INDUSTRIAL CRYSTALLIZATION FROM SOLUTION · crystallization in the chemical industry and most of the sepecific examples will be drawn from applications involving crystallization from

Chemical EitgMring Schtce, Vol. 40, No. 1. pp. 3-26. 1985. F%inted in Great Britain.

ow-2509/85 s3.00 + 0.00 PergnmOP Press Ltd.

REVIEW ARTICLE NUMBER 15 INDUSTRIAL CRYSTALLIZATION FROM SOLUTION

JOHN GARSIDE Department of Chemical Engineering, University of Manchester Institute of Science and Technology.

P 0 Box 88, Manchester M60 lQD, England

(Receiued 15 March 1984, accepted 18 May 1984)

Abstract-This review approaches crystallizer perfo rmance from a reaction engineering viewpoint in which emphasis is placed on the interaction of crystallimr fluid mechanics and residence time distributions with the physical chemistry of nucleaton and growth kinetics to produce the crystal size distribution within a crystallizer. The present state of knowledge in these various areas is assessed. particular attention being paid to work carried out over the past decade. Great advances have been made during this period but significant gaps in our understanding still exist, particularly in the areas of crystallizer fluid mechanics (especially the role of micromixin g), primary nucleation, habit modiiication, comparison of predicted crystallizer performance with actual operating characteristics, and the control of full scale crystallizers.

CONTENTS 1. Introduction

2. Crystallizer Fluid Mechanics 2.1. Liquid phase mixing 2.2 Crystal suspension and residence time distribution

3. Nucleation Kinetics 3.1 Primary nucleation 3.2 Secondary nucleation 3.3 Scale-up of contact secondary nucleation

4. Growth Kinetics 4.1 The crystal surface 4.2 Crystal growth kinetics 4.3 Solution supersaturation 4.4 Convection and crystal growth 4.5 Growth rate dispersion

5. Crystallizer Performance 5.1 Mixed suspension mixed product removal (MSMPR) crystallizer 5.2 Steady state continuous operation 18 5.3 Unsteady state continuous operation 20 5.4 Batch operation 21 5.5 Crystallizer design 21

6. Conclusions 21

Notation 22

References 23

1. IN-l-RODUCl-ION

This review is primarily concerned with the use of crystallization in the chemical industry and most of the sepecific examples will be drawn from applications involving crystallization from solution. Although melt crystallization is becoming of increasing importance, particularly in cases where considerable energy savings are possible, the chemical engineering description and characterization of melt processes is at a much earlier stage of development. Nevertheless the basic principles underlying melt crystallization are similar to those outlined in this paper and significant developments may be expected over the next decade.

and a separation process extends far outside the traditional chemical industry. For example the recent spectacular advances in microelectronics have been made possible in part because of the ability to grow single crystals of precisely controlled composition and structural perfection. To make these advances it has been necessary to understand the basic physics of crystal growth and to solve engineering aspects of the associated fluid mechanics and heat and mass transfer processes, subjects at the heart of chemical engineering.

The use of crystallization as a purification technique

Crystallization in the chemical industry is of enor- mous economic importance. World wide production rates of basic materials such as sucrose, sodium

3

8

t 10

11 12 13 13 14 15

16 17

3

4 JOHN GARSIDE

chloride, and many fertilizer chemicals (potassium chloride, urea, ammonium phosphates, ammonium nitrate, etc.) all exceed lo6 tonnes per annum [l] and in the manufacture of all of these chemicals crystallization is an important processing step. Many low- output high added-value products such as phar- maceuticals, dyestuffs, catalysts and proteins are also subject to crystallization steps during processing.

Our understanding of the factors affecting the performance of crystallizers has increased enormously over the last two decades and, as will become apparent, this largely stems from the adoption of a “chemical reaction engineering” approach to what was previously seen as an isolated unit operation. This review attempts to s ummarise our present understanding of the factors affecting crystallizer design and performance. It will concentrate on advances made over the past 5 or 10 years during which time several general reviews have appeared, e.g. [2--S] and the proceedings of three important international symposia [6-43] and three AIChE Symposium Series volumes on Crystallization [P-11] have been published. The present work will aim to be indicative of current research and progress rather than to be encyclopedic.

lizer configurations had been derived previously [14-161 the need for this additional conservation law was first formal&d in general chemical engineering terms by Randolph and Larson [17] and brought to maturity with the subsequent publication of their book [lS]. Randolph 1191 has discussed some.of the his- torical aspects of this work and recent developments will be considered further in Section 5 of the present review.

Levenspiel[12] has suggested that a framework for understanding the behaviour of chemical reactors is provided by the simple outline in Fig. l(a). The corresponding scheme for crystallizers, Fig. l(b), was originally outlined by Randolph [13] in a somewhat different form. The similarities are obvious but it is the recognition of three key features that has enabled crystallization to be put on a sound “reaction engineering” basis:

(1) Since crystallization is a particulate process a population balance must be developed in addition to the usual mass and energy balances. Although the form of crystal size distribution (CSD) from simple crystal-

Input I I

(2) The mechanisms underlying the kinetic processes are now more clearly understood. This is particularly true of nucleation, and the realization that secondary contact nucleation plays a dominant role in many crystallizers has led to a breakthrough in describing the effect of crystallizer hydrodynamics. In contrast to reaction engineering two distinct kinetic processes are involved-nucleation and growth. This is a consequence of the particulate nature of crystallization in which the formation of new particles (nucleation) is followed by their subsequent growth.

(3) The third key feature follows naturally from the other two; interactions between the kinetics, process flows or fluid mechanics and the CSD dominate much of crystallizer behaviour.

The last of these features can be best illustrated by the diagramma tic representation in Fig. 2. A somewhat simplified version of this was first introduced by Randolph and Larson in their pioneering paper [ 171 to illustrate the feedback relations that exist in all crystallizers. The pivotal role of fluid mechanics is clear and the various feedback relations which make the control of crystallizers so challenging are emphasised. This diagram will be used as a basis for the remainder of this review and the contents of the various sections are indicated in Fig. 2.

ptput Y Heactor I -z

Ial

Input _

4 Chemical Kinetics mass transfer

heat transfer

Contacting

Chemical reactor (after Levenspiel 11211

Fig. 1. A framework for describing crystallizer behaviour.

Industrial crystallization from solution

V rration

< 2’ pd-ian 5. cry&ol

h size IZer mechanics distribution

I 1\

, crysmlli ri _j+q I

I

Total crystal <

mass

I 1 Total

) L.cirow+h kinetics

Product

Fig. 2. Interactions influencing crystallizer behaviour.

The emphasis in this paper is therefore on the “population balance” approach to a description of crystallization processes. This reflects the widespread adoption and success that this approach has achieved through its ability to predict the detailed interactions between the conservation laws, rate equations and fluid mechanics of the system. Two other approaches have developed in parallel; those of Nyvlt and his group in Czechoslovakia which are well documented in two hooks [3,20] and of the Iapanese group of Toyokura to which a recent paper forms a good introduction [21].

2. CRYSTALLKZER FLUlD MECHANICS

The central role of fluid mechanics in determining the performance of a crystallizer is clear from Fig. 2. The influence of fluid mechanics on the two kinetic processes can be considerable but since these effects are closely connected with the mechanisms of secondary nucleation and of crystal growth their consideration will be deferred to Sections 3 and 4 respectively. This section will concentrate on the mixing characteristics of the liquid and solid phases.

Experimental studies in continuous laboratory crys- tallisers, which are generally performed to determine system kinetics, tend to obscure mixing effects. In such experiments special efforts are made to ensure that the residence time distributions of both liquid and solid phases conform to back-mix conditions (in which the slurry is well mixed) and to achieve representative continuous removal of slurry from the crystallizer. This so-called mixed suspension mixed product removal (MSMPR) crystallizer can be easily analysed and it forms a reference case with which other crystallizers can be compared; it will be considered

further in Section 5. Large-scale crystallizers do not in general exhibit such easily defined behaviour.

2.1 Liquid phase mixing Supersaturation can be produced within a crystal-

lizer in one of four ways; cooling,_ evaporation, addition of a third component to change the solubility of the solute, or reaction. In all these cases generation of supersaturation is achieved locally within the crystallizer, at heat transfer surfaces, boiling liquid surfaces or near the addition point of a third component or reactant(s). Spatial variations in this locally generated supersaturation would be expected to be significant if the circulation time within the crystallizer is long compared to the time required to deplete a significant part of this supersaturation by growth or nucleation.

The possibility that liquid phase mixing may be important has been largely ignored although in- homogeneities in the liquid phase clearly exist in many large crystallizers [22,23-J. Calculations in two recent papers [24,25] have however indicated that the supersaturation can decay very rapidly. That this is so for a number of different systems can be shown using an approach similar to, but rather more general than, that developed by these authors.

The rate of depletion of supersaturation (expressed in terms of the concentration driving force AC) in an element of slurry under plug flow conditions is

dAc -e- = A,R,.

dt (1)

If the overall growth rate is given by

R, = KcAcg (2)

then for constant e and A, it can be easily shown that if

6 JOHN GARSIDE

AC = Aci at time r = 0, the time variation of AC is

and

AC = Aci exp ( - K, A,t/e) for g = 1 (3)

AC’-’ = AC! -*+ (g - l)K, Art/e for g # 1. (4)

Defining now a supersaturation half-life ~~~,r,~ as the time at which AC = Aci/2 gives

and

t&.,,* -O&/&A, for g = 1 (5)

t&J/2 = (2’_’ - l)e/@ - l)K,Acf-‘AT for g # 1 (6)

t&,,/, provides a measure of the time taken for a significant depletion of supersaturation to occur. If the crystal surface area is characterised in terms of the equivalent spherical diameter L, of the size distribution then

A, = 6%/L, PC. (7)

Table 1 provides some estimates oft&, 1,2 for a number of different systems for which growth kinetics are available (in a number of cases the value of K, has had to be converted from that given in the original paper to provide data in a uniform set of units). The values would be lower for denser crystal beds (i.e. higher MT and lower e), for a smaller average crystal size, or for higher growth rate constants such as would be favoured by higher temperatures. In general th,t,2 appears to vary from a few seconds to several minutes.

A measure of the time taken for a given element of solution to circulate round the crystallizer is the mean circulation time, tc, which is usually estimated from the ratio of the total slurry volume to the circulation rate. Middleton [31 J has shown that tc can be much greater than this for stirred, baffled tanks larger than about 0.2 m3 capacity and suggested the empirical equation

in which the tank volume V is expressed in m3. Assuming a liquid depth equal to the tank diameter, a stirrer diameter one-third the tank diameter and a stirrer tip speed of 3 m/s, eqn (8) predicts circulation times of u 35 and - 0.2 s in tanks of diameter 3 m ( V = 21 m3) and 0.2 m ( V = 6.3L) respectively.

Comparison of these estimates for th,,,r and rC indicates that in many instances the supersaturation decay in large vessels is significant. Two implications follow: first, design procedures based on the assumption of good mixing in the liquid phase and constant nucleation and growth rates throughout the vessel volume may be in serious error; second, actual crystallizer volumes may be considerably in excess of those required to achieve required production rates.

Poorly designed liquour flow patterns can also reduce the efficiency of heat transfer processes in evaporative crystallizers as has been demonstrated by Asselbergs et al. [32] on a pilot-scale salt evaporator. With external circulation of magma through a heat exchanger, some of the returning liquor can flow directly to the bottom outlet of the evaporator rather than rising to the boiling zone. The temperature in the liquid flowing through the heat exchanger is thereby raised and the temperature driving forces for heat transfer are reduced. It was suggested that an internal circulation evaporator, in which the main flow direc- tions are vertical rather than horizontal, had significant advantages over the external systems.

Liquid phase mixing is also of great importance in precipitation processes where relatively insoluble materials are produced. Supersaturation is usually generated by adding one or more liquid streams to a stirred tank, the process frequently being operated on a batch basis. Because the material being precipitated under such conditions has a very low solubility, extremely high local supersaturations can be produced at the point where the feed streams mix. Values of lo* times the solubility have been quoted [33].

A number of studies with silver halide [3335] suggest that in the region adjacent to the mixing point very high supersaturations exist, so producing large numbers of nuclei up to perhaps 0.1 ,um in size. These nuclei are swept into the bulk of the vessel where the prevailing level of supersaturation is much lower. The Gibbs-Thomson equation predicts that at the lower supersaturation levels in the bulk of the vessel very small crystals will dissolve and so provide solute for the further growth or “ripening” of larger crystals. As a result two size classes of crystals are present in the precipitate; fine-grain nuclei are produced at a steady rate, always being formed at the same size unless conditions are changed, while a coarser-grain wm-

Table 1. Estimated supersaturation half-lives

Data Temperature Solute ref. (“C)

KG fAc l/Z 9 [kg/m’ s(Wm3)~l (Lt&‘I 6)

NaCl Es;; g 1.0 1.0 x 10-a 4.8 (NI-USO, 1.0 4.4 X 10-S - 11 &SO, 2.0 4.9 x 10-h 4.0 41 K alum

[El Z 1.5 5.8 x 1O-6 4.0 57

Sucrose c301 51 1.0 2.5 x 10-e - 190

Data used for all systems: MT = 100 kg/m3 slurry] L, = 0.3 lnm PC = 2000 kg/m3 e = 0.8

A, = lo3 m2/m3 slurry.

Industrial crystallization from solution 7

ponent grows continually with time to larger grain crystals smaller than a fines removal size L, were sixes [33]. assumed to have a residence time tF where

Changes in the hydrodynamics would be expected to alter the relative sixes of the two zones within the precipitator and there is some experimental evidence for this [35].

In a much earlier theoretical study Becker and Larson[36] considered a number of concepts that have been used to describe mixing in reactors and attempted to apply them to the prediction of crystal size distributions. Combinations of well-mixed and plug flow regions were discussed as was the possibility of using the concept of different degrees of segregation. The resulting equations were difficult to handle and there has been little further development in this field although recently Pohorecki and Baldyga [37,38] adapted a diffusional model of micromixing [39] to evaluate the influence of mixing intensity on the rate of precipitation and particle size distribution. Numerical results obtained for the case of an instantaneous ionic reaction showed that very large effects were possible.

R = T/T~. (91

For enhanced fines removal, R > 1. Similarly variations in the removal rate at larger sixes was accounted for by writing

z = r/rp (101

for L > L,, the classification size, where again z > 1 if the larger crystals are removed preferentially_ The discontinuities in behaviour at L, and L, are probably unrealistic in most practical cases but the resulting expressions for crystal size distribution are easy to handle and there is good experimental evidence that real size distributions sometimes conform closely to the theoretical predictions [48,49].

2.2 Crystal suspension and residence time distribution The distribution of crystals throughout a crystallizer

has received considerable attention, in part because non-uniform distribution of solids can have a considerable effect on the crystal size distribution. The conditions required to keep solid particles in suspension have been studied frequently but most work has been concerned with tanks of very simple geometry. Thus the well-known correlation of Zwietering [40] and its subsequent modifictions [41,42] only apply to flat-bottomed tanks with impeller agitation. Musil and Vlk [43,44] have however studied the conditions required to suspend particles in vessels with conical bases and in crystallizer-like tanks both with and without a draft-tube. Subsequent correspondence [45,46] clarified some of the theoretical concepts involved.

A smooth continuously-varying function is generally a better representation of the gradual size classification that occurs in most crystallizers. Both Janse and de Jong[50] and Boume [23] have developed the concept of size-dependent removal of product crystals using a separation coefficient based on particle mass concentration [SO] or a classification function defined by c231.

p(L) = z = 2 ‘F fL)

n,, the number density of particles in the product stream, is thus p times the number density in the well mixed region of the crystallizing vessel while r(L) is the size-dependent residence time of the particles.

Aeschbach and Boume [47] devoted considerable effort to defining conditions that produced homogeneous suspensions and representative continuous removal of product crystals from laboratory stirred tank crystallizers. They found that conventional tanks were incapable of achieving homogeneity; fines were washed out preferentially while the largest particles tended to sediment. This internal classification was the cause of instability in the CSD during continuous crystallization as will be further discussed in Section 5. Scale-up experiments showed that constant tip speed was the relevant criteria for the achievement of a homogeneous suspension.

The R -z model of Randolph and Larson can be simulated by writing p(L) = R for L < L, and p(L) = z for L > L, as shown in Fig. 3. Examples of experimental data showing various forms of size- dependent removal rates are also shown. The two lower curves correspond to settling of larger particles which then become less likely to leave the vessel through an off-take situated in the upper part of the tank wall; larger crystals are preferentially retained [51]. Decrease in the stirrer speed accentuates the degree of classification and so p(L) decreases. The other curve represents enhanced removal of crystals smaller than about 500 pm while larger crystals are again preferentially retained in the vessel [47]. Janse and de Jong [SO] have also measured solids segregation effects and found that large changes in the concentration of removed solids could be produced by simply changing the depth to which the off-take tube is inserted into the crystallizer.

Variations of crystal residence time as a function of crystal size within continuous crystallizers may be introduced deliberately as in both fines dissolution and product classification devices, or it may occur as a result of inadequate agitation, short circuiting, poor design of the off-take, etc. Randolph and Larson [ 18) developed a simple way of incorporating these variations into a description of the resulting CSD. All

The classification function for a particular vessel under given agitation conditions can be determined from wash-out tests [23] but the use of inert particles such as glass beads to simulate suspension characteristics of crystals may produce misleading information. Boume and Zabelka [Sl] have shown that it is not suflicient simply to match the settling velocity of particles to the settling velocity of the crystals; particles of the same settling velocity but different size produce suspensions of different qualities. It was speculated that this effect arose because particles of different size

JOHN GARSIDE

C

m and Borne IL71 R-z model 1181 with enhanced removal of both fine and large crystals

1 LF L ? Crystol size , L

Fig. 3. Examples of the classificaGon function p(L)_

projected through the boundary layer near the vessel base to different extents.

Once p(L) is known the population balance equation (42) can be integrated to obtain the CSD. The empirical relation

l+aL’ P(L) = 1 (12)

has the properties p(L) + 1 as L -+ 0; p(t) + a/b as L ~oo;dp(L)/dL-,OasL-,OandL~oo.Itappears to fit some experimental data reasonably well [52] and has the advantage that analytical solutions for the resulting population density distributions are possible as will be discussed below.

New designs of commercial crystallizer frequently have, as a novel feature, innovations in the fluid mechanics of the crystal suspension. In the “turbulence crystallizer” for example suspension of large crystals is encouraged while at the same time contacts between crystals and the impeller are minimized [53].

3. NUCLEATION KINFTICS During the course of a crystallization new particles

are born into the size distribution by nucleation processes; gross crystal breakage is usually of little or no significance. The nucleation rate, which appears as a boundary condition at L = 0 in the population bal-

ance equation, is generally the dominating factor influencing the crystal size distribution. Nucleation is also the least understood of the two rate processes involved in crystlflilntion and the most difficult to describe by well-founded kinetic expressions.

As summarised in Fig. 4 (after Botsaris [54]) three main categories of nucleation can be distinguished, primary homogeneous, primary heterogeneous and secondary. !?+econdary nucleation can be further sub- divided as will be discussed in Section 3.2. The mechanisms governing these three types are all different, the resulting rate equations have correspondingly different forms and their relative importance varies with the particular crystallization operation and perhaps even with spatial position within a given crystallizer.

3.1 Primary nucleation Classical theories of primary, or spontaneous,

homogeneous nucleation assume that in supersaturated solutions solute atoms or molecules combine in a series of bimolecular reactions to produce ordered aggregates or “embroyos”. The overall free energy of these embryos goes through a maximum at some critical size which can be shown to be inversely proportional to the logarithm of the solution supersaturation [SS]. Embryos larger than this critical size will decrease their free energy by further growth; they

Nucleation in absenw of solid interface

a homogeneous primary

ol- spontaneous

foreign interface -heterogeneous Nucleation In presence of solid interface

crystal of solute opporent

> secondary T true k contact

Fig. 4. Classification of nucltation mechanisms.

Industrial crystallixation from solution 9

are “stable nuclei” and grow to form macroscopic crystals. Formation of new nuclei is determined by the rate at which embryos surmount the maximum in the free energy curve and the resulting nucleation kinetic equation is of the form

B = C, exp G v: - T3 (In S)2 1 ’

The primary nucleation rate is therefore highly non- linear in solution supersaturation, being near-zero for low values of S (the metastable region) but increasing extremely rapidly once some critical supersaturation is reached (the labile region). The boundary between the two regions is commonly called the metastable limit.

Most primary nucleation that occurs in practice is likely to be heterogeneous, i.e. induced by surfaces other than that of the solute. This may require significantly lower supersaturations than homogeneous nucleation and so the width of the metastable zone is usually reduced. Nucleation on a foreign surface will in general require a lower free energy change than that necessary to induce nucleation in the bulk solution and although the exact mechanism by which this occurs is unclear, it is thought to be the result of a local ordering process brought about by interactions across the interface [56]. The rate equation appears to be of similar form to that of eqn (13) but the catalytic effect of heteronuclei reduces the critical supersaturation at which a rapid increase in nucleation occurs and which defines the limit of the metastable zone.

Because of the form of the kinetic equation, primary nucleation would be expected to dominate at high supersaturations. Such conditions are characteristic of precipitation processes where relatively insoluble materials are produced as a result of mixing two or more reactant streams. Local regions of high supersaturation are also sometimes found when crystallizing relatively soluble materials, points such as cooling surfaces, vessel walls where lagging is inadequate, and boiling surfaces being particularly vulnerable.

Attempts to measure primary nucleation kinetics are fraught with difficulty, in large part because the specific mechanisms that contribute to the overall rate in any situation are extremely hard to define. The critical supersaturation at which the primary nucleation rate increases rapidly (the metastable limit) is comparatively easy to detect experimentally and attempts have been made to use this point to verify the form of the kinetic equation [57], to estimate surface energies [SS] or to deduce kinetic information C59-611. Un- fortunately in all such experiments the nucleation process is followed by growth of the newly-formed nuclei before crystals can be detected. A number of authors have attempted to incorporate details of this growth process into the analysis [6265] but the assumptions made in each of these analyses are rather different and no unambiguous approach appears to be available. Further the actual method of detecting the metastable limit depends on the technique adopted and Mullin and Jan& [65] demonstrated how results

using two detection methods could be reconciled given a knowledge of the growth kinetics.

Because the theoretical basis for primary nucleation is so difficult to adapt to practical situations progress in this area is likely to be slow and experimental data will probably continue to+be interpreted in terms of the highly idealised basic concepts. described here.

3.2 Secondary nucleation The occurrence of secondary nucleation depends on

the presence of existing solute crystals in the solution and so secondary nucleation may be formally defined as “nucleation which takes place only because of the prior presence of crystals of the material being crystallized” [66]. Recent reviews [66,67] have emphasized that secondary nuclei can originate from a number of different sources and the division of the phenomenon into three separate categories, apparent, true and contact secondary nucleation (see Fig. 4) is a reflection of these origins.

Apparent secondary nucleation is a somewhat trivial case and refers, for example, to the small fragments washed from the surface of a dry crystal when it is introduced into solution. The only industrial crystallization operation where such a mechanism could be important is when crystallizers are seeded with fresh material as is sometimes practiced in batch- crystallixation.

In true secondary nucleation the presence of solute crystals is envisaged to disturb the steady state distribution of the ordered aggregates or embryos present in the solution [68]. Under such conditions introduced embryos smaller than the critical size can apparently survive and become nuclei and at low supersaturations where primary nucleation is negligible the periodic addition of only subcritical clusters can induce nucleation at observable rates.

Contact secondary nucleation has been more widely studied than the other categories. Bennett [69] has pointed out that Young [70] made reference to a similar phenomenon in 1911; it has recently been the subject of a review paper [71]. Contacts between a growing crystal and walls of the container, the stirrer or pump impeller, or other crystals result in the formation of contact nuclei. Present evidence suggests that this is the most significant secondary nucleation mechanism in crystallizers handling materials of high or moderate solubility and the mechanisms contributing to the overall contact secondary nucleation rate in operating crystallizers are becoming clear. Nucleation mechanisms in precipitation systems are less well understood.

The empirical evidence pointing to the importance of contact secondary nucleation in crystallizers is contained in the influence of three operating variables; the supersaturation, the magma density and the fluid mechanics interactions. These effects can be expressed through the power law relation

B oc AC” M;N’ (14) in which N (a stirrer or pump rotation rate) is used as a

10 JOHN GARSIDE

measure of the fluid mechanics phenomena. Typical values of b lie between about 0.5 and

2.5 [71]. These are much lower than the values that would be found if the primary nucleation rate (eqn 13) was approximated by a power function of AC. The influence of magma density points directly to the importance of particle concentration. Most values ofj are close to unity [71,72] suggesting the dominance of collisions between crystals and stirrers or vessel walls rather than between two crystals, although occasion- ally much lower values ofj have been reported, e.g. 0.4 for potassium sulphate [73] and 0.14 for potassium chloride [74]. Specific values of h are predicted by various semi-theoretical models of contact secondary nucleation rates in crystallizers (see Section 3.3) and although measured values range from 0 to about 8 [72] most are between about 2 and 4 as suggested by these theories. Primary nucleation rates can also be increased by mechanical energy inputs to the system but one way to distinguish between the two modes of nucleation is to cover surfaces within the crystallizer with a soft coating or replace a metal agitator with one made of softer material. If these changes reduce the nucleation rate then collision nucleation is strongly suggested. Several such studies [75-783 have been reported and in all cases significant reductions in the nucleation rates have been observed.

Much work has been directed at clarifying the mechanisms contributing to contact secondary nucleation. A series of elegant experiments by Denk and Botsaris [79] made use of the left- and right-handed optical properties of sodium chlorate to distinguish between nuclei originating from a parent crystal and from the solution. They showed that under a wide range of conditions nuclei originated from the crystal surface rather than from the solution. Many investi- gations in the late 1960s and 1970s were directed at defining the inffuence of supersaturation, impact energy and contact frequency on the number of crystals resulting from contact secondary nucleation [71,80]. Direct observation of micro-attrition at a crystal surface was first reported in 1978 [Sl]. Large numbers of particles were shown to be produced directly into size ranges between 1 and 10 pm with some larger fragments up to 50 pm. The size distribution of such fragments has also been measured [82,83]. This distribution and the total number of crystals depend on the solution supersaturation; at higher supersaturation more larger fragments (or “nuclei”) are produced although the number smaller than about 5 pm is relatively independent of supersaturation.

These effects of supersaturation imply that contact secondary nucleation results from a more complicated process than straightforward attrition and many authors have speculated about the actual mechanism involved. Strickland-Constable [84] suggested that the “mosaic structure” of the crystal provides the basic fragments. During a collision plastic deformation of the crystal takes place, stresses build up at the surface and large numbers of particles corresponding to the

mosaic structure but modified by the deformation are produced. The modulus of elasticity and the elastic limit of the material may now be seen as possible important parameters determining the nature and extent of plastic deformation and the initiation of brittle fracture. The influence of fluid shear is unclear although there is substantial evidence that such forces can initiate secondary nucleation, e.g. [U--88]. Considerable hydraulic forces may build up im- mediately before a solid object touches a crystal and when the object retreats vigorous vortices may be produced causing cavitation adjacent to the crystal surface. Solution inclusions may also play a role since they promote weak points in the crystal.

Secondary nucleation mechanisms are still an active area of research and one specific application related to the separation of multiple solutes has been suggested [89]. The consequences of secondary nucleation however still have to be quantified in terms of empirical power law expressions such as eqn (14). It should also be mentioned here that the presence of growth rate dispersion greatly complicates the interpretation of secondary nucleation kinetic measurements; this point will be returned to in Section 4.5.

3.3 Scale-up of contact secondary nucleation The ultimate objective of the work discussed above

is to enable crystallizer design and operation to be put on a more rigorous basis. The overall nucleation rate in a crystallizer is determined by the interaction of the secondary nucleation characteristics of the material being crystallized with the duid mechanics of the crystal suspension. Changes in agitation levels, flow patterns and crystallizer size for example will all modify the nucleation rate.

A number of authors [69,9&93] have developed mechanistic descriptions of the processes causing contact secondary nucleation in agitated crystallizers. The energy and frequency of crystal collisions are determined by the fluid mechanics of the crystallizer and crystal suspension and can be represented by a different function to that describing the number of nuclei produced by a given contact. So, following Botsaries [66],

B = J~,F, F,. (15)

The processes described by eqn (15) are represented diagrammatically in Fig. 5. Et gives the rate of energy transfer to the crystals. If this is produced by crystal collisons then

A$ = f

O3 E(L)w(L)n(L)dL. (16) 0

The product of the collision energy E(L) and collision frequency w(L) is integrated over all crystals in the distribution to obtain the total rate of energy transfer. Different approaches have been used to estimate E(L) and o(L).

F, is a production function giving the number of particles generated per unit of transferred energy while F2, a survival function, represents the fraction of these

Induskxl crystallization from solution 11

..o-.: injected .d;‘.b -iv01

into ; -*- -. I - on / sdution m-&r_ 0 0

energy _ kcdact a- fluid shear)

ct Irate of energy tmnsfw I

5 1 production

functitnl~

‘=2 t survival

function)

Fig. 5. Secondary nucleation in crystallizers (after Botsaris C541).

particles that survive to become nuclei and subsequently grow to populate the size distribution. F1 depends on the particular crystallizing system and on the supersaturation, temperature and impurity level. F2 is related to the size of the fragments and their growth characteristics. At present these two functions cannot be determined separately but are combined and written as a simple power function of the supersaturation or concentration driving force that must be determined experimentally.

As shown by Garside and Davey [71] all the various approaches lead to rate equations that can be written in the form

B = K,f (Geom) AC* Ml Nh (17)

(see eqn 14) in which f(Geom) is a function of the geometry and size of the crystallizer and agitator. For crystallizers of similar geometry and of size defined by a length scale 1 eqn (17) can be written

B oc ildAcbMjNA. WI

Values of f(Geom), d, j and h as given by three approaches are summarised in Table 2.

A number of different criteria have been proposed for the scale-up of secondary nucleation rates, for example constant specific power input i?, constant stirrer speed N, constant tip speed u,, or stirrer speed to just maintain all crystals in suspension NjS. Equation (18) can be used to predict the corresponding relation between the resulting secondary nucleation rate and the crystallizer size as expressed by

B oc A4. (19)

Values of q are included in Table 2. The three approaches give similar results and all show that scale-up on the basis of constant z should at most produce a modest increase in nucleation rate. Constant tip speed or the particle suspension criterion should both result in a decrease in nucleation rate with increasing scale of operation.

Results of a number of experimental studies [69, S&95] generally confirm these relations although particular sensitivity has been recorded for the influence of the impeller draft tube clearance [96] and changes in nucleation mechanism can result from excessively long residence times [97] or at very high magma densities [98].

4. GROW-I-H KINETICS Once crystals have been produced by nucleation

processes they will grow and many problems related to crystallization are rooted in the crystal growth process. Crystal size and, often of greater importance, shape or habit are common crystal properties related to the growth process. Crystal purity, perfection, strength and abrasion resistance are other particle parameters that frequently determine the suitability of particular crystals for specific applications and are also frequently related to the growth process; they have received comparatively little attention in the literature.

The process of crystal growth can be described at several different levels of magnification, various theories having evolved to represent the processes taking place at these different size scales. As illustrated in Fig. 6 these span the molecular, microscopic and macroscopic scales.

At the molecular level “growth units” are envisaged to attach themselves to the crystal surface, diffuse over this surface and eventually either integrate into the lattice at a “kink site” or return to the fluid phase. The chance of reaching such a site depends on the concentration of kinks in the surface and so the mechanism and rate of growth depends on the nature of the cry@ surface at this molecular level. In a rough interface there are many potential kink sites and neither surface diffusion nor fine details of the surface topography are important. Under such conditions continuous or

Table 2. Scale,up of secondary nucleation kinetics (see eqns 18 and 19)

Ottens and de Jong [91]

Evans et al. C921

Garside and Jancic [93]

f O=om) d

~$1 V 2

""is/V PW':/D;)( Vpl VI 3

i 3 2:5 4 h 3 3 4

Exponent q in cqn (19) when scale- up on the basis of constant

(i) F 0 0.5 0.33 (ii) N 2 2.5 3

(iii) 0, -A.55 -0.5 -1 (i+) IV* calculated using -0.05 -0.4

correlation of Zwietering [40]

JOHN GARSIDE 12

a

molecular

microscopic

Size

lnm -

lm_ r

lmm _

Morphology. effect of gmwttl

dispersion

Tmnsport C-- limitations

Fig. 6. Crystal growth phenomena at various levels of magnification.

normal growth models apply. On the other hand when the interface is smooth growth is more difficult. Kink sites are only present in the edges either of two- dimensional nuclei or of surface steps. Surface diffusion of growth units is now likely to be important and the surface topography must be defined. Layer growth models are now applicable.

At the microscopic scale surface layers or “step bunches” are often observed. These are many hundreds of atomic dimensions in height and are made up of groups of smaller steps that have become bunched together, probably because of perturbations in the advance velocities of an otherwise equidistant train of steps.

At still larger size scales the effects of transport limitations on growth rate can be seen. Heat transfer seldom controls crystal growth rates from solution but mass transfer limitations are frequently important. The resulting supersaturation gradients in the solution phase can then influence the surface profiles and cause instabilities in the growth process. Dendrites and solution inclusions are both caused by such effects.

The interplay of all these factors finally results in the overall crystal morphology and size as manifest at the macroscopic scale.

4.1 The crystal surface Jackson [99] and later Tempkin [lOO] used a sueie

entropy factor, a, to characterise the state of the crystal surface or interface structure at the molecular level. This is defined by

4& a = kT

where the potential energy change per solid-fluid bond is given by

s=f(#/,+L-$d+ (21)

Larger values of a correspond to a smoother crystal surface and so as a increases the growth process changes from a continuous to a layer mechanism.

As the strength of interactions between solute and solvent in the solution increase, and hence as the solubility increases, c#,/ will increase and so E and consequently CL will decrease. Thus an increase in solubility will result in a rougher interface and so will in general accelerate growth [lOl].

Estimates have been made of the a values at which changes in growth mechanism occur, the most recent work of this type being based on Monte Carlo simulations of growing surfaces [102]. These show that if a is less than about 3 the interface is rough and continuous growth occurs, while values greater than about 4 correspond to substantially smooth interfaces and layer growth mechanisms.

If values of a can be predicted for specific systems it should be possible to define the growth mechanism by which such systems will grow. The most recent attempts to do this have led to the expression

a = <(l -xcs)* (Af -lnx,,) (22)

as derived by Bennema and van der Berden [ 1033, and the suggestion [104, 1051 that this can be simplified to

a=< ( an, WT

-lnx, . >

(23)

A number of authors [105-1093 but most notably Bourne and Davey [llO-1131 have combined estimates of a with growth kinetic measurements. Generally such studies have shown that changes in growth mechanism resulting from changes in solvent can be predicted and that equations such as eqns (22) and (23) can be used successfully to indicate the specific observed growth mechanism. These studies have been

Industrial crystallization fkom solution 13

reviewed in some detail by Bennema and van der Eerden [103], Davey [lOl, 1041 and Bourne [IWJ.

4.2 Crystal growth kinetics The structure of the crystal/solution interface im-

poses constraints on the mechanism by which a crystal can grow and a range of theories is therefore available to describe growth under particular conditions. Three recent works include wide-ranging discussions of such theories [114-l 161.

If cI is less than about 3 the surface will be sufficiently rough for continuous growth to proceed. The face growth rate u will then be linear in the supersaturation 0:

0 = ccr (24) where C is a constant which determines the maximum growth rate for a given system.

With smoother interfaces for which layer models apply two possibilities exist. Stable two-dimensional nuclei may form on the surface and growth can then proceed either by the addition of further similar nuclei or through the attachment of growth units to the edge of the nuclei via a surface diffusion flux. Computer simulations of crystal growth have provided a stimulus to the development of such models [ 1021 which appear to apply for values of a between about 3 and 4 and are variously known as “birth and spread” or “nuclei upon nuclei” models. The equation

u = A,o~/~ exp (- AZ/c) (25)

seems to give a satisfactory representation of such a process. The form of eqn (25) is shown in Fig. 7. At low

‘I

0.1 1 10 Dimensionless superraturotion i u/4 OT U/C r,)

Fig. 7. Growth ratMupersaturation reiation predicted by models of crystal growth.

supersaturations all such nucleation models are domi- nated by the exponential term so that there is a range of supersaturations where the growth rate is negligibly small.

For crystal surfaces with values of a greater than about 4 the high energy barrier preventing surface nucleation at low-supersaturations only allows growth by some other mechanism. The presence of screw dislocations in the crystal lattice allows self-per- petuating steps to provide ready sources of kink sites [117]. Growth via surface diffusion of growth units to a line sink provided by such a step forms the basis of the Burton, Carbrera and Frank (BCF) theory [118] which has probably been the most successful and well- developed theory of crystal growth. In its simplest form this predicts that the face growth rate is given by

u = C(a’/a,) tanh (a,/~). (26)

For c 4 cc (i.e. at low supersaturations) this reduces to

v = co=/a,

while when 0 + o= (high supersaturations)

(27)

v=Ca (28)

as previously given by eqn (24). Figure 7 illustrates these features of the BCF equation.

The effects of relaxing many of the assumptions inherent in the original derivation of this theory have been explored, e.g. [115,119-1221 and the specific application to solution growth has been considered [119,123]. Consequent changes in the form of eqn (26) are however usually minor.

For engineering and correlation purposes the simple power law equation

u = k,o’ (29)

has been frequently used (see eqn 2). This clearly represents the two limiting cases of the BCF equation (eqns 27 and 28 respectively) and is a good approximation in the intermediate regime when 1 < r < 2. It is also a satisfactory approximation to the two- dimensional nucleation model over a limited range of supersaturation as can be inferred from Fig. 7.

The results of many measurements and subsequent correlations of crystal growth kinetics have been published. Comparison and use of such data particularly for design purposes is hindered by two considerations: what is the appropriate expression for the supersaturation c, and what is the effect on the growth kinetics of bulk or volume diffusion in the concentration boundary layer surrounding the crystal. These two points, which have each given rise to frequent confusion, are briefly considered in the following sections.

4.3. Solution supersaturation Although the term “supersaturation” has been used

loosely in the previous section to represent the driving force for the growth process, the term has not been rigorously defined. The difficulty in doing so was first alluded to by Mullin [124] who pointed out that the

14 JOHN GARSIDE

supersaturation ratio S evaluated from the ratio of the bulk solution concentration to the equilibrium (i.e. saturation) concentration could have very different values depending on the measure and the units used to represent concentration. A number of papers have subsequently considered the problem of defining the fundamental driving force for crystal growth and of expressing this in a convenient form for general use [125-1321.

Briefly the driving force for a crystallization process, Q., is the difference in chemical potential between the substance in the supersaturated solution, p, and in the crystal, p,. This can be expressed in dimensionless terms as

0 =p-p~=vln~=y]n- YC II 4eT (30)

% Y,%

where a is the solute activity, c is a measure of concentration (e.g. molar or mass concentration, mass fraction, etc.) y is the corresponding activity coefficient and v is the number of ions in a molecular unit.

Equation (30) is seldom used in practice but rather three distinct approximations are generally made. First it is assumed that y = ysg so that the activity coefficient is taken to be independent of concentration; this is likely to be valid in dilute solutions and if c and coq are close together. Second v is invariably put equal to unity which is justifiable only for nonelectrolytes. Thus

0,311nC = In (0,+ 1) CD9

where cc is defined by

(31)

r7, = (c -c~)/css_ (32)

The third approximation is that a’r Q 1 in which case eqn (31) reduces to

cr_ -u a, (33)

uc as defined by eqn (32) is the most commonly-used expression for supersaturation in the various growth kinetic expressions. Various units could still be used for concentration. No general rule appears to govern this choice although the obvious empirical decision would be to select those units for which the activity coefficient varies least over the concentration range of interest.

4.4 Convection and crystal growth The solute concentration at the crystal/solution

interface determines the magnitude of the integration kinetics described in Section 4.2 but this concentration is less than that in the bulk solution owing to the convective resistance to transport of solute through the concentration boundary layer. Traditionally the interaction between convection and crystal growth has been formulated in terms of the Nemst “stagnant film” concept [133] and the value of boundary layer theory in the description of crystal growth has been neglected. Wilcox [134,135] anlh Westphal and Rosenberger [136] have emphasized boundary layer applications

and have taken particular care in the formulation of the appropriate equations.

The linear face growth rate of material A under conditions where no solvent is incorporated in the crystal is given by

P,D do, ’ = -p,(l -aA) dy Y=O’

(34)

The factor (1 - oA) arises from the bulk or “crystallization” [135] flow term in the diffusion equation. For hydrates this equation is valid so long as rates and concentrations are written in terms of the hydrated species. Mass fraction o is used here as a measure of concentration but the equation could be equally well formulated in, for example, molar concentrations or mole fractions.

If all the change in solution concentration is local- ised in the boundary layer of thickness 6, the boundary conditions

WA = WA0 at y= 0; oA = aArn at y = 6

allow eqn (34) to be integrated to give

PfD u=-ln(l+B) Ps6

where the concentration driving B is defined by

B = ~Ad---~Aa,. ’ -OAO

(36)

If B Q 1, eqn (35) simplifies to

v,=p,Djj= P,D +A0 - WA av) Pd PS6 c1 -0.4,) . (37)

In the absence of knowledge about the boundary layer thickness or the interfacial concentration gradient the above is usually written in terms of the mass transfer coefficient k,, = pID/d:

v _ k, @A0 - wAm)

P,tl--w,‘d - (38)

The term (1 - wAO) is frequently ignored although it is only negligible for sparingly soluble materials when wAO + 0. For example if wAo = 0.3, which corresponds to the solubility of potassium chloride at 22”C, l/(1 -wAo) = 1.43. Materials of higher solubility give correspondingly larger values of this correction term.

Two other points are worthy of note. First the effect of concentration dependent physical properties is almost always ignored in the analysis of convection and crystal growth even though both diffusion coef- ficients Cl373 and viscosities frequently show significant variations around the saturation concentration. Second, when small crystals, the growth rates of which are controlled by diffusion, are present at high concentrations such that interparticle distances are wm- parable with the boundary layer thickness, significant increases in growth rate can be obtained. Jaganathan and Wey [138,139] have presented calculations for growth in such a “crowded environment*’ and these effects are likely to be of significance for analysing


precipitation of most sparingly soluble salts. The concept of effectiveness factors, well established

in reaction engineering, is useful in characterising the extent to which any diffusional resistance influences growth rate. A crystal growth effectiveness factor q defined by the expression

growth rate at the interface conditions ’ = growth rate that would be obtained if the

interface were exposed to the bulk conditions

(39)

is given by [141,142]

q- (l-_tlDa) (40)

where the Damkohler number for crystal growth is defined by

Da = k,(c, - c_),- l/k, (41)

and represents the ratio of pseudo first order rate coefficient at the bulk conditions to the mass transfer coefficient. Equations (40) and (41) assume a power law expression for the integration step (see eqn 29).

The relation represented by eqn (40) is plotted in Fig. 8. When Da is large growth is diffusion controlled and q + Da-‘. Conversely when Da is small PJ -P 1 and growth is controlled by the surface integration step. Figure 9 shows the effect of relative crystal/solution velocity on both the growth rate and the effectiveness factor [121] and demonstrates how the diffusion resistance is only gradually eliminated as the relative velocity is increased.

4.5 Growth rate dispersion When exposed to constant conditions of supersatu-

ration, temperature and hydrodynamics different crystals of the same material frequently, and perhaps usually, grow at different rates. This phenomenon is now known as growth rate dispersion and the results of many experiments can be used to demonstrate its widespread occurrence; a selection of such work is

collated in Table 3. Such behaviour seems characteristic of crystals from many sources.

Observations on single crystals generally support the view that, although different crystals have different growth rates, a given crystal grows at a constant rate at least for periods of up to a few hours [149, 151, 1531. Growth rate measurements on single crystals over much longer periods (up to 15 days) have shown that the growth rate of a given face undergoes abrupt changes, often by as much as a factor of 5 or 6 [154].

The origin of growth rate dispersion appears to lie in the mechanism of the controlling surface integration process and to be related particularly to the presence and orientation of dislocations [71, 1551 and to ad- sorption of impurities. If the point of emergence of a screw dislocation changes from one face to an adjacent face then a step change in the growth rates of both faces will result. The absence of a dislocation greatly reduces the corresponding growth rate particularly at low supersaturations where layer growth mechanisms dominate. Thus the random way in which dislocations can occur provides a link between growth mechanisms and dispersion and emphasizes the stochastic nature of the process.

It is though perhaps more important to emphasise some of the consequences of growth rate dispersion.

First it complicates the interpretation of growth kinetic data, particularly that obtained from multipar- ticulate systems. For example fast-growing crystals increase in size more rapidly than slow-growing so that the larger crystals in the distribution are eventually more likely to be the faster-growing. The system then appears to exhibit a size-dependent growth rate in which the larger crystals grow faster than the smaller. Subsequent size analysis tends to separate the larger faster-growing from the smaller slower-growing crystals and any subsequent kinetic measurements with these fractions reinforces such an interpretation.

Much experimental growth data has been interpreted in terms of size-dependent growth, e.g. [156,157] and several size-dependent growth rate

>

1-o -? =‘-O (p”re surface integmt ion gmwth I _-_-------

Fig. 8. The effectiveness factor for crystal growth.

16 JOHN GARSIDE

0.L 0.8 Relatwe crystal / Solution velocity I m/s1

Fig. 9. Influence of relative crystal/solution velocity on crystal growth rate and the corresponding effectiveness factors.

Table 3. Selection of growth kinetics data illustrating growth rate dispersion

Material

KH,PO, Sucrose K,Cr,O, K,SO, Pentaerythritol NaCl K alum Citric acid K alum Sucrose NH,H2P0, NH4H,P0,

System investigated

large single crystals populations of large crystals populations of large crystals populations of large crystals attrition fragments attrition fragments small single crystal-ntact secondary nuclei small single crystals-co ntact secondary nuclei populations of secondary nuclei small single crystalsprimary nuclei small single crystals--primary nuclei small single crystals-primary nuclei

equations have been proposed [158-1603 for use in rates from the steady state crystal size distribution in combination with population balance equations and an MSMPR crystallizer is greatly complicated because CSD modelling. These will be considered further in of the difficulty in defining the reasons for the par- Section 5. titular form of the population density plot.

The second consequence of growth rate dispersion is therefore the influence that it has on the crystal size 5. CRYSTALLIZER PERFORMANCE

distribution and product quality obtained in a crystal- The crystal size distribution (CSD) produced within lization process and this again will be considered a crystallizer is often of overriding importance in subsequently. determining the ease and efficiency of subsequent

Thirdly the determination of apparent nucleation solid/liquid separation steps, the suitability of crystals


for further processing, caking and storage characteristics and the eventual customer appeal of the product. Equally important though is the interaction of CSD with crystallizer operation through the feedback relation illustrated in Fig. 2. In particular the size distribution influences the supersaturation at which the crystallizer operates and so has an effect on the crystal nucleation and growth rates, crystal habit and purity, fouling of solid surfaces and the stability of operation. The population balance approach to the description of CSD is the most widely accepted and has proved the most fertile in germinating new developments to describe and model crystallizers.

The population balance equations were first for- malised by Randolph [161] and Hulburt and Katz [162] as a population balance for countable entities; Randolph and Larson [ 183 provide a general review. The macro-distributed form of the equation is the most useful for crystallizer modelling and for a mixed suspension constant volume system can be written as

&I L?(Gn) %QIL at+== zY+B(L)-D(L). (42)

k

For the size range L to L+dL the terms in this equation represent respectively the accumulation of crystals, the net efllux of crystals due to growth along the size axis, the net crystal input from entry and exit streams to or from the crystallizer, and finally the birth or production and death or destruction of crystals directly into the size range under consideration by processes such as nucleation, agglomeration, abrasion or fracture.

Equation (42) has been solved using many different simplifying assumptions so as to represent the behaviour of particular crystallizing systems or crystallizer configurations. Some of these cases will be summarised in the following sections.

5.1 Mixed suspension mixed product removal (MSMPR) crystallizer

The simplest case to consider is that analogous to a back-mix reactor in which each element of fluid has, at all times, an equal probability of removal; this corresponds to the MSMPR crystallizer. The steady state CSD when growth rate is independent of size, the feedstream is free of crystals, and no crystal breakage or agglomeration occurs is thus given by the solution of

dn n _= -- dL Gr (43)

i.e. by n = no exp ( - L/G7) (44)

where 7( = V/Q) is the mean residence time of both crystals and solution. The number density no at L = 0 is related to the two kinetic rates by

B=n’G (45) ‘\

and so eqn (44) can be written

: n = (B/G) exp ( - L/G7). (9

The size distribution is thus completely determined by the mean residence time and by the rates of the two kinetic processes, nucleation and growth.

The number, length,area and mass distributions can be easily calculated from these equations [18]. For example the cumulative number oversize distribution is given by

N, = Br exp ( - L/G7) (47)

while the differential mass fraction distribution can be written in dimensionless form as

m(X)=iX3exp(-X) (48)

and the cumulative oversize mass fraction distribution is

M(X)= (l+X+fX’+dX”)exp(-XX) (49)

where X is the dimensionless size L/Gr. The various average sizes can then be determined, e.g. the mode of the mass distribution occurs at X = 3 (i.e. L,,, = 3G7) while the mass median size is given by L-,, = 3.67 G7. A convenient measure of the width or spread of the distribution is the coefficient of variation (c.v.) which for these mass distributions is constant at 50%.

Although a number of industrial crystallizers wn- form reasonably well to the assumptions inherent in the derivation of eqn (46) and size distributions from such crystallizers are well represented by this equation (see for example [163]), the MSMPR crystallizer with its simple exponentially-decaying size distribution is important for two other reasons. First it forms a reference against which size distributions from other crystallizers can be compared. Deviations from the reference case assumptions are then often fairly easy to detect. Second, and perhaps most important, it suggests the use of a crystallizer satisfying the appropriate assumptions as a laboratory or pilot-plant tool for determination of crystallization kinetics. Measurement of the steady state CSD produced in such a crystallizer allows the growth and nucleation rates to be determined, most conveniently by plotting either log nor log N, vs L so that the growth rate can be calculated from the slope and the nucleation rate from the intercept at L = 0 (see eqns 46 and 47). Figure 10 shows such a plot obtained for the crystallization of MgSO, . 7H,O from a naturally occurring brine in a 4L laboratory crystallizer. In addition to kinetic measurements observation of crystal shape and fil- tration characteristics can conveniently be made.

Nucleation and growth rates from such experiments depend on the supersaturation or concentration driving force through equations of the form

B = k,Acb (50) and

G = k,Ac@. (51)

Equation (50) is similar to eqn (17) but with the dependence of geometry, magma density and stirrer speed incorporated into the rate constant k,. Likewise

18 JOHN GARSIDE

Intercept = B/G I 3.6 x 10’2 #vi’ rK3

:.B i 6.2 x105 s-’ rn-3

_ ‘c = tlmin

:. G =1.71~10-~ m,’

t 1 a I

o-5 1.0 Crystal 9~62 L (mm1

Fig. 10. Crystal size distribution obtained from a laboratory scale MSMPR crystallizer: crystallization of MgSO, .7H,O

from a natural brine.

eqn (51) is of the same form as eqn (2) but the growth rate is here expressed as the linear rate, G, rather than the mass deposition rate R,. It is frequently found that the driving forces in operating crystallizers are very small and cannot be measured accurately. Combination of the above two equations then allows the growth rate to be used as a measure of supersaturation:

B = KaG’ (52)

where i( = b/g) is the relative kinetic order and KR( = k,/ka) the relative rate coefficient. A recent paper [72] assesses published kinetic data deduced in this way.

In spite of being widely adopted for experimental work the MSMPR crystallizer suffers from a number of disadvantages. Many of the assumptions made in deriving eqn (46) are difficult to achieve in practice. Experiments are often time consuming and laborious,

Fig. 10 involves the implicit assumption that the small, unobserved (and probably unobservable) crystals behave in the same way as larger crystals, a highly unlikely situation. Consequently it is probably best to regard B as the “effective” or “apparent” nucleation rate.

5.2 Steady state continuous operation Much published work has been directed at calculat-

ing the crystal size distribution obtained under conditions more nearly approaching those found in real crystallizers. This has involved relaxing many of the restrictive assumptions made in deriving eqn (44). Such work is referenced in Table 4; a brief indication of the nature of each study is also given.

Both size dependent growth and growth rate dispersion arise from the nature of the inherent growth process. The effect of each phenomenon is to introduce curvature into the population balance plot. Crystal breakage is generally of only minor importance, but agglomeration of crystals can present severe problems; it is frequently observed in crystalline products and can have a significant effect on solid-liquid separation and subsequent product purity. Little fundamental work has been done in this area. The cause of agglomeration is often unclear and prevention is difficult. Further the effect on CSD is difficult to calculate because of the nature of the equations that must be solved.

Fines removal and classified product removal systems both impose size-dependent removal rates on the crystallizer contents as described in Section 2.2. The classification function p(L) defined by eqn (11) must now be included in the population balance equation. Retaining all the assumptions inherent in eqn (43) except that of mixed product removal results in the differential equation

dn rip(L)) -= --_ dL GT (53)

The R-z model of Randolph and Larson [18] then gives

n = no exp(-RL/Gz) :o <L<L, n=n’exp[(l-R)L,/Gr]exp(-L,‘Gr):L,<L<L, n = no exp [(z - l)L,/Gr] exp ( - zL/Gr): L, < L

(9)

they may require an elaborate experimental arranage- while the classification function of Boume [52] given ment, and a large number of experiments are necessary in eqn (12) results in the size distribution to elucidate kinetic expressions of the type represented by eqns (14), (17), (SO) and (51). Other difficulties arise 1 in handling supersaturated solutions and suspensions

n=nOexp -- ( [

&+ (1 -ua/b)tan-’ (b112L) GK b b”’ I>-

and the solution hold-up requirement is usually relatively large. (55)

A conceptual problem also arises. The number These distributions are illustrated in Fig. 11 which density no and the nucleation rate B are introduced therefore corresponds to the classification functions in from the boundary condition L = 0. In practice nuclei Fig. 3. are produced at some finite size (see Section 3) but this Theoretical and experimental studies have con- is typically orders of magnitude smaller than the firmed the great advantages in flexibility and control minimum crystal size that can be measured as part of that arise from operating with fines removal systems. the size distribution Linear extrapolation of the The advantages of classified product removal are not number density distribution to L = 0 on plots such as so clear-cut. Although narrower size distributions


Table 4. Crystal size distribution studies

19

A. Continuous: steady state (a) Size dependent growth, G(L)

Bransom [158] C . 8 and Randolph [159] Abeaa er ~2. rmi

G(L) = KLk: analytic solution for n(L) G(L) = K(1 +yL): analytic solution for n(L) ClL.1 = KI1 + vLIk: analvtic solution for n(L)

Gas and >an& [164] . _ . ., . _

Rousseau and Woo [165] >

modification, development and experimental data based on

O’Dell and Rousseau [16] equation of Abegg et al. [160]

(b) Growth rate dispersion Randolph White [167] described via growth rate diffusivity Janse and de Jong [50] assumed each individual crystal had a constant characteristic Larson et al. Cl683 growth rate

(c) Crystal breakage Randolph [I691 D(L) = Kn(L)L&, B(L) = 2k+ i Kn(2L)Lh Fitzgerald and Yang Cl703 conservation of crystal volume

(d) Agglomeration Liao and Hulburt Cl713 agglomerisation in MSMPR crystallizer Shah 11721 experimental study based on [ 17 l]

(e) Fines removal and/or classified product removal Han and Shinnar El733 theoretical, product classi8cation Larson and Randolph Cl747 R-z model for tines removal and product classi8cation Larson and Randolph [18] R-z model for fines removal and product classification Larson and Garside Cl753 design-oriented, R-z approach Juzaszek and Larson [176 experimental, R-z model applied Kraljevich and Randolph 2 1771 experimental, R-r model applied Boume [23] classiication function approach

(f) staging Robinson and Roberts Cl783 nucleation only in 1st tank Nyvlt and Moudry [179] equal nucleation rates in each tank Randolph er al. [180] combination of size classification and staging Randolph and Larson [18] includes expressions for mass distributions Abegg and Balakrishnan Cl813 nucleation in all tanks Wolff and Larson [182] explored range of optimal solutions Rojkowski [183] non-isothermal stages, optimization attempted Skrivanek and Vacek [184] effects of alternate growth and dissolution Randolph and Tan [ 1851 dynamics with classification and staging Tavare and Chivate Cl863 two-stage, classitied product

B. Continuous: unsteady state (a) Dynamics and stability

Randolph and Larson [17] Hulburt and Katz Cl62 Randolph and Larson I? 1871 Murray and Larson Cl883 Sherwin et al. [ 1891 Sherwin et al. [190] Hulburt and Stefango [191] Mullin and Nyvlt [192] Lei et al. Cl933 Randolph et al. Cl943 Yu and Douglas [195] Song and Douglas [196] Shields El973 de Leer et al. 11981 Randolph et al. [74] Beckman and Randolph [199] Randolph and Tan [ 185) Ishii and Randoiph [200-J Randolph [201] Epstein and Sowul [202] Rovang and Randolph 1203 ] Akoglu et al. 12043

(b) Control Han [205] Gupta and Timm [206 Rousseau and Howell I! 2071 Randolph and Low [208] Hashemi and Epstein [209] Randolph et al. [210] Bennett and Randolph [Zll]

transients and stability, stability criteria, theoretical transients and stability, stability criteria, theoretical transients and stability, stability criteria, theoretical experimental study of dynamics theoretical stability study for well-mixed system efkct of product classification effect of fines removal includes classification effects and experimental data effect of fines removal stability of R-z configuration, theoretical possibility of increased output via cycling cycling observed experimentally transient hehaviour related to plant experience effect of tines removal and product classification low order cycling observed experimentally developments in analytical solutions dynamics of recycle systems with classltication stability for size-dependent growth system review paper effect of difierent nucleation mechanisms, limit cycles on-line CSD analysis in fines loop dynamics under non-isothermal conditions

analog simulation study theoretical, B known, manipulate 8nes dissolving R-z model, measure AC, manipulate feed rate experimental, on-line CSD measurement observability and controllability considerations experimental. on-line CSD measurement preliminary plant results

JOHN GARSIDE Table 4. (Continued)

C. Batch Baliga and Larson [212] Mullin and Nylt [213] Wey and Estrin [214] Larson and Garside Cl753 Jones and Mullin [215] Jones [216] Hulburt [2 173 Nyvlt [218] Tavare and Chivate [219] Tavare et al. [220] Tavare et al. [221] Melikov and Berliner [222] Nyvlt [223] Chang and Epstein [224] Jones [225]

evaporative operation, theoretical and experimental results controlled cooling operation, includes experimental data production of ice, theoretical and experimental controlled evaporation rate operation cooling, experimental data cooling, different operating strategies general theoretical population balance approach review paper evaporative operation effect of seed concentration in dilution crystallizer genera1 analytical technique for all modes of operation cooling. effect of growth rate dispersion two-stage cooling operation identification of optima1 control schemes review paper

log l-3”

: - R/G ‘t

Crystal size L LP

Fig. 11. Crystal size distributions resulting from various classification functions (compare with p(L) in Fig. 3).

result this is generally at the expense of production rate and control is usually much more difficult.

Staging, whereby the product from one crystallizer is passed to a second and perhaps subsequent crystallizer, can in principle achieve significant narrowing of size distribution. Such narrowing depends on preventing any appreciable nucleation in the second and subsequent stages and this is very difficult to achieve in practice. Most work reported in Table 4 is of a theoretical nature; there is a dearth of good experimental data in this area.

5.3 Unsfeady state continuous operation Section 3 of Table 4 lists studies relating to the

behaviour of continuous crystallizers operating under unsteady state conditions. Most of this work has been

directed at investigating dynamics and/or stability and a brief indication of the specific area of each study is included in the table. In all these cases the partial differential equation (42) must be solved, simplifi- cations being made to the r.h.s. of the equation to reflect the specific configuration under consideration. In addition to this population balance, associated mass balance and kinetic equations together with the initial CSD must be incorporated into the solution.

It was shown at an early stage [17,162,187-j that for the so-called high yield or Class II system, for which the mass balance is written assuming the solution concentration in the crystallizer is constant at the saturation value, the criterion for instability is given by

d(logB)/d(logG) = i > 21. (56)


Instability of this type, which results from the feedback relationship between supersaturation and the crystal area available for growth (Fig 2), is probably only obtained in practice as a result of discontinuities in the nucleation mechanism which may #occur, for example, when the metastable limit is exceeded. A relative kinetic order (see eqn 52) of i > 21 is unlikely [72].

Instability is far more likely with size dependent removal rates in the large size range as was first illustrated by Sherwin et al. [190]. On the other hand fines destruction tends to stabilize the system [191, 1931.

Control studies are comparatively few in number. They have all shown that the practical implementation of on-line control schemes depend crucially on the availability of an on-line size distribution measuring device. Recent work by Randolph [208,210,21 l] using instruments based on low angle laser light scattering together with an associated minicomputer shows great promise althoughresults of full scale plant tests are not yet available.

5.4 Batch operation Batch crystallizers are used extensively in the chemi-

cal industry, usually for low production rate oper- ations. Many valuable high added-value products are handled in this way although the equipment is usually extremely simple and unsophisticated.

There has been considerable theoretical effort aimed at modelling the product CSD and defining the best operating strategy in batch systems. This work is summarised in Table 4, Section C. For batch operation the population balance (eqn 42) becomes, in the absence of breakage and agglomeration,

au a(Gn) at+-= aL

o. (57)

Again this equation must be solved with the associated mass balance, kinetics and initial and boundary conditions for any specific mode of operation (cooling, evaporation, reaction, etc.). Whatever the operating mode it is clear that far greater control of the CSD can be achieved if the solution is maintained at a constant supersaturation level within the metastable zone throughout the course of the batch. This gives rise to so-called “controlled” operation. For a simple batch seeded cooling crystallizer in which the growth rate is independent of size and temperature, the solubility is a linear function of temperature and no nucleation occurs it can be shown [213,215] that a cooling curve of the form

e=e,-c(l+C,t+C,r2) (58)

will result in a constant level of supersaturation. Other solutions for which these somewhat restrictive assumptions are relaxed are listed in Table 4.

At present there is a lack of thorough experimental work fully to test the concepts of “contro.lled” operation. The greatest difficulty in matching theoretical and experimental work lies in defining the initial conditions. Experimentally it is very easy to move into

the labile part of the supersaturated region during the early stages of a batch while theoretically the appropriate initial condition is often unclear. Great scope exists for further work in this area, not least because of the real economic incentive for better plant utilization and product quality.

5.5 Crystallizer design In spite of the extensive work on crystal size

distribution there is comparatively little published information on the incorporation of these equations into design procedures. There is now a pressing need for the development of design-oriented applications of population balance modelling.

Larson and Garside [175, 2261 have proposed specific procedures and given numerical examples for a selection of both batch and continuous units while the group of de Jong have also aimed much of their work towards the improvement of design procedures. For example Asselbergs and de Jong [227] combined the heat exchanger specification with that of the crystallizing vessel for an MSMPR cooling crystallizer. Other studies from the same group [32,, 228, 2291 concentrate on the interaction between crystallizer geometry, flow patterns, supersaturation distribution and the resulting CSD and this work, carried out in large pilot-scale equipment, is invaluable in providing a link between laboratory studies and the very limited amount of data from industrial units.

Two papers by Mullin and Nyvlt have also proposed specific design methods for classifying [230] and mixed suspension [231] crystallizers while the methods adopted by the schools of Nyvlt and of Toyokura are compared in a further publication [232]. These three works all make some use of the population balance concept although not in the conventional form adopted in this present review.

Few publications quote size distributions obtained in commercial units and fewer still discuss the means by which crystallizers are actually designed. In the former category Canning [233], Kern and Abegg [234] and Bennett [163,235] provide useful data while Wohlk [236] in particular has provided a valuable insight into economic considerations, especially those associated with rising energy costs [237]. A particularly useful paper by Tousssaint and Fortuin [238] considers design criteria for DTB-vacuum crystallizers. Much industrial data is no doubt commercially sensitive but until design methods and crystal size distribution predictions have been set alongside information obtained from operating units it is unlikely that further significant progress can be made in the design area.

6. CONCLUSIONS

It is clear that a vast amount of work has been carried out in the field of industrial crystallization over the past decade. This has led to significant progress in a number of areas. For example the importance of fluid mechanics on crystallizer performance has been emphasized by studies both on crystal suspension and

22 JOHN GARSIDE

distribution within a crystallizer and on the interaction i of this spatial distribution with the crystal size distri- j bution. An elementary mechanistic description of k secondary nucleation has been established and pro- kb gress made in quantifying the role of secondary k, nucleation on scale-up through knowledge of the k, crystallizer fluid mechanics. The physical description k, of crystal growth has undergone a major transform- ation and it is now possible to predict some of the ways K, in which growth rates change in response to alterations K, in the crystal environment. Finally the mathematics of ~a crystal size distribution modelling has come to ma- ,L< turity and most steady or unsteady state configurations L, can be described. 4x1

In spite of such progress significant gaps still exist. ~j Some aspects of fluid mechanics are still only poorly MT understood and the whole area of primary nucleation M(X) is still particularly difficult to relate to industrial precipitation processes. These two aspects are linked n through the role of micromixing and significant ad- no vances may be expected in this difficult area over the N next decade. Crystal habit modification has been NC barely touched on in this review especially when it is p brought about by impurities rather than changes in P(L) supersaturation, temperature or solvent. Again this is a 4 particularly difficult area where progress can be ex- Q petted. Control of full scale units operating in both the r batch and continuous mode will also see great ad- R vances once the technology of on-line size distribution R, measurement improves. Finally far greater interaction 6% between those developing design procedures and CSD S predictions on the one hand and potential industrial t users of such information on the other would be t, invaluable and would serve to finally demystify much T of the “art” so often associated with industrial u crystallization. V

NOTATION VP

a activity z --I,& constants AT total crystal area

Y z

b nucleation order

relative kinetic order (= b/g) nucleation order w.r.t. MT Boltzmann constant nucleation rate coefficient mass transfer coefficient growth rate coefficient rate coefficient for surface integration step nucleation rate coefficient overall growth rate coefficient ralative rate coefficient crystal size equivalent spherical diameter differential mass fraction distribution jth moment of CSD total crystal mass cumulative oversize mass fraction distribution number density nuclei number density stirrer speed cumulative number propeller pitch classification function exponent volumetric flow rate surface integration rate order r/rr overall growth rate expressed as mass flux gas constant supersaturation ratio (= c/c& time circulation time absolute temperature face growth rate crystallizer volume swept volume of propeller mole fraction dimensionless size (= L/Gr) direction coordinate r/rp

B 23 B(L)

:, Cl, c2 d D DD J4 DT D(L)

&I & f (G-4 FI, Fz

iii h

nucleation rate concentration driving force birth function concentration constants exponent diffusion coefficient draft tube diameter stirrer diameter tank diameter death function voidage collision energy rate of energy transfer function of geometry production and survival functions growth order linear growth rate ( = d L/dr) nucleation order w.r.t. N

Greek symbols a surface entropy factor Y activity coefficient

2 surface energy boundary layer thickness

AC r?r

concentration driving force (= c -c_) difference in internal free energies of solute and solid

AH, heat of fusion & potential energy change per solid-fluid

bond 25 specific power input

3 crystal growth effectiveness factor temperature

1 length scale P chemical potential V number of ions in a molecular unit r crystallographic factor P density


supersaturation activity based supersaturation ( = ln WGJ) concentration based supersaturation (= @ -c,kJ residence time bond energy mass fraction collision frequency

23

c251

CW

c271

C281

[Zj c311

c321

Grootscholten P. A. M. and de Jong E. J., ZChemE 6th Ann. Res. Meeting, University College, London 1979. Scrutton A. J. and Grootscholten P. A. M.. Trans. I.

a

a,

r

9 w

w(L)

Subscripts A C

eq f F

; 0 P s

PI

PI

133

E41

123

c73

PI

c91

[K]

[:;] Cl41

Cl51

[it 3

WI

Cl91

PO1

PI

E'2j

c241

component A crystal equilibrium or saturation value fluid fines inlet/initial stream number value at y = 0 or t = 0 product solid

REFERENCES van Damme M. A., Crystal Growth: An Introduction (Edited by Hartman P.), p. 248. North-Holland, Amsterdam 1973. Mullin J. W., Encyclopedia of Chemical Technology (Kirk-Othmer), Vol. 7, p. 243. Wiley, New York 1979. Nyvlt J., IndustrialCrystallization: the State of the Art, 2nd edn. Verlag Chemie, Wenheim 1982. Mersmann A. B., Beer W. F. and Seifert D., Ger. Chem. Engng 1979 2 1. Rousseau R. W., Chemtech 1980 (Sept) 566. Mullin J. W. (Ed.), Industrial Crystallization. Plenum Press, New York 1976. de Jong E. J. and Jancic S. J. (Eds.) Industrial Crystallizarion 78. North-Holland, Amsterdam 1979. de Jong E. J. and Jancic S. J. (Eds.) Industrial Crystallization 8 1. North-Holland, Amsterdam 1982. AZChE Svmv. Ser. No. 153. 1976 72. AZChE S;rni. Ser. No. 193; 1980 76. AZChE Symp. Ser. No. 215, 1982 78. Levenspikl o., Chem. Engng Sci. 1980 35 1821. Randolph A. D., Chem. Engng 4 May 1970 77 80. Peet R. B.,Theoryof continuous vacuum crystallization, Company Report V-45, American Potash and Chem. Corp., Trona, California 193 1. Bransom S. H.. Dunnina W. J. and Millard B.. Disc. Faraday Sot. 1449 5 83.- Saeman W. C., A.Z.Ch.E. J. 1956 2 107. Randolph A. d. and Larson M. A., A.Z.Ch.E. J. 1962 8 639. Randolph A. D. and Larson M. A., Theory of Particulate Processes. Academic Press, New York 1971. Randolph A. D., Industrial Crystallization 78 (Edited by de Jong E. J. and Jancic S. J.), p. 295. North- Holland, Amsterdam 1979. Nyvlt J., Industrial Crystallization from Solutions. Butterworths, London 1971. Toyokura K., Industrial Crystallization 78 (Edited by de Jong E. J. and Jancic S. J.), p. 357. North-Holland, Amsterdam 1979. Ramshaw C.. Parker I. B.. Trans. 1. Chem. E. 1973 5182. Boume J. R.1 Industrial &rystallizarion 78 (Edited by de Jong E. J. and Jancic S. J.), p. 215. North-Holland, Amsterdam 1979. Ramshaw C., ZChemE 6th Ann. Res. Meeting, University College London 1979.

[ii] c351

C3'51

c371

C381

c393

[:I c421

c431

c511

c521

c551

C561

(571

T581

c591 WI

C611

WI

E]

C651

Chem. E. 1981 59 238. Mullin J. W.. Chakrabortv M. and Mehta K.. J. Rvvl. Chem. 1970 i0 367. _

. .

Garside J., Mullin J. W. and Das S. N., Znd. Engng Chem. Fundls. 1974 13 299. Garside J., Mullin J. W.. Trans. I. Chem. E. 1968 46 11. Smythe B. M., Aust. J. Chem. 1967 20 1087. Miidleton J. C., Third European Conf: on Mixing, p. 15. York 1979. As&bergs C. J., Grootscholten P. A. M. and de Jong E. J.. Industrial Crystallization (Edited by Mullin J. W.). D. 447. Plenum Press. New York 1976. Be& C. R., Photo. Sci. Engng 1976 20 1. Maruolis G. and Gutoff E. B., A.1.Ch.E. J 1974 20 467. Gut&E. B., Cottrell F. R. and Denk E. G., Photo. Sci. Engng 1978 22 325. Becker G. W. and Larson M. A., Chem. Engng Prog. Symp. Ser. No. 95, 1969 65 14. Pohorecki R. and Baldyga J., Industrial Crystallization 78 (Edited by de Jong E. J. and Jancic S. J.), p. 249. North-Holland, Amsterdam 1979. Pohorecki R. and Baldyga J., Chem. Engng Sci. 1983 38 79. Costa P. and Trevissoi C., Chem. Engng Sci. 1972 22 2041. Zwietering T. W., Chem. Engng Sci. 1958 8 244. Nienow A. W.. Chem. Enana Sci. 1968 23 1453. Kueule F. and Weinspac‘h ‘P. M.. Verfahrenstechnik 1967 12 531. Musil L. and Vlk J., Industrial Crystallization (Edited by Miillin J. W.), p. 229. Plenum Press, New York 1976. Musil L. and Vlk J., Chem. Engng Sci. 1978 33 1123. Ditl P. and Rieger F.. Chem. Engng Sci. 1980 35 763. Musil L. and Vlk J., Chem. Engng Sci. 1981 36 789. Aeschbach S. and Bourne J. R., Chem. Engng J. 1972 4 234. Canning T. F., Chem. Engng Prog. 1970 66 (7) 80. Juzaszek P. and Larson M. A., A.Z.Ch.E. J. 1977 23 460. Janse A. H. and de Jong E. J., Industrial Crystallization, (Edited bv Mullin J. W.). D. 145. Plenum Press. New ir’ork 197&.

I . I

Bourne J. R. and Zabelka M., Chem. Engng Sci. 1980 35 533. Bourne J. R., Hungerbuehler K. and Zabelka M., Industrial Crystallization (Edited by Mullin J. W.), p. 283. Plenum Press, New York 1976. Larson M. A., Chem. Engng 13 February 1978, p. 91. Botsaris G. D., Lecture at British Association for Crystal Growth meeting on Secondary Nucleation, March 1980. Walton A. G., in Nucleation (Edited by Zettlemoyer A. C.), p. 225. Marcel Dekker. New York 1969. Walton A. G.. The Formarion and Properties of Precipitates. Interscience, New York 1967. Nielsen A. E., Crystal Growh (Edited by Peiser H. S.). p. 419. Pergamon Press, New York 1967. Nielsen A. E. and Sohnel O., J. Crystal Growth 197 1 11 233. Nyvlt J., J. Crystal Growth 1968 3/4 377. Nyvlt J.. Rychly R., Gottfried J. and Wurzelova J., J. Crystal Growth 1970 6 151. Mullin J. W., Chakraborty M. and Mehta K., J. Appl. Chem. 1970 20 367. Sohnel 0. and Nyvlt J.. Coil. Czech. Chem. Commun. 1975 40 511. Hulburt H. M., Chem. Ing. Technik 1975 47 375. Janse A. H. and de Jong E. J., Trans. I. Chem. E. 1978 56 187. Mullin J. W., Jan& S. J., Trans. I. Chew. E. 1979 57 188.

JOHN GARSIDE 24

l-661

C671

C681

C691

EE]

c7*1

1731

c741

c751

E761

c771

C781

c791

cw

Botsaris G. D., Indusfrial Crystallization (Edited by Mullin J. W.), p. 3. Plenum Press, New York 1976. Estrin J., Preparation and Properties of Solid State Materials (Edited by Wilcox W. R.), Vol. 2. Marcel Dekker, New York 1976. Viola M. S. and Botsaris G. D., Chem. Engng Sci. 1979 34 993. Bennett R. C., Fiedelman H. and Randolph A. D., Chem. Engng Prog. 1973 69 86. Young S. W., J. Am. Chem. Sot. 1911 33 148. Garside J. and Davey R. J., Chem. Engng Commun. 1980 4 393. Garside J. and Shah M. B., Znd. Engng Chem. Proc. Des. Dev. 1980 19 509. Randolph A. D. and Rajagopol K., Ind. Engng Chem. Fundls. 1970 9 165. Randolph A. D., Beckman J. R. and Kraljevich K., A.I.Ch.E. J. 1977 23 500. Shah B. C., McCabe W. L. and Rousseau R. W., A.1.Ch.E. J. 1973 19 194. Ness J. N. and White E. T., A.1.Ch.E. Symp. Ser. No. 153 1976 72 64. Randolph A. D. and Sikdar S. K., A.1.Ch.E. J. 1974 20 410. Evans T. W., Margolis G. and Sarofim A. F., A.1.Ch.E. J. 1974 20 950. Denk E. G. and Botsaris G. D., J. Crystal Growth 1972 13/14 493. Larson M. A., paper presented at A.1.Ch.E. Ann. Meeting, Washington D.C.. November 1983.

[8 l] Garside J. and La&on M. A:, J. Crystal Growth 1978 43 694.

[82] Garside J., Rusli I. T. and Larson M. A., A.I.Ch.E. J. 1979 25 57.

(831 Purves W. T. and Larson M. A., Solids Separation Processes, IChemE Symp. Ser. No. 59, p. 715/l. 1980.

[84] Strickland-Constable R. F., J. Chem. Sot. Farad. Trans. I. 1979 7s 921.

[SS] Powers H. E. C., Ind. Chem. 1963 39 351. r861 Suna C. Y.. Estrin J. and Youngauist G. R.. A.I.Ch.E. J.

L _ 1973 957. -_ 19

[87] Jagannathan R., Sung S. Y., Youngquist G. R. and Estrin J., A.I.Ch.E. Svm~. Ser. No. 193 1980 76 90.

[SS] Wang G. L., Huang-H.-T. and Estrin, J., A.I.Ch.E. J. 1981 27 312.

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[90] Ottens E. P. K., Janse A. H. and de Jong E. J., J. Crystal Growth 1972 13/14 500.

[91] Ottens E. P. K. and de Jong E. J., Ind. Bngng Chem. Fundls 1973 12 179.

[92] Evans T. W., Margolis G. and Sarofim A. F., A.I.Ch.E. J. 1974 20 959.

[93] Garside J. and Jancic S. J., A.1.Ch.E. J. 1979 25 948. [94] Bourne J. R. and Hungerbuehler K., Trans. I. Chem. E.

c951

C961

1971

C981

c991

ClW

1980 58 51. Grootscholten P. A. M., de Leer B. G. M., de Jong E. J. and As&bergs C. L., A.I.Ch.E. J. 1982 28 728. Scrutton A.. Grootscholten P. A. M. and de Jona E. J.. Trans. I. Chem. E. 1982 60 345.

_ _

Keight D. V., Rolfe N. and Scrutton A., 1. Chem. E. Ann. Res. Meeting, London 1979. Nienow A. W. and Conti R., Chem. Engng Sci. 1978 33 1077. Jackson K. A., Liquid Metals and Solidification, p. 174. Amm. Sot. Metals, Cleveland 1958. Tempkin D. E., CrystaUization Processes, p. 15. Consultants Bureau, New York 1964.

[loll Davey R. J., Industrial Crystallization 78 (Edited by de Jong E. J. and Jancic S. J.). p. 169. North-Holland, Amsterdam 1982.

Cl023 Van der Eerden J. P., Bennema P. and Cherepanova

PO31

Cl@+1

Cl051

[Ej

PO’31

w91

CllOl

Cl111

c1121

Cl 131

Cl 141

Cl151

T. A., Prog. Crystal Growth Characterisation 1978 1 219. Bennema P. and van der Eerden J. P., J. Crystal Growth 1977 42 201. Davey R. J.. Current Topics in Material Science (Edited by Kaldis E.), Vol. 8, p. 429. North Holland, Amsterdam 1982. Human H. J., van der Eerden J. P., Jetten L. A. M. J. and Odekerken J. G. M., Paper presented at ICCG 6, Moscow 1980. Bourne J. R., A.1.Ch.E. Symp. Ser. No. 193 1980 76 59. Davey R. J., Mullin J. W. and Whiting M. J. L., J. Crystal Growth 1982 58 304. Boistelle R. and Doussoulin A., J. Crystal Growth 1976 33 335. Simon B., Grassi A. G. and Boistelle R., J. Crystal Growth 1974 26 77, 90. Boume J. R. and Davey R. J., J. Crystal Growth 1976 36 287. B&me J. R., Davey R. J., Gros H. and Hungerbuhler K.. J. Crvstal Growth 1976 34 221. Bourne J: R. and Davey R. J., 1. Crystal Growth 1977 39 267. Bourne J. R.. Davev R. J. and McCullock. J.. Chem. Engng Sci. 1478 33.199. Ohara M., Reid R. C, Modellina Crvstal Growth Rates from Solution. Prentice-Hall. I&g&wood Cliffs, New Jersey 1973. Bennema P. and Gilmer G. H., Crystal Growth: an Introduction (Edited by Hartman P.), p. 263. North- Holland, Amsterdam 1973. Pamplin B. R. (Ed.), Crystal Growth, 2nd edn. Pergamon Press, Oxford 1980. Frank F. C., Disc. Farad. Sot. 1949. 5 48. Burton W. K., Cabrera N. and Frank F. C., Phil. Trans. Roy. Sot. 1951 243 299. Behnema P., J. Crystal Growth 1969 5 29. Bennema P., J. Crystal Growth 1974 24/25 76. Garside J., Crysrai Growth and Mater& (Edited by Kaldis E. and &heel H. J.), p_ 484. North-Holland, Amsterdam 1977. van der Eerden J. P., J. Crystal Growth 1981 52 14. Bennema P., J. Crystal Growth 1967 1 278. Mullin J. W., Chem. Engr (London) 1972 261 186. Sohnel O., Garside J. and Jancic S. J., J. Crystul Growth 1977 39 307. Mullin J. W. and Sohnel 0. Chem. Engng Sci. 1977 32 683. Sohnel 0. and Mullin J. W., Chem. Engng Sci. 1978 33 1535. van Leeuwen C., J. Crystal Growth 1979 46 91. van Leeuwen (3. and Blomen L. J. M. J., J. Crystal Growth 1979 46 96. Sohnel 0 and Garside J., J. Crystal Growth 1979 46 238. Cardew P. T., Davey R. J. and Garside J., J. Crystal Growth 1979 44 534. Sohnel 0. and Garside J., J. Crystal Growth 1981 54 358. Nernst W.. 2. Phvs. Chem. 1904 47 52. Wilcox W.. R., M&. Res. Bull. 1969 4 265. Wilcox W. R., J. Crystal Growth 1972 12 93. Westpbal G. H. and kosenberger F., J. Crystal Growth 1978 43 687. Sore11 L. and Myerson A. S., A.I.Ch.E. J. 1982 28 772. Jagannathan R. and Wey J. S., J. Crystal Growth 1981 51 601. Jagannathan R. and Wey J. S., Photo. Sci. Engng 1982 26 61. Janssen-van Rosmalen R.. van Leeuwen C. and Smith J. M., Delft Progr. Rep. Ser. A., 1970 1 150. Garside J., Chem. Engng Sci. 1971 26 1425. Garside J. and Tavare N. S., Chem. Engng Sci. 1981 36 863.


Natal’ina L. N. and Treivus E. B., Sov. Phys. Crystallog. 1974 19 389.

Cl801

Cl811

L-1821

Cl831 Cl841

Cl851

Cl861

Cl871

Cl881

Cl891

Cl901

Cl911

11921

Cl931

Cl941

[Ej Cl971

Cl981

Randolph A. D., D&pak C and Iskander M., A.I.Ch.E. J. 1968 14 824.

Cl431

Cl441

Cl451

Cl~l

Cl471

Cl481

Cl491

Cl501

[:::3

Cl531

Cl541

Cl551

Cl561

%j E 1591

Cl601

Cl611 Cl621

Cl631

ElW

Cl651

Cl661

Cl671

Cl681

[::J

Cl751

Cl761

Cl771

Cl781

Cl791

White E. T. and Wright P. G., Chem. Engng Prog. Svm~. Ser. No. 110 1971 67 81. M&n J. W. and Gaska C., Can. J. Chem. Engng 1969 47 483. Bujac P. D. B., Industrial Crystallization (Edited by Mullin, J. W.), p. 23. Plenum Press, New York 1976. van? Land C. M., Wienk B. G., Industrial Crystallization (Edited by Mullin J. W.). p. 51. Plenum Press, New York 1976. Garside J., Industrial Crystallization 78 (Edited by de Jong E. J. and Jancic S. J.). p. 143. North-Holland, Amsterdam 1979. Berglund K. A. and Larson M. A., 2nd World Cong. Chem. Engng, Montreal, Canada 1981. Rusli I. T.. Larson M. A. and Garside J.. A.I.Ch.E. Symp. Ser. ‘No. 193 1980 76 52. Valcic A. V., J. Crystal Growth 1975 30 129. Davey R. J., Ristic k. I. and Zizic B., J. Crystal Growth 1979 47 1. Garside J. and Ristic R. I.. J. Crystal Growth 1983 61 215. van Enckevort W. J. P., Verification of crystal growth models by detailed surface microtopography and X-ray diffraction topography. Ph.D. thesis, University of Nijmegen 1982. _ Garside J., Phillips V. R. and Shah M. B., Ind. Engng Chem. Fun& 1976 15 230. White E. T., Bending L. L. and Larson M. A., A.I.Ch.E. Symp. Ser. No. 153 1972 72 41. Garside J. and Jancic S. J., A.I.Ch.E. J. 1976 22 887. Bransom S. H., Br. Chem. Engng 1960 5 838. Canning T. F. and Randolph A. D., A.X.Ch.E. J. 1967 13 5. Abcgg C. F., Stevens J. D. and Larson M. A., A.I.Ch.E. J. 1968 I4 118. Randolph A. D., Can. J. Chem. Engng 1964 42 280. Hulburt H. M. and Katz S., Chem. Engng Sci. 1964 19 555. Bennett R. C. and van Buren M., Chem. Engng Prog. Symp. Ser. No. 95, 1969 65 44. Garside J. and Jancic S. J., Chem. Engny Sci. 1978 33 1623. Rousseau R. W. and Woo J., Paper presented at A.I.Ch.E. 84th Nat. Meeting, Atlanta 1978. O’Dell F. P. and Rousseau R. W., A.I.Ch.E. J. 1978 24 738. Randolph A. D. and White E. T., Chem. Engng Sci. 1977 32 1067. Larson M. A., White E. T., Ramanarayan K. A. and Beralund K. A., Pacer oresented at A.I.Ch.E. 75th Ann. Meeting. Los Angeles; November 1982. Randolph A. D., Ind. Engng Chem. Fundls 1969 8 58. Fitzgerald T. J. and Young T-C, Ind. Engng Chem. Fundls 1972 11 588. Liao P. F., Hulburt H. M., Paner presented at A.I.Ch.E. 6%-d Ann. Meeting, .Ch&go i976. Shah M. B., Crystallization kinetics and agglomeration of nickel ammonium sulphate in a continuous crystallizer. Ph.D. Thesis, University of London 1980. Han C. D-and Shinnar R., A.I.Ch.E. J. 1968 14 612. Larson M. A. and Randolph A. D., Chem. Engng Prog. Symp. Ser. No. 95 1969 65 1. Larson M. A. and Garside J., Chem. Engr (London) 1973 June 318. Juzaszek P. and Larson M. A., A.I.Ch.E. J. 1977 23 460. Kraljevich Z. I. and Randolph A. D., A.I.Ch.E. J. 1978 24 598. Robinson J. N. and Roberts J. E., Can. J. Chem. Engng 1957 35 105. Nyvlt J. and Moudry F.. Coil. Czech. Chem. Commun. 1966 30 1759.

Cl991

Pwi

PO11

PO21

c2031

F-w

c2051

PO61

c2071

PO81

PO91

c2101

c-=11

c2121

w31

w41

c2151

[%j

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INDUSTRIAL CRYSTALLIZATION FROM SOLUTION · crystallization in the chemical industry and most of the sepecific examples will be drawn from applications involving crystallization from