor inclusions.
processes such as filtration or washing and the Ultrasonic irradiation may suppress adherence of
handling properties of the dried product and its bubbles or particles to a growing crystal face and,
stability on storage. This may be done by con- hence, reduce inclusion formation. Fast crystal
trolling the rate of crystallization (e.g., by ad- growth is probably the most common cause of
justing the rate of cooling or evaporation, the inclusion formation; this means that, in general,
degree of supersaturation, or the temperature at high supersaturation should be avoided.
which crystallization occurs). Alternative meth- Reviews and accounts of crystal inclusions are
ods involve choosing an appropriate solvent, available in [7], [51–53].
adjusting the pH of the solution, or deliberately
adding (or perhaps removing) some habit-
modifying impurity to (or from) the system. A 4.6. Caking of Crystals
combination of several of these methods may
have to be used. Crystalline materials frequently cake (i.e., ce-
The search for a habit modifier is complex, ment together) on storage. The size of the crys-
and the results of small-scale laboratory investi- tals, as well as their shape, moisture content,
gations may not always be useful for large-scale and storage conditions (time, temperature and
industrial application; in some cases, they can humidity fluctuations, pressure, etc.), can all
even be misleading. Realistic pilot-plant trials on contribute to the caking tendency.
batches greater than about 100 L, however, gen- In general, caking is caused initially by damp-
erally yield useful information. ening of the crystal surfaces in a storage con-
Reviews on the industrial applications of habit tainer, e.g., because of inefficient drying or an
modification and the selection of habit modifiers increase in atmospheric humidity above some
are given in [7], [49], [50]. critical value that depends on both substance and
temperature. For example, at 15 C, crystals of
Na2SO4 10 H2O become damp when atmo-
4.5. Inclusions in Crystals spheric humidity exceeds ca. 93 % saturation;
the same applies to NaCl at 78 % saturation and
Inclusions are small pockets of solid, liquid, or CaCl2 6 H2O at 32 % saturation. The presence
gaseous impurities entrapped in crystals. They of a hygroscopic trace impurity in the crystals,
usually occur randomly throughout the crystal, therefore, can greatly influence their tendency
but sometimes a regular pattern may be observed. to absorb atmospheric moisture. Moisture may
A simple technique for observing inclusions is also be released from inclusions if crystals frac-
to immerse the crystal in an inert liquid of similar ture under storage conditions (Section 4.5). If
refractive index or, alternatively, in its own crystal surface moisture later evaporates, e.g.,
saturated solution. In the latter case, the inclusion because of atmospheric temperature or humidity
can be identified under the microscope by raising changes, adjacent crystals become firmly joined
the temperature slightly to dissolve the crystal. together with a cement of recrystallized solute.
Precautions to reduce caking include efficient Because cooling is slow, large interlocked crys-
drying, packaging in airtight containers, and tals are usually obtained and retention of mother
avoiding compaction on storage. In addition, liquor is unavoidable. As a result, the dried crystals
crystals may be coated with an inert dust that are generally impure. Because of the uncontrolled
acts as a moisture barrier; e.g., crystals of table nature of the process, product crystals range from a
salt are sometimes coated with finely powdered fine dust to large agglomerates.
magnesium carbonate. However, the crystals Labor costs are generally high, but the method
themselves play a dominant role in caking. is economical for small batches because capital,
Small crystals are more prone to cake than large operating, and maintenance costs are low. How-
crystals because of the greater number of contact ever, the productivity of this type of equipment is
points per unit mass, but actual size is less low and space requirements are high.
important than size distribution and shape. The
narrower the size distribution and the more gran-
ular the shape, the lower is the tendency of 5.1.2. Agitated Vessels
crystals to cake. Crystal size distribution can be
controlled by adjusting operating conditions of Installation of an agitator in an open-tank crystal-
the crystallizer (Section 5.4), and crystal shape lizer generally results in smaller, more uniform
may be influenced by the use of habit modifiers crystals and reduced batch time. The final product
(Section 4.4). tends to have a higher purity because less mother
Methods employed for the conditioning of liquor is retained by the crystals after filtration and
crystals and testing procedures for caking ten- more efficient washing is possible. Water jackets
dency are discussed in [54–56]. A comprehen- are usually preferred to coils for cooling because
sive account of caking inhibition by trace addi- the latter often become encrusted with crystals
tives is given in [57]. and cease to operate efficiently. Where possible,
the internal surfaces of the crystallizer should be
smooth and flat to suppress encrustation.
5. Crystallization from Solutions An agitated cooler is more expensive to oper-
ate than a simple tank crystallizer, but it has a
Solution crystallizers are generally classified much higher productivity. Labor costs for prod-
according to the method by which supersatura- uct handling may still be rather high. The design
tion is achieved, e.g., cooling, evaporation, vac- of tank crystallizers varies from shallow pans to
uum (adiabatic cooling), reaction, salting out. large cylindrical tanks.
The designation controlled denotes supersatura- The large agitated cooling crystallizer shown
tion control; classifying refers to classification in Figure 22 A has an upper conical section which
of product size. The term mixed-suspension mixed- slows down the upward velocity of liquor and
product removal is abbreviated as MSMPR (see prevents the crystalline product from being swept
Section 5.8). out with the spent liquor. An agitator located in
the lower region of a draft tube circulates the
crystal slurry (magma) through the growth zone
5.1. Cooling Crystallizers of the crystallizer. If required, cooling surfaces
may be provided inside the crystallizer.
5.1.1. Nonagitated Vessels Use of external circulation allows good mix-
ing inside the crystallizer and high rates of
The simplest type of cooling crystallizer is the heat transfer between the liquor and coolant
unstirred tank: a hot feedstock solution is charged (Fig. 22 B). An internal agitator may be installed
to the open vessel where it is allowed to cool, in the crystallization tank if needed. The liquor
often for several days, by natural convection. velocity in the tubes is high; therefore, small
Metallic rods may be suspended in the solution temperature differences are usually adequate
so that large crystals can grow on them and for cooling purposes and encrustation on heat-
reduce the amount of product that sinks to the transfer surfaces can be reduced considerably.
bottom of the crystallizer. The product is re- The unit shown may be used for batch or contin-
moved by hand. uous operation.
ble or latent heat. The coolant may or may not boil

during the operation, and it can be miscible or
immiscible with the process liquor. Thus, four
basic types of DCC crystallization are possible [7]:
1. Immiscible, boiling, solid or liquid coolant:

heat is removed mainly by transfer of latent
heat of sublimation or vaporization.
2. Immiscible, nonboiling, solid, liquid, or gas-
eous coolant: mainly sensible heat transfer.
3. Miscible, boiling, liquid coolant: mainly la-
tent heat transfer.
4. Miscible, nonboiling, liquid coolant: mainly
sensible heat transfer.
Crystallization processes employing DCC

have been used successfully in the dewaxing of
lubricating oils, the desalination of water, and the
production of inorganic salts from aqueous solu-
tion [7].
5.2. Evaporating Crystallizers
If the solubility of a solute in a solvent is not

appreciably decreased by lowering the tempera-
ture, the appropriate degree of solution supersat-
uration can be achieved by evaporating some of
the solvent. Evaporation techniques have been
used for centuries to crystallize salts; the simplest
method – utilization of solar energy – is still em-
ployed commercially throughout the world [58].
Figure 22. Cooling crystallizers A) Internal circulation Common salt is produced widely from brine in
through a draft tube; B) External circulation through a heat
exchanger a) Calming section; b) Growth zone; c) Draft tube steam-heated evaporators, and similar evaporat-
ing crystallizers, often in multiple-effect series,
5.1.3. Direct-Contact Cooling are used in sugar refining. Many types of forced-
circulation evaporating crystallizers are now in
The use of a conventional heat exchanger and the large-scale use [1–8].
problems caused by crystal encrustation can be Evaporating crystallizers are normally oper-
avoided by employing direct-contact cooling ated under reduced pressure to aid in solvent
(DCC) in which supersaturation is achieved by removal, minimize heat consumption, or de-
allowing the process liquor to come into contact crease the operating temperature of the solution;
with a cold heat-transfer medium. Other potential they are best described as ‘‘reduced-pressure
advantages of DCC over conventional indirect- evaporating crystallizers’’.
contact methods include better heat transfer and
smaller cooling load. However, problems are
also associated with DCC crystallization; these 5.3. Vacuum (Adiabatic Cooling)
include product contamination from the coolant Crystallizers
and the cost of extra processing required to
recover the coolant for further use. A vacuum crystallizer operates on a slightly differ-
A solid, liquid, or gaseous coolant can be used; ent principle from the reduced-pressure evaporat-
heat exchange may occur via the transfer of sensi- ing crystallizer described in the previous section.
Supersaturation is achieved in a vacuum crys- exchanger and reintroduced tangentially into the
tallizer by simultaneous evaporation and adia- evaporator below the liquor level to create a
batic cooling of the feedstock. A hot, saturated swirling action and prevent flashing (sudden
solution is fed into an insulated vessel maintained evaporation). Feedstock enters on the pump inlet
under reduced pressure. If the feed liquor tem- side of the circulation system. Product crystal
perature is higher than the boiling point of the magma is removed below the conical section.
solution under the low pressure existing in the
vessel, the liquor cools adiabatically to this tem- Fluidized-Bed Crystallizers. In an Oslo
perature. The sensible heat and any heat of fluidized-bed crystallizer, a bed of crystals is
crystallization liberated by the solution evapo- suspended in the vessel by the upward flow of
rate some of the solvent and concentrate the supersaturated liquor in the annular region
solution. surrounding a central downcomer (Fig. 24).
Although originally designed as classifying
crystallizers, fluidized-bed Oslo units are now
5.4. Continuous Crystallizers frequently operated in a mixed-suspension mode
to improve productivity, although this reduces
Many different continuously operated crystal- product crystal size. A cooling-type Oslo crys-
lizers are available, but the majority can be tallizer operates in the classifying mode as fol-
divided into three basic types: forced-circulation, lows. The hot, concentrated feed solution is fed
fluidized-bed (Oslo), and draft-tube agitated into the vessel at a point directly above the inlet
units. A small selection of the large number of to the circulation pipe. Saturated solution from
commercial types available is described. the upper regions of the crystallizer, together
with the small amount of feedstock, is circulated
Forced-Circulation Crystallizers. A Swen- through the tubes of the heat exchanger, which is
son forced-circulation crystallizer that operates cooled by forced circulation of water or brine.
under reduced pressure is shown in Figure 23. A On cooling, the solution becomes supersaturated,
high recirculation rate through the external heat but not enough for spontaneous nucleation to
exchanger is used to provide good heat transfer occur; great care, in fact, is taken to prevent this.
and minimize encrustation. The crystal magma is Product crystal magma is removed from the
circulated from the lower conical section of the lower regions of the vessel.
evaporator body through the vertical tubular heat
Draft-Tube Agitated Vacuum Crystalli-
zers. A Swenson draft-tube-baffled (DTB) vac-
uum unit is shown in Figure 25. A relatively
slow-speed propeller agitator is located in a draft
tube which extends to a few inches below the
Figure 23. Forced-circulation Swenson crystallizer a) Evap- Figure 24. Oslo cooling crystallizer a) Downcomer;
orator; b) Heat exchanger; c) Pump b) Pump; c) Heat exchanger
Figure 25. Swenson draft-tube-baffled (DTB) crystallizer

a) Boiling surface; b) Draft tube; c) Baffle; d) Settling zone;
e) Elutriating leg Figure 26. Standard–Messo turbulence crystallizer a) Draft
tube; b) Downcomer; c) Circumferential slot
liquor level in the crystallizer. Hot, concentrated

feedstock enters at the base of the draft tube. between the ejector tube and the baffle, and a
The steady movement of magma and feedstock secondary flow circuit is formed in the lower
up to the surface of the liquor produces a gentle, region of the vessel. Feedstock is introduced into
uniform boiling action over the whole cross- the guide tube and passes into the vaporizer
sectional area of the crystallizer. The degree section where flash evaporation takes place.
of supercooling thus produced is very low Nucleation, therefore, occurs in this region, and
(< 1 C), and in the absence of violent vapor the nuclei are swept into the primary circuit.
flashing, both excessive nucleation and salt Mother liquor can be drawn off via a control
buildup on the inner walls are minimized. The valve, thus providing a means of controlling
internal baffle in the crystallizer forms an annular crystal slurry density.
space in which agitation effects are absent. This The Escher–Wyss Tsukishima double-pro-
provides a settling zone that permits regulation peller (DP) crystallizer (Fig. 27) is essentially
of the magma density and control of the removal a draft-tube agitated crystallizer with some
of excess nuclei. An integral elutriating leg novel features. The DP unit contains an annular
may be installed underneath the crystallization baffled zone and a double-propeller agitator
zone (as depicted in Fig. 25) to effect some which maintains a steady upward flow inside the
degree of product classification. draft tube and a downward flow in the annular
The Standard–Messo turbulence crystallizer region. Very stable suspension characteristics
(Fig. 26) is another successful draft-tube vacuum are claimed.
unit. Two liquor flow circuits are created by
concentric pipes: an outer ejector tube with a 5.5. Crystal Yield
circumferential slot and an inner guide tube.
Circulation is effected by a variable-speed agita- The crystal yield for simple cooling or evaporat-
tor in the guide tube. The principle of the Oslo ing crystallization can be estimated from the
crystallizer is utilized in the growth zone; partial solubility characteristics of the solution. For
classification occurs in the lower regions, and aqueous solutions, the following general equa-
fine crystals segregate in the upper regions. The tion applies:
primary circuit is created by a fast upward flow of
liquor in the guide tube and a downward flow in WR ½c1 c2 ð1VÞ
Y¼ ð25Þ
the annulus; liquor is thus drawn through the slot 1c2 ðR1Þ
solution, C; C is the specific heat capacity of the

solution, J kg1 K1; and c1 and c2 have the
same meaning as in Equation (25).
5.6. Controlled Crystallization
Carefully selected seed crystals are sometimes

added to a crystallizer to control the final product
crystal size. The effect of rapid cooling on an
unseeded solution is shown in Figure 28 A. The
solution cools at constant concentration until the
limit of the metastable zone is reached, where
nucleation occurs. The temperature increases
slightly due to the release of latent heat of crystal-
lization, but cooling reduces it and more nucleation
occurs. The temperature and concentration sub-
sequently fall as indicated. In such a process,
Figure 27. Escher–Wyss Tsukishima double-propeller (DP)
nucleation and growth cannot be controlled.
crystallizer a) Baffle; b) Draft tube; c) Elutriating leg; d) Heat Figure 28 B demonstrates the slow cooling of
exchanger a seeded solution in which temperature and
solution composition are controlled within the
where c1 is the initial solution concentration, kg metastable zone throughout the cooling cycle.
anhydrous salt per kg water; c2 is the final solu-
tion concentration, kg anhydrous salt per kg
water; W is the initial mass of water, kg; V is
the water lost by evaporation, kg per kg of
original water present; R is the ratio of molecular
masses of hydrated to anhydrous salts; and Y is
the crystal yield, kg.
The actual yield may differ slightly from that
calculated by Equation (25). For example, if the
crystals are washed with fresh solvent on the
filter, losses may occur through dissolution.
On the other hand, if mother liquor is retained
by the crystals, an extra quantity of crystalline
material will be deposited on drying. Further-
more, published solubility data usually refer to
pure solvents and solutes. Because pure systems
are rarely encountered industrially, solubilities
should always be checked on the actual working
liquors.
Before Equation (25) can be applied to vacu-
um (adiabatic cooling) crystallization, the quan-
tity V must be estimated:
qR ðc1 c2 ÞþC ðt1 t2 Þ ð1þc1 Þ ½1c2 ðR1Þ
V¼ ð26Þ
l½1c2 ðR1ÞqRc2
where l is the latent heat of evaporation of the Figure 28. Effect of seeding on cooling crystallization
solvent, J/kg; q is the heat of crystallization of A) Rapid cooling of an unseeded solution; B) Slow cooling
of a seeded solution a) Supersolubility curve of the solute;
the product, J/kg; t1 is the initial temperature of b) Cooling curve of the solution; c) Solubility curve of
the solution, C; t2 is the final temperature of the the solute
Crystal growth occurs at a controlled rate only for example, produces a supersaturation peak in
on the added seeds; spontaneous nucleation is the early stages of the process when rapid, un-
avoided because the system is never allowed to controlled heavy nucleation inevitably occurs.
become labile. This batch operating method is However, nucleation can be controlled within
known as controlled crystallization; many mod- acceptable limits by following a cooling path that
ern large-scale crystallizers operate on this maintains a constant low level of supersaturation
principle. (Fig. 29 B).
If crystallization occurs only on the added The calculation of optimum cooling curves
seeds, the mass Ms of seeds of size Ls that can for different operating conditions is complex
be added to a crystallizer depends on the required [59], but the following simplified relationship is
crystal yield Y (Eq. 26) and the product crystal often adequate for general application:
size Lp:
qt ¼ q0 ðq0 qf Þðt=tÞ3 ð28Þ
Ms ¼ Y L3s =ðL3p L3s Þ ð27Þ
where q0, qf, and qt are the temperatures at the
beginning, end, and any time t during the process,
The product crystal size from a batch crystallizer respectively, and t is the overall batch time.
can also be controlled by adjusting cooling or The potential benefits of controlled cooling
evaporation rates. Natural cooling (Fig. 29 A), are sometimes diminished by the occurrence of
secondary nucleation, although a fines destruc-
tion loop may be installed on the crystallizer to
combat this problem [7], [62].
5.7. Comparison of Batch and

Continuous Crystallization
Although continuous, steady-state operation is

often regarded as the ideal procedure for much
processing plant equipment, this is not always
true for crystallization processes. Batch opera-
tion often offers considerable advantages, such
as simplicity of equipment and minimization of
encrustation on heat-exchanger surfaces. In
many cases, only a batch crystallizer can produce
the required crystal form, size distribution, or
purity. On the other hand, the operating costs of a
batch system can be significantly higher than
those of a comparable continuous unit, and pro-
blems of product variation from batch to batch
may be encountered.
The particular attraction of a continuous crys-
tallizer is its built-in flexibility for control of
temperature, supersaturation, nucleation, crystal
growth, and all the other parameters that influ-
ence crystal size distribution. A continuous crys-
tallizer, however, does not discharge its product
under equilibrium conditions (a batch unit can, if
the batch time is adjusted appropriately) so the
product slurry may have to be passed to a holdup
Figure 29. Natural and controlled cooling in batch crystalli- tank to allow equilibrium to be reached. Omis-
zation A) Temperature profile; B) Supersaturation profile sion of this step may cause problems due to
further crystallization occurring in other parts of mixed-product removal) crystallizer operated

the plant (e.g., unwanted deposition in pipelines continuously in the steady state. The assumptions
and effluent tanks). A holdup (aging) tank may are made that no crystals are present in the feed
also be necessary in a continuous system if the stream, that all crystals are of the same shape, that
product exists in a phase (polymorph, hydrate, crystals do not break down by attrition, and that
etc.) that differs from the one which appears crystal growth rate is independent of crystal size.
initially. The relationship between crystal size L and
A distinct advantage of batch crystallization, population density n (number of crystals per unit
widely acknowledged in the pharmaceutical in- size per unit volume of the system), derived
dustry, is that the crystallizer can be cleaned directly from the population balance over the
thoroughly at the end of each batch to prevent system [36], is
contamination (seeding) of the next charge with
any undesirable phase that might have arisen n ¼ n0 expðL=Gt Þ ð29Þ
from transformation, rehydration, dehydration, 0
where n is the population density of nuclei (zero-
air oxidation, etc., during the batch cycle. Con- sized crystals) and t is the residence time. Equa-
tinuous crystallization systems often self-seed tion (29) describes the crystal size distribution
undesirably after a certain operating time, which for steady-state operation. Rates of nucleation
necessitates frequent shutdown and washout. B and growth G (¼ dL/dt) are conventionally
Semicontinuous crystallization processes of- written in terms of supersaturation as
ten combine the best features of both batch and
continuous operation. For example, a rapid mixer B ¼ k1 Dcb ð30Þ
with a short residence time (possibly an on-line and
device) can discharge its product slurry into an
agitated residence tank. G ¼ k2 Dcg ð31Þ
Continuous crystallizers may also be operated These empirical expressions can be combined to
in a linked series of well-mixed vessels, with the give
crystal magma flowing from one stage to another.
The most frequent objective of series or ‘‘cas- B ¼ k 3 Gi ð32Þ
cade’’ operation is to economize on heat utiliza-
where
tion, e.g., by dividing the overall temperature
gradient over several stages and operating each i ¼ b=g ð33Þ
successive stage at a lower temperature down the
in which b and g are the kinetic orders of nucle-
cascade. In cooling crystallization encrustation
ation and growth, respectively, and i is the rela-
problems can be significantly reduced, because
tive kinetic order. The relationship between nu-
smaller temperature drops are needed across the
cleation and growth may be expressed as
individual heat exchangers. Accounts of cascade
operation are given in [7], [36], [63], [64]. B ¼ n0 G ð34Þ
or
5.8. Crystallizer Modeling and Design n0 ¼ k4 Gi1 ð35Þ
5.8.1. Population Balance Experimental measurement of crystal size distri-

bution (recorded on a number basis) in a steady-
As described in Section 4.3, the processes of state MSMPR crystallizer can thus be used to
growth and nucleation interact in a crystallizer, quantify nucleation and growth rates. A plot of
and both contribute to the final crystal size dis- log n vs. L should give a straight line of slope –
tribution (CSD) of the product. In such assess- (Gt)1 with an intercept at L ¼ 0 equal to n0
ments, the utility of the population balance [36] is (Eq. 29 and Fig. 30 A); if the residence time t is
widely acknowledged. known, the crystal growth rate G can be calcu-
Application of the population balance is de- lated. Similarly, a plot of log n0 vs. log G should
scribed most easily with reference to the simple, give a straight line of slope i 1 (Eq. 35 and
idealized case of an MSMPR (mixed-suspension Fig. 30 B); if the order g of the growth process is
This interesting relationship [36] enables the effect

of changes in residence time to be evaluated. For
example, if i ¼ 2 (a typical value for many inor-
ganic salt systems), a doubling of the residence
time would increase the dominant product crystal
size by only ca. 15 %. To double the residence
time, however, either the crystallizer volume
would have to be doubled or the volumetric feed
rate, and hence the production rate, would have to
be halved. Therefore, residence time adjustment is
usually not a very effective means of controlling
product crystal size.
Population-balance-based CSD modeling can
be applied to crystallizer configurations other
than MSMPR [36] and has become a distinct,
self-contained branch of reaction engineering.
The ability to simulate process configurations,
however, presently exceeds the capabilities for
measuring CSD on-line, predicting growth and
nucleation rates, maintaining crystal magmas in a
well-mixed state, and measuring supersaturation.
5.8.2. Design and Scaleup Problems
Industrial crystallizers are commonly designed

by using data measured on laboratory-scale (1 –
10 L) or pilot-scale (50 – 250 L) units. In diffi-
cult cases, information may have to be obtained
for both scales of operation. One of the main
problems in crystallizer scaleup is characteriza-
Figure 30. Population plots for a continuous mixed-suspen- tion of particle-fluid hydrodynamics and assess-
sion mixed-product removal (MSMPR) crystallizer A) Crys- ment of their effects on the kinetics of nucleation
tal size distribution, slope ¼ (Gt)1; B) Nucleation and
growth kinetics, slope ¼ i 1 and crystal growth.
For explanation of symbols, see text. In fluidized-bed crystallizers, for example,
evaluation of the crystal suspension velocity is
known (Eq. 33), the order of nucleation b can be necessary. This parameter is related to crystal
calculated. size, size distribution, and shape, as well as bed
The total mass MT of crystals in the system, voidage and other system properties such as
the so-called magma density (mass of crystals per density differences and viscosity. Possible ways
unit volume of the system), is given by of estimating crystal suspension velocity are
discussed in [7]. In practice, however, determi-
MT ¼ 6a rn0 ðGtÞ4 ð36Þ
nation of suspension velocities on actual crystal
where a is the volume shape factor (Eq. 23) and samples by simple experimental techniques is
r is the crystal density. often advisable.
The peak of the mass distribution, the domi- In agitated vessels, the ‘‘just-suspended’’ agi-
nant size LD of the CSD, is given by tator speed NJS must be established, i.e., the
minimum rotational speed necessary to keep all
LD ¼ 3Gt ð37Þ crystals in suspension. Not only do the crystals
and can be related to the crystallization kinetics by have to be kept in suspension, but the develop-
ment of ‘‘dead spaces’’ in the vessel must also be
LD tði1Þ=ði3Þ ð38Þ avoided because they are unproductive zones and
regions of high supersaturation in which vessel (Section 3.2.1), whereas a solid solution can only
surfaces can become encrusted. Fluid and crystal deposit a mixture of components (Section 3.2.2).
properties, together with vessel and agitator Other more complex phase diagrams may be
geometries, are important in establishing NJS encountered in organic melts, but a survey [67]
values [7]. of several hundred binary organic mixtures re-
Agitated vessel crystallizers are often scaled ported that more than 50 % of these mixtures
up successfully on the crude basis of either exhibited simple eutectic behavior, about 25 %
constant power input per unit volume or constant formed intermolecular compounds (Fig. 5) and
agitator tip speed. A refinement of the latter about 12 % formed solid solutions of one kind or
criterion, for draft-tube agitated vessels, is to another.
maintain the quantity (TS)2/(TO) constant,
where TS is the agitator tip speed and TO is the
turnover time, i.e., TO is the vessel volume 6.1. Single Stage Processes
divided by the volumetric circulation rate [65].
Crystallizer design procedures based on the Two basic techniques of melt crystallization are
population balance and other methods, together
with practical examples, are described in [4], [7], 1. Gradual deposition of a crystalline layer on a
[8], [36], [64]. chilled surface in a static or laminar flowing
melt
2. Fast crystallization of discrete crystals in the
6. Crystallization from Melts body of an agitated vessel.
Melt is the common name given to a liquid or a An example of category 1 is found in the
liquid mixture at a temperature near its freezing Proabd refiner [68] which is essentially a batch
point. Melt crystallization is the process of sepa- cooling process. A static liquid feedstock is
rating the components of a liquid mixture by progressively crystallized onto extensive cooling
cooling until a quantity of crystallized solid is surfaces (e.g., fin-tube heat exchangers supplied
deposited from the liquid phase. with a cold heat-transfer fluid) located inside a
Melt crystallization is often considered to be crystallization tank. As crystallization proceeds,
commercially attractive, compared with distilla- the remaining liquid becomes increasingly im-
tion, for the separation of close-boiling organic pure and, in some cases, crystallization may be
substances. It offers the potential for low-energy continued until virtually the entire charge has
separation because enthalpies of fusion are gen- solidified. The crystallized mass is then slowly
erally much lower than enthalpies of vaporiza- melted by circulating a hot fluid through the heat
tion. A further advantage is that it operates at exchanger. The impure fraction melts first and
much lower temperatures than distillation, and drains out of the tank. As melting proceeds, the
this can be beneficial for processing thermally melt runoff becomes progressively richer in the
unstable substances. Technical limitations to the desired component, and fractions may be taken
theoretical possibilities for melt crystallization off during the melting stage if required. A typical
are discussed in [66]. flow diagram, based on a scheme for the puri-
The basic requirement of melt crystallization fication of naphthalene, is shown in Figure 31.
is that the composition of the crystallized solid In this case, the circulating fluid is usually cold
differ from that of the liquid mixture from which water which is heated during the melting stage by
it is deposited. The ease or difficulty of separating steam injection.
one component from a multicomponent mixture Another example in the first category is the
by crystallization is best represented by a phase rotary drum crystallizer which usually consists of
diagram as in Figures 3 and 4, both of which a horizontally mounted cylinder that is partially
depict binary systems: the former shows a eutec- immersed in the melt or supplied with feedstock
tic, and the latter shows a continuous series of in some other way. The coolant enters and leaves
solid solutions. These two systems behave quite the inside of the hollow drum through trunnions.
differently on freezing; as described previously, As the drum rotates, a crystalline layer forms on
a eutectic system can deposit a pure component the cold surface and is subsequently removed
oratory tests and employed to facilitate process

scaleup.
An example of melt crystallization in catego-
ry 2 is the scraped-surface heat exchanger, which
is basically a cylindrical tube surrounded by a
cylindrical heat-exchange jacket. The tube is
fitted with close-clearance scraper blades and
rotates at relatively low speed. Two basic types
are available: the large (> 200 mm in diameter,
> 3 m long) slow-speed (< 10 rpm) unit and the
Figure 31. Batch cooling crystallization of melts: flow dia- small (< 150 mm in diameter, < 1.5 m long)
gram for the Proabd refiner a) Crystallizer; b) Pump; c) Heat
exchanger high-speed (> 500 rpm) machine. Both types,
but especially the latter, can handle viscous
magmas, and operate at temperatures as low as
with a scraper knife. Two feed and discharge 80 C. They are widely used, for example, in
arrangements are shown in Figure 32. Rotary the manufacture of margarine (crystallization of
drum behavior and design have been discussed triglycerides), dewaxing of lubricating oils (crys-
in [69], [70]. tallization of higher n-alkanes), and large-scale
Analysis of general layer freezing processes processing of many organic substances (naphtha-
shows that the structure and impurity levels of lene, p-xylene, chlorobenzenes, etc.). The mag-
growing crystal layers are determined primarily ma emerging from a scraped-surface crystallizer
by mass-transfer effects at the layer front [71]. generally contains very small crystals (often
Effective distribution coefficients described by a < 10 mm) which can cause separation and sub-
single parameter that combines growth velocity, sequent reprocessing problems unless the crys-
mass-transfer coefficient, and concentration of tals are first grown to a larger size, e.g., in a
mother liquor can be determined by simple lab- separate holdup tank.
Figure 32. Two feeding modes (A) and (B) for drum crystallizers
6.2. Multistage Processes
The single-stage crystallization described in

Section 6.1 might not always be sufficient to
achieve the required purity of the final product, in
which case further separation, melting, washing,
or refining may be required. Two basic models
can be considered:
1. a repeating sequence of crystallization, melting,

and recrystallization steps (cf. Section 9.2)
2. a single crystallization step followed by coun-
tercurrent contacting of the crystals with a
relatively pure liquid stream
Scheme 1 is preferred if the concentration of

impurities in the feedstock is high; it is essential
if the system forms a continuous series of solid
solutions. Scheme 2 is applicable if the concen-
tration of impurities is low. Some industrial
operations, however, require a combination of
both systems. For a comparative analysis of
different types of multistage crystallization
schemes, see [72]. Figure 33. Sulzer MWB process A) Multistage flow diagram
Symbols: C ¼ crystals, L ¼ liquor
B) Schematic of practical layout a) Residue melt storage
Sulzer MWB Process. A highly successful tanks; b) Crystallizer; c) Heat exchanger; d) Collecting tank;
industrial example of multistage operation is the e) Pump
Sulzer MWB process [73] that operates by crys-
tallization on a cold surface; it also has features
that permit it to operate effectively as a multi- used on a large scale in the purification of a range
stage separation device. Consequently, it can be of organic substances (e.g., chloro- and chloro-
used to purify solid solutions. An effective mul- nitrobenzenes, nitrotoluenes, cresols, and xyle-
tistage countercurrent scheme is illustrated for nols) and in the separation of fatty acids.
four-stage operation in Figure 33 A. Stage 1 is
fed with melt L2 and recycle liquor L1 L (L
denotes the impure reject liquor stream). Crystals 6.3. Column Crystallizers
C1 are deposited in stage 1, and after melting,
they are mixed with melt L3 and fresh feedstock. Because melt feedstock components can form
Crystallization of this mixture yields crystals C2 both eutectic and solid-solution systems with one
and melt L2 in stage 2. Similar patterns are another, sequences of washing, partial or com-
followed in stages 3 and 4, and the final high- plete melting, and recrystallization are often
purity stream C4 is remelted and split into product necessary to produce one of the components in
C and recycle melt C4 C. Only one crystalliz- near-pure form. However, the operation of a
er, a vertical multitube heat exchanger, is re- sequence of melt crystallization steps can be
quired in this scheme. The crystals do not have to time-consuming and costly, especially if the
be transported; they remain deposited on the liquid feedstock has to be cooled until it crystal-
internal heat-exchange surfaces in the vessel, lizes and the crystals have to be separated from
until they are melted for further processing. The the residual melt, washed, and then remelted
intermediate storage tanks and crystallizer are before the cycle can be repeated. Many attempts
linked by a control system consisting of a pro- have been made to effect some of these events in
gram timer, actuating valves, pumps, and the a single unit, such as the column crystallizer
cooling loop (Fig. 33 B). The process has been developed by SCHILDKNECHT in the late 1950s.
Figure 34. Schildknecht column
The basic features of a Schildknecht column

are shown in Figure 34. Liquid feedstock enters Figure 35. Phillips pulsed-column crystallizer a) Scraped-
surface chiller; b) Piston; c) Wall filter; d) Crystal bed;
the column continuously at an arbitrary mid- e) Heater
point. Freezing at the bottom of the column is
accomplished with a suitable refrigerant fluid,
melting at the top, with a hot fluid or an electrical leum Company in the 1960s for large-scale pro-
heating element. The crystals and liquid pass duction of p-xylene [76]. The key features of the
through the column countercurrently, the solid Phillips pulsed-column crystallizer are shown in
phase being transported downward by a helical Figure 35. A cold slurry feed, produced in a
conveyor fixed on a central shaft. The purifica- scraped-surface chiller, enters at the top of the
tion zone is usually operated at a virtually con- column. Crystals in the vertical bed are pulsed
stant temperature between those of the freezing downward by a piston, and impure mother liquor
and melting sections. Crystals are formed mainly leaves through a wall filter. The upwardly flow-
in the freezing section, but they can also deposit ing wash liquor is generated by the bottom heater
on the inner surface of the column from which the which melts pure crystals before they are re-
helical conveyor removes them by scraping. moved from the column.
During conveyance, crystals come into contact The Brodie purifier [77] developed in the late
with the counterflowing liquid melt and are thus 1960s has several features of the column crystal-
subjected to surface washing. The reverse mode lizers described above, but it also has the poten-
of operation has also been used, i.e., upwardly tial to deal effectively with solid-solution sys-
flowing liquid in contact with crystals being tems. It is essentially a center-fed column which
conveyed downward. In this case, the locations can convey crystals from one end to the other
of the freezer and melter are the reverse of those (Fig. 36). As the crystals are conveyed through
depicted in Figure 34. Comprehensive studies of the unit, their temperature is gradually increased
the modeling of column crystallizers appear in by a deliberately imposed temperature gradient
[74], [75]. along the flow path; they are thus subjected to
Although successful, the Schildknecht col- partial melting which encourages the release of
umn is basically a laboratory apparatus; no low-melting impurities. The interconnected
large-scale industrial applications have been re- scraped-surface heat exchangers are of progres-
ported. A melt crystallizer of the wash column sively smaller diameter to maintain reasonably
type, however, was developed by Phillips Petro- constant axial flow velocities and prevent
The Tsukishima Kikai (TSK) countercurrent

cooling crystallization process [78] is, in effect, a
development of Brodie technology. The flow
sheet in Figure 37 shows three conventional
cooling crystallizers connected in series. Feed
enters the first-stage vessel and partially crystal-
lizes. The slurry is then concentrated in a hydro-
cyclone before passing into a Brodie purifying
column (Fig. 36). After passage through a set-
tling zone in the crystallizer, clear liquid over-
flows to the next stage. Slurry pumping and
overflow of clear liquid in each stage result in
a countercurrent flow of liquid and solid. The
process has been applied in the large-scale pro-
duction of p-xylene.
6.4. High-Pressure Crystallization
Pressure, as well as temperature, can alter the

equilibrium relationships in a crystal – melt
system. The potential of high-pressure crystalli-
zation as a purification technique has been dem-
Figure 36. Brodie purifier a) Cooling jackets; b) Scraper
conveyors; c) Purifying column; d) Slow agitator; e) Heater onstrated with impure organic melt feedstocks
subjected to pressures up to 300 MPa under
back-mixing. The vertical purifying column acts adiabatic conditions. As the pressure and
as a countercurrent washer in which falling, temperature of the charge increase, fractional
near-pure crystals meet an upflow of pure melt. crystallization ensues and the impurities are
The Brodie purifier has been used in the large- concentrated in the liquid phase which is then
scale production of high-purity 1,4-dichloroben- discharged from the pressure chamber. At the
zene and naphthalene. end of the cycle, further purification is possible
Figure 37. Tsukishima Kikai (TSK) countercurrent cooling crystallization process a) Hydrocyclone; b) Conventional
crystallizer; c) Brodie purifying column; d) Pump; e) Heater
because residual impurities in the compressed below the triple point. Substances such as
crystalline plug may be ‘‘sweated out’’ when the zinc selenide and gallium arsenide are grown
pressure is released. So far only relatively small by this technique. Sublimation – desublimation
( 2 L) pressure chambers have been employed, processes are also used on a large scale by
but a single-cycle operation lasting less than the chemical industry to produce a wide range
5 min is claimed to be sufficient to effect sub- of organic and inorganic substances (!
stantial purification in a wide range of organic Sublimation).
binary melt systems [79].
8. Precipitation
6.5. Prilling and Granulation
Precipitation is widely used in the laboratory for
Prilling is a melt spray crystallization process that chemical analysis and in industry for the manu-
results in the formation of solid spherical gran- facture of paints, pigments, pharmaceutical and
ules. It is employed widely in the manufacture of photographic chemicals, etc. In the production of
fertilizer chemicals such as ammonium nitrate ultrafine crystalline powders, precipitation is often
and urea. In the ammonium nitrate prilling pro- considered an attractive alternative to comminu-
cess [80], a very concentrated solution, containing tion, particularly for heat-labile substances (i.e.,
ca. 5 % water, is sprayed at 140 C into the top of a substances that are unstable when heated).
30-m-high, 6-m-diameter tower in which the No generally accepted, unambiguous defini-
droplets fall countercurrently to an upwardly tion of the term precipitation exists; it may refer
flowing air stream that enters the base of the simply to very fast crystallization, although pre-
tower at 20 C. The solidified droplets (prills), cipitation is often an irreversible process, i.e.,
which leave the tower at 80 C, contain ca. 4 % many precipitates are virtually insoluble sub-
water and must be dried to an acceptable moisture stances produced by a chemical reaction. The
content at < 80 C to prevent the occurrence of products of conventional crystallization, on
polymorphic transitions (see Section 3.1). the other hand, can often be redissolved when
In a development of the melt granulation the original conditions of temperature and con-
technique for urea [81], molten urea is sprayed centration are restored. Nevertheless, precipita-
at 148 C onto cascading granules in a rotary tion and crystallization have much in common
drum and seed granules (< 0.5 mm) are thereby and are governed by the same laws.
built up to product size (2 – 3 mm). Heat re-
leased by the solidifying melt is removed pri-
8.1. Solubility Products
marily by evaporation of a fine mist of water
sprayed into air that is passed through the granu-
The solubility of a sparingly soluble electrolyte
lation drum. Problems associated with the design
in water may be expressed in terms of the con-
of prilling towers are discussed in [82], [83].
centration solubility product Kc. For example, if
such an electrolyte dissociates in solution into x
cations and y anions according to
7. Crystallization from Vapors
Mx AY xMzþ þxAz ð39Þ
In the rapidly expanding field of single-crystal þ
where z and z are the valences of the metal
growth, a tendency exists nowadays to classify cation M and the anion A, respectively, then for a
the various processes of growth from the vapor saturated solution
according to the manner in which vapor is gen-
ðcþ Þx ðc Þy ¼ constant ¼ Kc ð40Þ
erated [84], e.g., sublimation, chemical vapor
transport (CVT), chemical vapor deposition where cþ and c are the ionic concentrations.
(CVD) (! Crystal Growth, Chap. 8.). For 1 – 1, 2 – 2, etc., electrolytes (i.e., x ¼
Sublimation processes are characterized by y ¼ 1, cþ ¼ c ¼ c*, the equilibrium solubility),
vapor production resulting from heating the Equation (40) becomes
solid phase and subsequent crystallization of
the sublimate by condensation under conditions c ¼ ðKc Þ1=2 ð41Þ
In general, 8.2. Ostwald’s Rule of Stages

c ¼ ðKc =xx yy Þ1=ðxþyÞ ð42Þ Ostwald’s rule of stages, or rule of successive
For a 2 – 1 electrolyte, therefore, transformations, was originally stated as follows
[86]: ‘‘An unstable chemical system does not
c ¼ ðKc =4Þ1=3 ð43Þ spontaneously transform directly into that state
which, under the given conditions, is the most
A more fundamental approach to the solubility stable of all the possible states, but into that
product involves the use of activities rather than which most closely resembles its own, i.e., into
concentrations; the activity solubility product Ka the state whose formation from the original is
is then defined by accompanied by the smallest loss in free energy.’’
Although many exceptions to Ostwald’s rule
ðaþ Þx ða Þy ¼ constant ¼ Ka ð44Þ have been recorded and little theoretical support
where aþ and a are the ionic activities, or by has been found, it provides a useful guide to the
possible behavior of precipitating systems. The rule
ðcþ g þ Þx ðc g Þy ¼ Ka ð45Þ appears, in fact, to be a manifestation of the fre-
quently noted behavior of chemical systems that, if
where g is the ionic activity coefficient. There- more than one reaction is thermodynamically pos-
fore, sible, the resulting reaction is not the one which is
Ka ¼ Kc ðg Þn ð46Þ thermodynamically most likely, but the one with
the fastest rate. In other words, kinetics are often
where g is the mean ionic activity coefficient more important than thermodynamics [7].
and n (¼ x þ y) is the number of moles of ions Therefore, a metastable solid phase may be
produced by one mole of electrolyte. precipitated first and then, at some later stage,
In practice, Ka and Kc may be assumed equal transformed into a more stable phase. Transfor-
for concentrations up to about 103 mol/L, but mations such as those of one polymorph to
above this, significant differences can occur. another, of one hydrate to another hydrate or to
The activity of an ion depends on the concen- an anhydrous form, and of an amorphous precip-
tration of all the other ions in solution, so the itate to a crystalline phase are quite common
presence of a foreign electrolyte can greatly (Section 3.5).
influence the value for g of a sparingly soluble
salt.
A number of cases that appear anomalous 8.3. Development of Precipitates
when the simple solubility product is used can
be explained when activity coefficients are con- Precipitation, like all crystallization processes,
sidered [85]. For instance, the addition of a consists of three basic steps: (1) the creation of
common ion generally decreases the solubility supersaturation, followed by (2) the generation of
of a given salt, but cases are known in which nuclei and (3) the subsequent growth of these
addition of a common ion increases the solu- nuclei to detectable size. The kinetics of nucle-
bility of the salt. This is because a large increase ation and growth are described in Sections 4.1
in ionic concentration can bring about a reduc- and 4.2, respectively. The agglomeration of
tion in the activity coefficients. Thus, from small crystals into clusters and changes in size
Equation (45), an increase in c will result in distribution caused by ripening can also play
a decrease in cþ (i.e., precipitation of the spar- important roles in the development of a precipitate.
ingly soluble salt) if g þ and g remain fairly
constant; however, an increase in c to a value
that reduces both g þ and g must result in an 8.3.1. Ripening
increase in cþ if Ka is to remain constant. The
addition of a salt without a common ion often When solid particles are dispersed in their own
increases the solubility; this again occurs because saturated solution, the smaller particles tend to
the increased ionic concentration reduces the dissolve and the resulting solute is then deposited
activity coefficients. on the larger particles. Thus, the small particles
disappear, the large ones grow larger, and theo- rate of agglomeration of colloidal particles in
retically, the particle-size distribution should suspension was first proposed by SMOLUCHOWSKI
ultimately become monodisperse. The reason for [89]. Two types of behavior may be distin-
this behavior is that the solid phase in the system guished: perikinetic (static fluid with particles
adjusts itself so as to achieve a minimum total in Brownian motion) and orthokinetic (agitated
surface free energy. This process of particle dispersions), which can both be important in
coarsening is called ripening, or more frequently precipitation processes. In agitated precipitators,
‘‘Ostwald Ripening’’ after the first proposer of orthokinetic agglomeration becomes more im-
the mechanism [86]. portant as the particle size and the shear rate
The driving force for ripening is the difference increases.
in solubility between small and large particles, as Double-layer repulsion forces and van der
given by the size–solubility (Gibbs–Thomson– Waals attraction forces operate independently
Ostwald–Freundlich) relationship (Eq. 15), al- in disperse systems. Repulsion forces decrease
though the effect only becomes significant for exponentially over a distance corresponding to
particle sizes < 1 mm (see Section 2.2). If mass the thickness of the ionic double layer, whereas
transport occurs between the particles in a poly- attraction forces decrease, over a larger distance
disperse precipitate and if the growth kinetics are from the particle surface, as an inverse power of
diffusion controlled, all particles of size the distance. Consequently, attraction normally
predominates at very small and very large dis-
r0 ¼ 2vgc =nRT ðcc Þ ð47Þ
tances, and repulsion over intermediate dis-
are in equilibrium with the bulk solution (dr/ tances [90].
dt ¼ 0) [7]; v is molar volume, g interfacial The assessment and modeling of agglomera-
tension and n the number of ions. All particles tion kinetics in precipitation processes are dis-
smaller than r0 will dissolve (dr/dt < 0) and all cussed in [5], [91], [92].
particles larger than r0 will grow (dr/dt > 0).
The speed at which ripening occurs depends to
a large extent on particle size r and solubility. For 8.3.3. Precipitate Morphology
diffusion-controlled growth kinetics, the linear
growthvelocitymaybeexpressedapproximatelyas The morphological development of a precipitate
is a complex combination of a variety of process-
dr=dt ’ gv2 Dc =3nRTr2 ð48Þ es including nucleation, habit modification,
where D is the diffusion coefficient. However, phase transformation, ripening, and agglomera-
because ripening generally occurs at very low tion. The most influential system parameters are
supersaturation, it is more likely to be controlled supersaturation and the concentration of active
by surface reaction than by diffusion; under these impurities, although pH can also exert a profound
circumstances, ripening could be considerably effect in some aqueous systems.
slower than indicated by Equation (48). The dominant influence of supersaturation on
Analyses of ripening mechanisms have been the particle-size characteristics of a precipitate
made in [5], [87], [88]. has been summed up in the so-called Weimarn
Ripening changes the particle-size distribu- laws of precipitation [93] which, while open to
tion of a precipitate over a period of time, even in theoretical criticism, provide very useful guide-
an isothermal system, but the change can be lines for batch precipitation behavior. They are
accelerated by controlled temperature fluctua- illustrated in Figure 38:
tion. This process, known as temperature cycling,
has been utilized to alter the physical character- 1. As the concentration of reactants increases,
istics of precipitates [5], [7]. the median particle size of the precipitate
(determined at a given time after mixing
the reactants) increases to a maximum and
8.3.2. Agglomeration then decreases. As the time interval in-
creases, the maximum is displaced to lower
Small particles in liquid suspension tend to ag- initial supersaturation and higher median
glomerate into clusters. A theoretical basis for the particle size.
10-mm crystals which could, under favorable

conditions, remain discretely dispersed.
8.3.4. Coprecipitation
All precipitates are contaminated to some extent

with materials originally present in the mother
liquor. The general term coprecipitation may be
used to describe the many different types of
impurity incorporation that can occur, including
surface adsorption and lattice entrapment of
foreign ions and solvent molecules, as well as
physical inclusion of pockets of mother liquor.
Figure 38. Illustration of Weimarn’s laws of precipitation
The adsorption of salts having an ion in
2. For a completed precipitation, the median common with the precipitate roughly obeys the
size of the precipitate crystals decreases as Paneth–Fajans–Hahn adsorption rule which pos-
the initially created supersaturation S is tulates that the less soluble the salt, the more
increased. easily is it incorporated into a precipitate. For
example, barium chloride is more readily ad-
For a given system, maximum agglomeration sorbed by barium sulfate than is barium iodide,
often appears to occur at a certain level of which is more soluble than the chloride. The
supersaturation; this behavior has been linked to dissociability of the adsorbed salt is also impor-
the character of the adsorption layer surrounding tant; adsorption decreases as the degree of dis-
a growing crystal which consists of loosely sociation of the adsorbed salt increases.
bonded, partially integrated groups of the crys- The distribution of an impurity between solid
tallizing species [7]. (i.e., solid solution) and liquid phases may be
An oversimplified but graphic example of the represented by the Chlopin [95] equation:
interactive effects of supersaturation, nucleation,
x ax
and growth in the development of precipitated ¼D ð49Þ
y by
particles is given by WALTON [94], who consid-
ered the homogeneous nucleation of three differ- where a and b are the amounts of components A
ent systems at an arbitrary value of supersatura- and B in the original solid, x and y are the amounts
tion S ¼ 100 (Eq. 2). If the number of particles of A and B in the crystallized solid, and a x and
nucleated is 106/cm3, the maximum precipitated b y are the amounts of A and B retained in the
particle sizes expected for three different solu- solution. D is a distribution coefficient. Alterna-
bilities c* of 107, 104, and 101 mol/L, were tively, the logarithmic Doerner – Hoskins [96]
concluded to be 1, 10, and 100 mm, respectively. equation may be used:
Alternatively, the approximate particle size
lnða=xÞ ¼ llnðb=yÞ ð50Þ
can be estimated if the above three solutions are
all assumed to have the same concentration, e.g., The constant l has been called a heterogeneous
1 mol/L. The first (S ¼ 107) would nucleate distribution coefficient to distinguish it from
homogeneously, forming approximately 1-nm the homogeneous distribution coefficient D in
particles and producing a colloidal system (gel) Equation (49). Under ideal conditions D ¼ l.
which could remain stable for long periods be- If component A is the impurity, l > 1 indi-
fore the primary particles agglomerated. The cates that the impurity will be enriched in the
second (S ¼ 104) would also nucleate homo- precipitate; conversely, if l < 1 it will be de-
geneously, forming primary particles around pleted. The effect of precipitation rate on l is
0.1 mm which would agglomerate easily and shown in Figure 39 [94]. In enrichment systems,
develop rapidly into a conventional precipitate. l ! le ¼ De as the precipitation rate tends to
The third solution (S ¼ 10) would probably nu- zero. For fast rates of precipitation l ! 1. In
cleate heterogeneously, yielding approximately depletion systems, an analogous situation exists,
Figure 40. A typical desupersaturation curve a) Develop-

ment of nuclei; b) Induction period; c) Growth of crystals;
Figure 39. Effect of precipitation rate on the heterogeneous d) Ripening of precipitate; e) Equilibrium saturation
distribution coefficient l [94] concentration
Broken lines denote very slow precipitation; thickened line,
very rapid precipitation.
The mixing stage is followed by a time lag
with l ! ld ¼ Dd for very low precipitation (induction period) before nuclei appear, which
rates and l ! 1 for rapid precipitation. depends on the temperature, supersaturation,
Both the Chlopin and the Doerner – Hoskins efficiency of mixing, state of agitation, and pres-
relationships have been widely used to correlate ence of impurities (see Section 4.1.4). After the
the results of fractional precipitation schemes induction period, rapid desupersaturation ensues
(see Chap. 9) although neither is entirely satis- (Fig. 40), during which primary (homogeneous
factory from a theoretical point of view. and heterogeneous) and secondary nucleation
may occur together. The predominant process at
this stage, however, is growth of the nuclei. Later,
8.4. Precipitation Techniques if sufficient time is allowed to elapse, particle
coarsening may occur as a result of ripening or
8.4.1. Reaction Precipitation agglomeration.
Precipitation of solid particles resulting from
A common method for producing a precipitate is a chemical reaction between gases or liquids is a
to mix two reacting solutions together quickly to standard method for the preparation of many
create a highly supersaturated system. One prac- industrial chemicals. Precipitation occurs be-
tical difficulty, however, is to maintain reason- cause the gaseous or liquid phase becomes highly
ably uniform conditions throughout the reaction supersaturated with respect to the solid phase. A
vessel. The choice of method used to mix the crude precipitation operation, therefore, can be
reactants is, therefore, very important because transformed into a crystallization process by
zones of excessive supersaturation should not be careful control of the degree of supersaturation.
allowed to develop. The sequence of reactant Reaction precipitation – crystallization is
mixing can also be of critical importance: addi- used widely in industries where waste gases
tion of A to B to produce a precipitate C often containing valuable or noxious substances are
yields a very different product from the addition produced. For instance, ammonia can be recov-
of B to A. Factors such as the development of ered from coke-oven gases by converting it into
local pockets of reactants in nonstoichiometric ammonium sulfate via reaction with sulfuric
ratios and undesirable pH levels can have highly acid. In this case, agitation within the vessel is
detrimental effects on precipitation. effected by a combination of the vigorous nature
Primary nucleation does not necessarily com- of the exothermic reaction and air sparging. The
mence as soon as the reactants are mixed, even heat of reaction is removed by the evaporation of
when the level of supersaturation is very high. water added to the reaction zone [1].
Problems of precipitation process plant de- A further use is in the preparation of monodis-
signs are discussed in [5]. perse suspensions of pigments and polishing
agents [97], [98].
Precipitation from Homogeneous Solution.
For the purpose of gravimetric analysis, when a
solid must be efficiently separated from a liquid, 8.4.2. Salting Out
precipitation is generally carried out slowly from
dilute solution. However, substances such as the A solution can be made supersaturated with re-
hydroxides and basic salts of aluminum, iron, and spect to a given solute by addition of a substance
tin demand extremely high dilution and excessively generally referred to as the precipitant, which
long time for coarse filterable particles to be pro- reduces the solubility of the solute in the solvent.
duced. Precipitation from homogeneous solution The precipitant may be a liquid, solid, or gas. This
(PFHS) offers a useful way of overcoming these operation is known by a variety of terms, salting
difficulties [97]. out being the most common. The term watering
Briefly, the technique consists of slowly gen- out is used in the pharmaceutical industry to
erating the precipitating agent homogeneously describe the precipitation – crystallization of or-
within a well-mixed solution by means of a ganic substances from water-miscible organic
chemical reaction. Undesirable concentration solvents by the controlled addition of water. The
effects are thus eliminated, a dense granular term solventing out has been applied to the use of
precipitate is formed, and coprecipitation is min- water-miscible organic solvents to precipitate
imized. For example, silver chloride crystals can electrolytes from aqueous solution [99].
be produced from an aqueous solution of silver The properties required of a precipitant are
nitrate by reaction with allyl chloride (3-chlor- that it be miscible with the solvent of the original
opropene): solution, that the solute be relatively insoluble in
it, and that the final solvent–precipitant mixture
CH2 ¼ CHCH2 ClþH2 O!Cl þCH2 ¼ CHCH2 OHþHþ be easily separable if it contains valuable com-
Cl þAgþ !AgCl ponents. The beneficial effects of using a precip-
itant prediluted with the system solvent to avoid
An example of a PFHS reaction in nonaque- excessive nucleation and encourage the devel-
ous solution is the precipitation of silver iodide in opment of larger precipitated particles are
ethanol: described in [100].
2 C2 H5 Iþ2 AgNO3 þC2 H5 OH!2 AgIþðC2 H5 Þ2 O Salting out has many advantages. For exam-
þHNO3 þC2 H5 NO3
ple, highly concentrated initial solutions can be
made by dissolving an impure crystalline mate-
Other PFHS methods used to produce crystal- rial in a suitable solvent. If the solute is very
line precipitates by controlled generation of the soluble in the chosen solvent, dissolution may be
required anions in an appropriate aqueous solu- effected at low temperature, which is advanta-
tion include the hydrolysis of dimethyl oxalate geous when heat-labile substances are processed.
(C2 O2 3
4 ), triethyl phosphate (PO4 ), dimethyl Solute recovery is usually high. Purification is
sulfate (SO2
4 ), and thioacetamide (S2). often better than in straightforward crystalliza-
Precipitation from homogeneous solution tion because the mixed mother liquor often re-
plays an important role in modern analytical tains more undesirable impurities than the origi-
chemistry. It is also used to investigate copreci- nal solvent does. On the other hand, salting out
pitation and nucleation because the slow, con- has the disadvantage that a recovery unit may be
trolled precipitation allows a close approach to needed to handle fairly large quantities of mother
equilibrium between the solid and the solution. liquor in order to separate valuable solvents and
Industrial applications of PFHS have so far been precipitants.
limited, but it appears to be a promising tech- Several potential large-scale applications of
nique. It generally improves fractional precipita- salting out have been reported [7]. Examples
tion methods and has been applied to the difficult are the production of pure inorganic salts with
separation of radium and barium used in the liquid organic precipitants (particularly anhy-
production of carriers for radioactive materials. drous salts from aqueous solution at ambient
temperature when a hydrated species is the solution of potassium chloride [105]. Conversion
thermodynamically stable phase [101]), the to a stable salt pair occurs; the Na2SO4 and KCl
treatment of seawater with alcohols to recover remain in solution and K2SO4 precipitates.
fertilizer-grade double salts (e.g., hydrated
potassium magnesium sulfate) [102], and the
separation of inorganic salt mixtures [99], 8.5. Precipitation Methods and
[103]. Equipment
Gases or solids may be used as precipitants
provided they are soluble in the original solvent Although continuous, steady-state operation is
and do not react with the solute to be precipitated. often regarded as ideal for process plant equip-
Ammonia can assist in the production of potas- ment, this is not always true for crystallization [7]
sium sulfate by the reaction of calcium sulfate and perhaps even less so for precipitation. The
and potassium chloride: in a pure aqueous medi- advantages and disadvantages discussed in Sec-
um the yield is low, but in aqueous ammonia the tion 5.7 also apply to precipitation.
yield is greatly improved. Hydrazine acts in a Most industrial precipitation units are con-
similar manner [104]. structed simply. The main aim is usually to mix
An example of the use of a solid precipitant is reacting fluids rapidly and allow the development
the addition of sodium chloride crystals to salt of a precipitate with certain desirable physical
out organic dyes from aqueous solution. The and chemical characteristics. Good mixing is
sodium chloride acts in the solution phase, i.e., essential to smooth-out supersaturation peaks in
it must dissolve in the water present before it can local regions. Both micromixing and macromix-
act as a precipitant; its precise mode of action is ing are involved.
probably quite complex. Micromixing is concerned with mixing at or
Crystalline salts can be added to solutions to near the molecular level, and is influenced by
precipitate other salts, for example, as a result of fluid physical properties and local conditions.
the formation of a stable salt pair. This behavior Macromixing, which is concerned with bulk fluid
is encountered when two solutes AX and BY, movement and blending, is influenced by agitator
usually without a common ion, react in solution speed, vessel geometry, etc. The two types of
and undergo double decomposition (metathesis). mixing should strictly be considered indepen-
dently, but the overall effects of mixing on the
AXþBY AYþBX
precipitation process are extremely complex [5],
The four salts AX, BY, AY, and BX constitute [101], [102].
a reciprocal salt pair. One of these pairs, AX – The position of the feedstock entry point(s) can
BY or AY – BX, is stable and is composed of have a great influence on the precipitate quality
compatible salts which can coexist in solution; [7]. Several choices are available. For example,
the other salt pair is unstable and composed of if two reactant feedstocks A and B are involved, A
incompatible salts which cannot coexist. This could be fed on or near the surface of reactant B
principle is used in the large-scale production of already in the vessel. This is the so-called ‘‘single-
potassium sulfate by addition of solid glaserite jet’’ mode (Fig. 41 A). Alternatively, A could be
(3 K2SO4 Na2SO4) to a concentrated aqueous introduced into the intensely agitated zone near
Figure 41. Some possibilities for introducing reactant feedstock streams to a precipitation vessel
the impeller blades (Fig. 41 B). The latter proce- ble in the solvent than the main product is.
dure often results in the production of larger Recrystallization may have to be repeated many
primary crystals since good mixing keeps local times before crystals of the desired purity are
levels of supersaturation low at the first point of obtained. A simple recrystallization scheme is
contact between the reactants and minimizes the
nucleation rate. The sequence of reactant addi-
tions can often have a significant effect on the
characteristics of the precipitate produced, i.e.,
reactant B could be introduced as a single jet into
reactant A charged first into the vessel, if required. An impure crystalline mass AB (A is the less
Both reactant streams A and B may be intro- soluble, desired component) is dissolved in the
duced to the vessel simultaneously, in the so- minimum amount of hot solvent S and then
called ‘‘double-jet’’ mode, and again several cooled. The first crop of crystals X1 will contain
choices emerge. For example, A and B could be less impurity B than the original mixture, and B is
introduced together near the surface (Fig. 41 C), concentrated in the liquor L1. To achieve a higher
or near the impeller blades (not illustrated). On degree of crystal purity, the procedure can be
the other hand, the two streams could be pre- repeated.
mixed before entering the vessel as a single jet In such a sequence, losses of the desired
(Fig. 41 D) at some appropriate point. Premixing component A can be considerable, and the final
of feedstocks is often used because it can provide amount of ‘‘pure’’ crystals may easily be a small
a means of exerting some control over the initial fraction of the starting mixture AB. Many
supersaturation levels. Impinging jets or in-line schemes have been designed to increase both the
mixers may be used for rapid premixing. yield and the separation efficiency of fractional
recrystallization. The choice of solvent depends
on the characteristics of the required substance
9. Fractional Crystallization A and the impurity B. Ideally, B should be very
soluble in the solvent at the lowest temperature
A single crystallization operation performed on employed and A should have a high temperature
a solution or melt can fail to produce a pure coefficient of solubility, so that high yields of A
crystalline product for a variety of reasons. For can be obtained from operation within a small
example, the impurity may have solubility char- temperature range.
acteristics similar to those of the desired pure
component, and both substances consequently
cocrystallize. Alternatively, the impurity may be 9.2. Recrystallization from Melts
present in such large amounts that the crystals
inevitably become contaminated. Furthermore, a Melts can be fractionally recrystallized by
pure substance cannot be produced in a single schemes similar to those described in Section
crystallization stage if the impurity and the re- 9.1 for solutions, although a solvent is not nor-
quired substance form a solid solution (see mally added. Usually, simple sequences of heat-
Section 3.2.2). Recrystallization (i.e., repeated ing (melting) and cooling (partial crystallization)
crystallization steps) from a solution or melt is, are followed by separation of the purified crystals
therefore, widely employed to increase crystal from the residual melt. Selected melt fractions
purity. may be mixed at intervals according to the type of
scheme employed, and fresh feedstock may be
added at different stages if necessary. Several
9.1. Recrystallization from Solutions such schemes have been proposed for purifica-
tion of fats and waxes (! Waxes, Section
Most of the impurities from a crystalline mass can 4.2.3.2.) [109].
often be removed by dissolving the crystals in a As described in Section 3.2, eutectic systems
small amount of fresh hot solvent and cooling the can theoretically be purified by single-stage crys-
solution to produce a fresh crop of purer crystals. tallization, whereas solid solutions always re-
However, the impurities must then be more solu- quire multistage operations. Countercurrent
fractional crystallization processes in column Fractionation schemes are simplified when frac-
crystallizers are described in Section 6.3. tions of repeating composition recur at regular
intervals. The first fraction in the above scheme
that can have the same composition (i.e., A : B
9.3. Recrystallization Schemes ratio) as the original mixture is 2 b. In this case,
every fraction has the same composition as the
A number of fractional crystallization schemes fraction vertically above it in the scheme. Frac-
have been devised [7], [97], the triangular tion 2 b will also be identical in composition to
scheme shown in Figure 42 [110] demonstrates the original if the fraction of A which reaches that
their essential features. Individual fractions, re- point is the same as the fraction of B reaching that
presented by the circles, are designated by a point, i.e.,
horizontal row number and a diagonal column
letter. Consider the separation of two compo- 2x ð1xÞ ¼ 2y ð1yÞ ð53Þ
nents A and B: if a constant fraction of A is
precipitated at each operation and fractions are This equation has two solutions (x ¼ y and x þ
combined as in the triangular scheme, then the y ¼ 1). The first represents a line of no separation
fraction x of the original A which appears at any which, when drawn as in Figure 43, divides the
given point in the triangular scheme is given by diagram into two zones: enrichment of compo-
the binominal expansion nent B in the precipitate occurs in the upper, left-
½xþð1xÞn ¼ 1 ð51Þ
hand zone (enrichment being expressed by the
ratio y/x) and enrichment of A in the lower, right-
Similarly, for component B, where a constant hand zone. The second solution to the equation
fraction y is precipitated at each step, the distri- (x þ y ¼ 1), represented by the other diagonal,
bution of B in various fractions is given by the gives repeating compositions for fractions in
expansion the same vertical columns and also gives enrich-
ment of (y/x)n in the end fractions (column a in
½yþð1yÞn ¼ 1 ð52Þ
Figure 42. Triangular fractional crystallization scheme [110]

Figure 43. Operating curves for systems with repeating composition [110]
Curves were calculated by assuming that l ¼ 7.21; l is the heterogeneous distribution, coefficient defined in Equation (50),
Section 8.3.4.
Fig. 42). This second diagonal may be called the Of all the solvents considered in recent years
operating line for a repeating composition in as possible SCFs for crystallization processes,
fraction 2 b. Operating lines can be calculated the only two that now command any notable
in a similar manner for repeating compositions in attention are water and CO2 primarily because
the other fractions, as depicted in Figure 43 [110]. they are non-flammable, non-toxic, low-cost, and
Examples of the use of such a diagram are readily available. Of these, CO2 is attracting
described in [110], [111]. greater support on account of its more accessible
critical point (31 C and 74 bar) compared with
that of water (374 C and 220 bar).
9.4. Recrystallization from
Supercritical Fluids
Solute solubilities in supercritical fluids (SCF)

can undergo considerable changes with relative-
ly small changes in pressure, and at constant
pressure they generally pass through a minimum
with temperature. These characteristics give
the possibility of separating different solutes by
manipulating pressure or temperature in the
so-called ‘‘cross-over’’ region (Fig. 44). Rapid
depressurization, e.g., through a nozzle, creates
high supersaturation, fast nucleation and conse- Figure 44. Solubility curve minima exhibited by two differ-
quently large numbers of small crystals. ent solutes A and B in a supercritical fluid
One problem with SCFs as crystallization tity of the D and L enantiomers (melting point,
solvents is that the solubilities of most organic enthalpy of fusion, etc.) giving a eutectic of
compounds are generally low. Whilst the super- equimolal racemic composition. Separation is
saturations developed can be high when ex- effected by alternate D and L seeding. Examples
pressed as the ratio c/c* (see Section 2.2 Satura- of the crystallization procedures are described in
tion and Supersaturation) they are usually low [117]. General reviews of the industrial manu-
when expressed as a mass concentration driving facture of optically active compounds are given
force (c – c*) and the consequent low yields and in [118], [119].
productivity can make the process appear com-
mercially unattractive. Nevertheless, SCF crys-
tallization could still be profitable in, for exam- 10. Miscellaneous Crystallization
ple, the separation of isomers and polymorphs Techniques
and the purification of high-value products such
as pharmaceuticals. 10.1. Salting-Out Crystallization
Potential uses for processing with SCFs are
discussed in [112–114] and examples of explor- A solute can be deposited from solution by the
atory crystallizations using supercritical CO2 are addition of another substance (a soluble solid,
described in [115], [116]. liquid, or gas) which effectively reduces the
original solute solubility. The process is com-
monly referred to as ‘‘salting out,’’ although it is
9.5. Separation of Enantiomers and often applied to electrolytes and nonelectrolytes
Racemates alike. For convenience this topic is dealt in
Section 8.4.2.
The resolution of racemic (optically inactive)
mixtures is becoming an important operation in
the manufacture of chiral (optically active) phar- 10.2. Reaction Crystallization
maceutical and agrochemical products because
most of the specific activity usually resides pre- The production of a solid crystalline product as
dominantly in only one of the enantiomers in the the result of chemical reaction between gases
equimolal mixture. and/or liquids is a standard method for the prep-
A crystalline racemate may be either a con- aration of many industrial chemicals. Crystalli-
glomerate (a physical mixture of two enantio- zation occurs because the gaseous or liquid phase
morphs) or a racemic compound (two enantio- becomes supersaturated with respect to the
mers homogeneously distributed in the crystal reactant.
lattice). Conglomerates, the much rarer of the Reaction crystallization is practiced widely,
two types of racemate, can be separated by especially in industries where valuable waste
recrystallization from solutions or melts. gases are produced. For instance, ammonia can
Crystallization from solution is the most com- be recovered from coke-oven gases by convert-
mon procedure. A mixture of D and L enantiomers ing it into ammonium sulfate by reaction with
dissolved in a solvent S constitutes a ternary sulfuric acid [1]; sodium bicarbonate is formed
system in which the equilibria are best repre- by the interaction between brine and flue gases
sented on a triangular diagram (see Fig. 8). The containing carbon dioxide [120]. A study of the
recrystallization procedure, which is possible crystallization reaction kinetics of a range of
only for conglomerates, involves alternate se- calcium phosphates is reported in [121].
quences of seedings using crystals of pure D and L
enantiomers.
Crystallization from the melt, usually at low 10.3. Adductive and Extractive
temperature, may also be a possibility. A tem- Crystallization
perature – composition phase diagram for a con-
glomerate is the same as that for a two-compo- The simple crystallization of a binary eutectic
nent eutectic system (Section 3.2.1) with perfect system can only produce one of the components
symmetry arising from the thermodynamic iden- in pure form, while the residual mother liquor
composition progresses towards that of the eu- The method is based on the addition to a
tectic (Section 3.2.1). There is often a need, crystallizing system of a small amount of an
however, to produce both components in pure immiscible liquid that preferentially wets the
form, and one way in which this may be achieved developing fine crystals and encourages them to
is to add a third component to the system which compact into spherical agglomerates 250 –
forms a compound with one of the binary com- 1000 mm. Chloroform appears to be the pre-
ponents. A typical adductive crystallization se- ferred organic liquid for use in association with
quence would be as follows. A certain substance crystallization from aqueous solution [126].
X is added to a given binary mixture of compo- Spherical agglomerates of salicylic acid, other
nents A and B so that a solid complex, say A X, pharmaceutical substances and precipitated cal-
is precipitated. Component B is left in solution. cium carbonate have been successfully made by
The solid and liquid phases are then separated, this technique [127].
and the solid complex is split into pure A and X,
e.g., by the application of heat or by dissolution in
some suitable solvent. Urea and thiourea, for 10.6. Freeze Crystallization
example, have the property of forming com-
plexes (adducts) with a wide range of hydrocar- Crystallization by freezing, more commonly
bons. Separation processes for other organic known as freeze crystallization, is a process in
mixtures based on the formation of adducts have which heat is removed from a solution to form
been described in [122]. crystals of the solvent rather than the solute.
An alternative to adductive crystallization for Subsequent steps include separation of crystals
separating a binary eutectic mixture into its from the concentrated solution, washing the
component parts is to alter the solid – liquid crystals with near-pure solvent, and finally melt-
phase relationships by introducing a third com- ing them to generate visually pure solvent. The
ponent, usually a liquid called the solvent. This product of freeze crystallization can be either the
process is generally known as extractive melted crystals (near-pure solvent), as in water
crystallization. desalination, or the concentrated solution, as in
Both adductive and extractive crystallization the concentration of fruit juice or coffee extract.
procedures are feasible for the separation of a Freeze crystallization is applicable in principle
wide range of close-boiling organic mixtures to a variety of solvents and solutions; however,
[122], [123] and for the recovery of inorganic because it is most commonly applied to aqueous
salts from concentrated aqueous solution [124]. systems, the following account refers exclusively
to the freezing of water.
One of the more obvious advantages of freez-
10.4. Spray Crystallization ing over evaporation for removal of water from
solutions is the potential for saving heat energy:
Spray crystallization is similar to spray drying. the enthalpy of crystallization of ice (334 kJ/kg)
The shape and size of the solid particles depend to is only one-seventh of the enthalpy of vaporiza-
a large extent on those of the spray droplets. The tion of water (2260 kJ/kg). Process energy con-
spray crystallization of a solution also has some sumption, however, may be reduced below that
features in common with prilling (see Section predicted by the phase-change enthalpy by uti-
6.5). Pilot plant investigations with a wide range lizing energy recycle methods, such as multiple-
of inorganic salts are described in [125]. effect or vapor compression, commonly em-
ployed in evaporation. In freeze crystallization
plants operating by direct heat exchange, vapor
10.5. Spherical Crystallization compression has been employed to recover
refrigeration energy by using the crystals to
An interesting technique for transforming small condense the refrigerant evaporated in the
crystals into dense spherical agglomerates during crystallizer.
the crystallization process, hence the name Another advantage of freeze crystallization,
spherical crystallization, appears to have poten- important in many food applications, is that the
tial application in the pharmaceutical industry. volatile flavor components normally lost during
conventional evaporation can be retained in the Direct-Contact Freezing processes utilizing

freeze-concentrated product. In fact, freeze crys- inert, immiscible refrigerants have been investi-
tallization is used mainly in the food industry. gated widely for desalination purposes. A typical
Despite earlier enthusiasm, large-scale applica- scheme is shown in Figure 45 [129]. Seawater,
tions in desalination, effluent treatment, dilute precooled close to its freezing point, is fed con-
liquor concentration, solvent recovery, etc., have tinuously into the crystallization vessel where it
not yet emerged. comes in direct contact with a liquid refrigerant
All freeze separation processes depend on the (e.g., n-butane) which vaporizes and causes ice
formation of pure solvent crystals from solution, crystals to form due to the exchange of latent
as described for eutectic systems in Section 3.2.1; heat. The ice–brine slurry is fed to a wash column
this allows single-stage operation. Solid-solution where it is washed countercurrently with fresh
systems, which require multistage operation, are water. The emerging brine-free ice is melted by
not usually handled. Several types of freeze the enthalpy of vapor condensation released from
crystallization can be designated according to the compressed refrigerant. Energy input is re-
the kind of refrigeration system used. quired for the compressors.
Indirect-Contact Freezing. In indirect-con- Vacuum Freezing processes do not require a

tact freezing, for instance, the liquid feedstock is conventional heat exchanger, and the problems
crystallized in a scraped-surface heat exchanger of scale formation on heat-transfer surfaces
(Section 6.1) fitted with internal rotating scraper are avoided. Cooling is effected by flash-
blades and an external heat-transfer jacket evaporating some of the solvent when the liquid
through which a liquid refrigerant flows. The feedstock enters a crystallization vessel main-
resulting ice–brine slurry passes to a wash col- tained at reduced pressure. Vacuum freezing is
umn where the ice crystals are separated and potentially attractive for aqueous systems (7 kg
washed before melting. One of a number of of ice can be produced for every kilogram of
commercial systems based on this type of freez- water evaporated) but has not yet achieved
ing process is described in [107]. commercial success.
Figure 45. Desalination of seawater by freezing [129] a) Washer–melter; b) Scraper; c) Wash column; d) Screens; e) Decanter;
f) Heat exchanger; g) Compressor; h) Crystallizer
A general review of freeze concentration as an 11 H. Stephen, T. Stephen: Solubilities of Inorganic and

industrial separation process is given in [130]. Organic Compounds, Pergamon, London 1963.
The potential of freeze crystallization in the 12 M. Broul, J. Nyvlt, O. S€ohnel: Solubilities in Binary
Aqueous Solutions, Academia, Prague 1981.
recycling and reuse of wastewater is reviewed
13 J. W. Mullin, O. S€ohnel, Chem. Eng. Sci. 32 (1977)
in [131]. The kinetics of ice crystallization in 683 – 686.
aqueous sugar solutions and fruit juice are 14 Wilhelm Ostwald, Z. Phys. Chem. (Leipzig) 34 (1900)
described in [132], [133]. 493 – 503.
The subject of gas hydrates has become highly 15 H. A. Miers, F. Isaac, J. Chem. Soc. 89 (1906) 413 – 454.
topical in recent years [134], particularly since 16 H. Feilchenfeld, S. Sarig, Ind. Eng. Chem. Process Des.
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(1982) 1083 – 1098.
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Article No : b02_03

published online 15 JAN 2003

Crystallization and Precipitation

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . 582 5.7. Comparison of Batch and Continuous

2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Symbols N: impeller rotational speed, Hz

1. Introduction zation is increasingly employed in the production

However, if the composition is expressed as In practice, however, supersaturation is generally

Alternatively, supersaturation can be expressed

and Equation (9) becomes

For low supersaturations (sa < 0.1), the follow-

If the solute particles dispersed in a solution are 3. Phase Equilibria

point. Polymorphic transformations are further

3.2. Two-Component Systems

Three variables (temperature, pressure, and con-

At a given temperature, the more stable phase

component B in system AB is plotted as the

melting and crystallization occur without any

3.3. Three-Component Systems

The phase equilibria in three-component (tern-

M binary eutectic A. Similarly, curves BD and

eutonic point or drying-up point of the system.

melting of systems represented by points in other 3.4. Multicomponent Systems

may also crystallize in the form of different

can be justified is a simple empirical relationship

which relates the primary nucleation rate J to

4.1.2. Secondary Nucleation

Secondary nucleation, by definition, can take

data truly represent homogeneous nucleation,

Figure 14. Interfacial tension as a function of solubility [37]

where D is the diffusion coefficient, v the molar

Figure 16. Spiral (BCF) crystal growth beginning at a screw dislocation

Figure 18. Equipment for measuring the growth of a single

where L is some characteristic dimension of the

For spheres and cubes, 6 a/b ¼ 1.

4.2.3. Dependence of Growth Rate on

A considerable amount of experimental evidence

Figure 20. Complex interactions in a continuous crystallization process

flat sucrose crystals from beet sugar feedstocks),

ble or latent heat. The coolant may or may not boil

1. Immiscible, boiling, solid or liquid coolant:

Crystallization processes employing DCC

5.2. Evaporating Crystallizers

If the solubility of a solute in a solvent is not

Figure 25. Swenson draft-tube-baffled (DTB) crystallizer

liquor level in the crystallizer. Hot, concentrated

solution, C; C is the specific heat capacity of the

5.6. Controlled Crystallization

Carefully selected seed crystals are sometimes

5.7. Comparison of Batch and

Although continuous, steady-state operation is

further crystallization occurring in other parts of mixed-product removal) crystallizer operated

5.8.1. Population Balance Experimental measurement of crystal size distri-

This interesting relationship [36] enables the effect

5.8.2. Design and Scaleup Problems

Industrial crystallizers are commonly designed

oratory tests and employed to facilitate process

6.2. Multistage Processes

The single-stage crystallization described in