The kinetics of the secondary nucleation of ice: Implications to the operation of continuous crystallizers

Desalinarion, 17 (1075) 3-16 @ Ekevier Scientik Publishing

THE

KINETICS

1MPLlCATIONS

Company,

Amsterdam

OF THE SECONDARY TO THE

OPERATION

- Printed in The Netherlands

NUCLEATION

OF ICE:

OF CONTINUOUS

CRYSTALLIZERS S. G. KANE.. Departmenr

T. W. EVANS**.

of Chemical

P. L. -I-. BRIAN***

Engineering.

Massachxserrs

AND

A. F. SAROFIM

Institute of Technology,

Cambridge,

Mass.

02139 (U.S.A.)

July 20.

(Rcceivcd

1974:

in revised form July 14. 1975)

XUMMARY

Nucleation rates of ia have been determined for a wide range of solution subcooling refrigerant subcooling, agitation power, impeller configuration. and salt concentration. The results of the study have been used to predict the effect of changes in operating conditions in a continuous crystallizer on crystal size and to draw some tentative conclusions on the mechanism of secondary nucleation.

The predictions study

are shown

made from the batch crystallizer

to provide

data from continuous

an adequate

generalization

nucleation

data of this

of all the past nucleation

crystallizers.

SYMBOLS

I A

-

growth rate Induction time Actual nucleation rate, Eq. (I)

P/V r AT

-

AT, B T

-

Agitation power per unit volume Average crystal size Bulk soiution subcooling Refrigerant subcooling Nucleation rate per crystal, Eq. (1) Average residence time of a continuous

PO

-

Total

G

Crystal

MSMPR

crystallizer

number of crystals within the crystallizer

1. SCOPE

The crystal size distribution

produced within an ice crystallizer determines

* Presently with Amoco Chemicals Corporation,

Naperville, III. (U.S.A.) * Prexntly with Upjohn Company, Kalamazoo. Mich. (U.S.A.) l ** Presently with Air Products Corporation, Allentown, Penna. (U.S.A.)

l

4

S. G. KANE et Ok

the east with which crystals may be separated from the liquid phase and the adhering liquid removed. The quality of ice produced in a continuous crystallizer can be shown by the use of population balance mathematics to be quantitatively related to the kinetics of nucleation and growth. In previous studies by Margolis ef al. (I), Brian et al. (2) and Sperry (3), significant progress has been made towards the development of generalized correlations for ice growth kinetics, but the situation is quite different as far as ice nucleation data is concerned. Previous studies by Margoiis et al. (I), Sadek (4), Thijssen et al. (S), Denton et al. (6). Estrin (7) and Schneider ef al. (8, 9) on ice nucleation have identified bulk solution subcooling, refrigerant subcooling, agitation rate, temperature nonhomogeneities, ice concentration. and salt concentration as variables affecting nucleation rates. Tne data generated, however, are too sparse and, in some cases, the test conditions are not sufficiently well documented to permit deveiopment of either an empirical correlation for the rate of ice nucleation or a mechanism for secondary nucleation. An experimental program was, therefore, designed to provide nucleation data over the range of conditions of practical interest. A major objective of this paper is to organize the nucleation data of this study and of previous studies in a general analytical framework so as to obtain a better understanding of the effects of crystallizer design parameters on the operation of continuous crystallizers. Greater understanding of the mechanism of secondary nucleation of ice is essential, however, before nucleation data can be translated into continuous crystallizer performance and results obtained in one study extrapolated to crystallizers of different dimensions and design. The mechanism of ice nucleation is not well-understood. It has been established conclusively by Sadek (4), Estrin (7) and Schneider et al. (8, 9) that the nucleation in an ice crystallizer is secondary nucleation. Previous studies by Kane et al. (Zi) have correlated the nucleation rate Ej with the nth moments of the crystal size distribution:

where the moment is proportional to crystal concentration for rr = 0, to perimeter forn = 1, area for n = 2, etc. The value of R has not been established and the parameters controlling a,, are not adequately understood. The above correlation is consistent with a simple model that secondary nucleation is a result of the interactions of an ice crystal with the surrounding fluid, agitators, baffles or crystallizer walls_ The relative contributions of these several mechanisms is unknown. It is also unknown whether crystal-crystal collisions make a significant contribution to secondary nucleation at the higher ice concentrations of interest in commercial units and whether mechanisms not involving collisions are significant- This paper seeks to answer some of the above questions. It should be noted that the inference of nucleation kinetics is complicated by the fact that the rate of secondary nucleation may be proportional to the nth

KINETICS

OF THE SECONDARY

NUCLEATION

OF ICE

5

moment of particle size distribution where n is unknown, a priori. Complete characterization of the nucleation kinetics requires the determination of two parameters n and a,. It has been shown, however, by Kane ef al. (/I) that a single composite parameter (fl) of n, a, and the growth rate G can characterize many of the important features of the operation of both batch and continuous crystallizers. It can be shown ,g =

1 r

=

(If) that

6- = (,,!amG")'i"+'

where T is the average residence time :n a continuous crystallizer. Since cl,, is the concentration of crystals, fi can be viewed as the nucleation rate per crystal. Experimental results reported in this paper show the effect of independent system parameters

on the composite

parameter,

/I. Guidelines

are then

developed

for the expected dependancy of the average crystal size on the design variables of a continuous crystallizer_ It is shown that the previous nucleation data by Msrgolis et al. (I), Sadek (4), Thijssen ef ni. (5), Denton et al. (6), Estrin (7) and Schneider et crl. (7, 8) obtained from both batch as well as continuous crystallizers can be successfully interpreted using the above guidelines. Thus. this paper also seeks to demonstrate the utility of an analytical framework developed by Kane er al. (II) in providing an adequate generalization of all the nucleation data from the past and the present 2.

EXPERMIENTAL

studies. AND DATA A?JALYSIS

The experimental apparatus was a batch crystallizer operated at constant subcooling described previously by Kane et al. (II). Crystallization was initiated in the crystallizer either by growing a single crystal on the tip of a hypodermic needle or by introducing a free polycrystalline seed. This seed nucleated new crystals which in turn grew and nucleated more crystals_ Eventually, the temperature in the crystallizer began to rise and finally reached the equilibrium freezing temperature. The temperature-time rates per crystal

trace was utilized

in the determination

of the nucleation

(/I) [see Kane et al. (II)].

3. RESULTS The range Table

of the variables

covered

by the experiments

is summarized

in

I.

3. I _ E#ecr of refrigerant subcooling The nucleation rate per crystal was found to be insensitive to the reftigerant subcooling, in agreement with Margolis et al. (I) but in contrast to Sadek (4) and Denton (6). The apparent contradiction between the different investigators’

6

S.

TABLE

G. KANE

eI

al.

I

RAT’iGE

OF VARIABLES

__-_-.-

.--..-

Paramef er

ZC(OK) ~TR (“K)

Agitation

SCUDlED

._----.- --_-.-..-. -._. -- .-... -_ ---- -..- -

--...--._.-

._-_..

__-__-

Variorion

__.._.

--

. _-__

0.07-0.30 0.7, 2.2 power

265.1,880

J/W) (s) Type cf agitation

Marine prqcller, 0. 5.3

Salt concentration (wt. %J

--.--.-

_-_.-_---

-.___ ._..-- .-- _._ _-_ -.-_._

Turbine

..- __ -.-.. .._ ..___.-.._._ .

results is possibly due to the effect of temperature non-homogeneities. which if significant will have an effect that will scale with refrigerant subcoolkg. In both Sadek’s and Denton’s experiments the mixing was poor and the explanation is a plausible one. In the present experiments. however, the refrigerant flow was only that required to compensate for heat leaks and. therefore. was low relative to those in continuous crystallizers. Since temperature non-homogeneities should scale with refrigerant flow rdte. the present results do not exclude the possibility that refrigerant subcooling may have an effect in a continuous crystallizer. 3.2.

Eflect

of solution

The nucleation

al,

subcooling

rates for four agitation

powers

are shown

as a function

of the

= 0.7 OK

t. ‘k

0

265J/m3s

0.10

0.20

0.40

fLTtK”) Fig.

1. Nucleation

rate as a function of solution subcooling

for four agitation powers.

KINE-TICS

OF

THE

SECOhRARY

SUCLEATlOS

OF

ICE

7

solution subcooling in Fig. I, /$ is found to be proportional to the subcooling raised to the 1.75 power. It shoutd be noted from Fig. 1 that the dependency of /I on the solution subcooling is independent of the agitation power.

The dependency of /3 on the agitation power is independent of the subcooling. The exponent on the power dcpencknce of /3 increases from 0.1 at agitation powers of 265-540 J/(m’#s) to 0.34 for, the range 560-1880 J/m3)(s). Thijssen er (II. (5) observed that the nucleation rate passed through a mjnimun~ as the ~~tatj~n power was increased. The)- ascribed this phenomenon to the opposing effects of increases in the nucleation rate and decreases in tempe!-ature inhomogeneities with increasing agitation power. One would expect that the temperature nonhomogeneities would increase with increasing refigerant subcooling and would decrease with increasing agitation nnd that the etkct of these non-homogeneities on the nucleation rate would decrease with increasing solution subcooling. Since the dependency of fi on the agitation power is independent of the solution subcooling, it is questionable whether the increasing dependency on power with increasing agitation can be accounted for by the effect of mixing on temperature non-homogeneities.

Agitation was provided by twin marine propellers were replaced by a turbine impeller in selected runs

I

i

0

-n

MARINE

in most of the runs. These to determine if agitation

PROPELLERS

TURBINE i;;‘L

O.GE 0.05

0.20

0.10 I3T

(

0.40

K')

Fig. 2. Comparison af nucleation rate as a function of solution subcooling for two im-

pcliers having widely difkring power numbers.

S. 0.

i

c 0.2

-

ef al.

I

/

265J/m3s T,= 0.7

0%.

I

KANE

*K

0.1

I G

F 0.05

0.02

IL-_0.05 AT (t:*)

Fig. 3. Comparison of nucleation rates in brine and tap wwr.

of agitator shape, The results shown in Fig. 2 indicate that the values of j3 are reduced at most by 7% when the substitution was made. power

per unit volume characterized the nucleation rate independent

3.5 Eflect of salt cortcentration Values of fl for tap water are found to be two to three times higher than the comparable results obtained with 5.3 wt. oA salt solution as shown in Fig. 3. The exponen?

on the subcooling

dependence

of the nucleation

to be 1.4 for tap water, or substantially solution at identical solution subcooling. 4.

DISCUSSIOX

rate per crystal

is found

less than that found for 5.3% NaCl

OF RESULTS

It is of interest to infer from the measured values of j3 a better understanding of the operation of continuous crystallizer and of the mechanism of secondary

nucleation of ice. Greater understanding of the mechanism is essential before results obtained in studies such as the present one can be extrapolated to crystallizers of different dimension and design. 4. I _ hpkatiot~s for the operation of continuous crystalkers For a continuous MSMPR crystallizer at steady state the average crystat size can be defined as the totaj. perimeter of the crystals divided by the total number of crystals or the square root of the total area of ihe crystals divided by the total number of crystals, or from the higher moments of particle size distribution.

KINETICS

OF THE

Regardless

SECONDARY

NUCLEATION

of which definition

the following

iCC---

is chosen

9

OF ICE

the average

crystal

size is found

to obey

proportionality G

P

where G is the crysml growth rate which can he calculated by the procedures developed by Brian er al. (2) and Margolis ef al. (I). The discussion below is to be based on consideration of the asymptotic value of the growth rate valid in the large Fartick limit. This is adequately approximated by G = 9.33 x 10m6 (P/V)“*ATm/s

in tap water

(3

G = 3.28 x 10m6 (P/V)“-LATm/s

in 5.3%

(3)

where P/V is the agitation

power

brine

per unit volume

the soiution subcooling in degrees centigrade. The nucleation rate per crystal can adequately concentration and agitator configuration as

in units of J/(m3)(s) be correlated

and AT is

at the given salt

B cc hW’V’!Vb

(4)

where (I and L, in this study are constants. u is a function of the salt concentration. In 5.3 wt. y0 salt solution. it follows from the above correlations that crystal size should vary with AT-a-75. The solution subcooling can be related to the average residence time(r)_ Since j3 CC AT’ *” and T cc I/& it is expected that AT a 7-‘/‘-” -o-57 - Thus the average crystal size should be proportional to the average or+ residence

time raised to the 0.43 power.

In water, the average

crystal size should

be

proportiona to the average residence time raised to the 0.28 power. With G proportional to (P/V)“* and /3( = I/T) proportional to (P/V)‘*’ I0 ‘w3*, the average crystal size at constant subcooling would be proportional to (p/v)o.15 to -0.09* The more realistic situation is that in which Pf Y is varied for a constant residence time. For this case the average crystal size is expected to be proportional to (P/Y)‘-” ‘OO-O’. Eqs. (3) and (4) are applicable to the larger crystals expected in ice crystallizers. For an average crystal size and typical agitation powers a dependence of the crystal growth rate on agitation power per unit volume raised to the 0.15 to 0.20 power is more realistic. For this dependency of the growth on the agitation power the average crystal size is found to decrease slightly with increasing agitation power at the high agitation rates.

10

s.

G. iiiwE

et

al.

The rcplacrment of the marine prapellors by a turbine increases the average crystal size by a maximum of ?‘?L at constant s&cooling or 4 percent at constant residence time. From Eqs. (3) and (4) the ratio of the growth rate in tap water versus that in 5.3 ‘?LNaCI is 2.85, which is identical to the ratio of the nucleation rates per crystal at a solution s&cooling of O.OS”K, suggesting that at this subcooling the same median crystal size will bz obtained when ice is grown in water and 5.3’:; salt solution, Since the dependency of fl on the solution subcooling is less for tap water. the average crystal size is expected to increase with decreasing salt concentration for subcoolings greater than 0.08. The above c~lnciusions are in general supported by the results obtain& on continaous crystallizers. From the data of Margolis M d. (1) for a 6% NaCI solution the average crystal size (G/B) can be shown to be proportional to the square root of resid:ncc time over the subcooling range 0.02 to 0.03%. while the average crystal size was found to be independent of the ;rgitation power for agitations of 338 and BOO f/m% For an agitation power of 4XKi .i/m3s and tap water Thijssen et cr/, (_F, observed an increase in average crystal size from 0.6 x 10m3m to 0.8 x IOm3m when the residence time was increased by a factor of 4. In other words the average crystal size was found to be proportional to the average residence time to the quarter power as compared with the 028 power caiculated from the data of this study. The dependency of the average crystal size on the design variables (X and P/V) shoufd be compared with the dependency of the crystallizer productkity on these variables. p or the inverse of the residence time is proportional to the crystalif the crystattizer productivity is increased by lizer pr~~ctivity. Therefore, decreasing the residence time, the average crystal size will decrease with the productivity to the -0.43 power. In theory (ignoring increases in the maximum possibfe energy removal with incrertsing agitation) the productivity of &he crystallizer would be independent of the agitation and. therefore, the agitation rate will effect the average cry&t -size without changing the crystallizer pr~uc~vity. 4.2. Mechanistic irrterpretGtiort Since secondary nucleation crystal, the original crystal. must

occurs only in the presence of a stable parent in some way induce this nucleation. There has

been much speculation in the literature on the source of these new nucIei and how the source is displaced into the bulk of the soiution. &fortunately, there are limited

experimental resuits which verify or disprove any of these speculations. It is the purpose of this section to review several of these theories and to consider what may be inferred from results of this study and other studies on the mechanism of secondary nucleation of ice. It should be remembered that in order to use the nucleation rate data

KiNETlCS

OF THE SECONDARY

NUCLEATION

OF ICE

I1

presently avaiiabie to design systems of a different scale it is essential that the mechanism of secondary nucleation be understood. More exciting is the possibility of reducing the nucleation rate and therefore, increasing the average crystal size at a given crystallizer productivity. A number of sources of the new crystals have been suggested. inciuding dendrites or microscopic surface irregularities, molecular clusters and macrobreakage of the parent crystals. Presently the most accepted source is the shearing of dendrites or irregularities from she surface of the parent crystals; this source will be discussed first. Melia and Moffitt (12) studied secondary nucleation of KC1 in a batch crystallizer and reported a great increase in the nucleation rate with the occurrence of dcndritic growth on the seed crystals. In a related study 113) these researchers reported that tiny dendrites were observed rising in the convective currents associated with the growth of NH,CI and NH,Br crystals. Although surface irregularities have been observed on ice crystals, there is presently no experimental evidence to directly link their presence with the secondary nucle- lion of ice. Dendrites and other surface irregularities were observed on the surface of the fixed ice crystal used to seed the crystallizer in this study; however. these irregularities were not observed to be sheared from the crystal by the fluid. Scallop type growths were seen on the crystals in the study of Margolis et al. (I) at subtoolings of 0.02 to 0.03”K. While limited data is available on dendrite growth in a turbulent field, numerous investigators have observed and studied dendrite growth on ice crystals in a stagnant fluid. The most convincing evidence of dendrite formation is provided by the photomicrographs taken by Hardy and Coriefl (14-16) of ice cylinders grown at subcooiings in the range of 0.1 “K. Perhaps the earliest reported hypothesis of moiecuiar clusters is due to Powers (17). He observed that a stationary sucrose crystal placed in a flowing supersaturated solution yielded new crystals downstream from the parent crystal. When the sucrose crystal was replaced by a plastic model, crystals were still observed downstream but less than those observed with the sucrose crystal. In order to explain the nucleation by the plastic model and the sucrose crystal in the apparent absence of any dendrites, Po-wers postufated that io&seiy bonded moiecular ciusten associated with the surface of the sucrose crystal or the piastic model may be displaced by the fluid shear and become stable nuclei. If the molecules in these clusters do not form a solid phase when they are under the influence of the parent crystai but solidify when they are displaced into the bulk, then the thermodynamics must be much more favorable in the bulk. From this logic it follows that the resulting nuclei must be smaller than the thickness of the boundary layer. Since the growth of ice crystals in salt water is largely controlled by mass transfer, only the mass boundary layer will be considered. The mass transfer boundary_iayer thickness for the ease of a NaCi solution is approximately 0.01 x iOe3 m, however, the smaiiest crystai observed in this study or that of Margoiis et al. was 0.1 x 1O”‘m. This observation casts considerable doubt on the possibility that molecular

I2

s* G. KANE et al.

clusters are the source of new nucIei for the ice-salt water system. The fin& source of the new nuclei to be considered is the macrobnzakage OF the parent crystals. This source contrary to the first source (microattrition) produces new crystals by fracturing the existing crystals into two or more nearly equal-sized parts. Margolis (I) was able to predict the crystals size distribution by assuming that new crystals were nucteated at essentially zero size. This lends credence to the assumption that the nucieatcd crystals are small with respect to the parent crystals and to the postulate that micr~att~t~~n is the principal source of seed crystals. Given a source of the new nuclei the source must be displaced from the surface of the parent crystal into the bulk. Three mechanisms ofremovaf have been suggested; col!isions of the ctyscals with the crystallizer, collisions of the crystals with one another and the shear of the fluid. Collisions with the crystallizer wil! be considered first. La1 ef al. (18) studied the secondary nucleation of MgSO,~7H 2O in a batch crystal&r. They observed if a seed crystal was held stationary in the agitated supersaturated solution of the crystallizer no new crystals were nucleated. However. if the seed crystal was touched with a glass rod or allowed to slide sfowly atong the bottom of the crystzdtier the crystal woufd nucleate, More recently, Cionu and +K%e (19) grew a stationary MgS04-7NZ0 crystal in a flowing suprsaturated solution. No crystals were observed downstream; however, when the crystal was contacted with a metal rod new crysrais were observed downstream. The number of new crystals per contact was found to increase linearly with the collision energy but was independent of the fluid velocity past the crystal, A later paper by Johnson, Rousseau and McCabe (20) ~rified the earlier observation plus it. was noted when a rubber plug was attached to the tip of the metal rod that the nucleation was eliminated. In experimenti with a batch crystallizer the replacement of a stainkss steel prop&or with 8 plastic one reduced the nucteation rate by a f-or of ten. This set ofexperiments definitely prove that crystal-crystallizer collisions rre :he dominant mechanism of secondary nucleation for BAgSO,Wi*O. TABLE E COMPARISOX

5.566

5.075 0.205 5.566

Of

MDUC’XtDF4

26s 2GS 26!s 265

TtMES

5.7

5.7 0.7 2.2

FOR

A F?XED

SlNGLE

5.523

5.52 t 0.154 5.528

CRYSTAL

AND

485 455 Ill 545

A FREE

PD&YC&~YS~ALLKNE

5.517 5.518 0.592 5.537

-

sFJXB

265 103 52 .171

The fls in each case determinedfrom the maximum slop: of the temperature-timecurve.

KlNETlCS

OF THE SECONDARY

NUCLE4TION

OF ICE

13

The experiments conducted with the two different methods of introducing the seed crystal provide indirect evidence rhat the mechanism of crystals colliding with the crystallizer dominated any mechanism dependent on fluid shear forces. The time (l) required for the temperature to depart appreciably from the initial vatue was found to be consistently lower when the crystal was injected into the solution than when it was grown out of the tip of the hypodermic needle (Table IT). The induction time can be thought of as a measure of the nucleation rate of the seed crystaf, the shorter the induction time the more productive the seed crystal. Thus the free polycrystailine seed was found to nucleate at D faster rate than the stationary single crystal. The small change in the nucleation rate when the two marine propeilers were replaced by a turbine ma: also suggest that collisions of the crystals with the crystallizer is a mechanism of secondary nucleation. The growth rate of crystals, freely suspended in a vigorously agitated tank. is dependent on the agitation power. but is independent of the type of agitation. Since secondary nucleation due to fluid shear is dependent only on small scale turbulence, one would expect this mechanism to be dependent only on the agitation power. Similarly if the nucleation was limited by the growth of surface irreg,uIarities, the rate would be independent of the type of agitation. However. secondary nucleation due to and limited by the collisions of the crystals with the agitator or the bafftes is determined by the circulation in the near region of these obstacles: therefore, this mechanism of nucleation would not be expected to be independent of the type of agitation. When the marine propellers were replaced by a radialIy mixing turbine, the nucleation rate per crystal was reduced by approximately 774, If the nucleation is limited by rhe removal of dendrites, this result would suggest crystal-crystallizer collisions at least make a small contribution fo the overall nucleaGon rate (7% if n = 0; 25% if I* = 3). Howsver. if the rate is onfy partially limited by the removal, this contribution would be much greater (21). When Clontz and McCabe (19) contacted the stationary MgSO,-7Hz0 crystat with another crystal, new crystds were produced_ This observation indicates that nucleation could possibly be due to collisions between crystals. If this is the dominant mechanism, one would expect the rate to correlate with the square of the number, perimeter, area, mass, etc.. of the crystals. It was noted earlier that the nucleation rate correlated well with the first power of the moment of the particle size distribution (II). The lack of importance of crystal-crystal collision nucleation may be due to the low ice concentrations (less than 0.04 7;) used in this study; however, the earlier study of Marsolis at higher IeveIs of the ice concentration (44% on a weight basis) showed that the nucleation rate per crystal was independent of the iceconcentration over this range. These resuits imply that the nucleation due to crystai-crystal coilisions is negligible when compared with the overall nucleation rate. It has been estimated by Evans et al, (22) that for conditions expected in a

14 continuous

S. G, KANE ef d.

MSMPR crystallizer operated at 30% by weight ice, crystal-crystal

collisions are responsible for 20% of the overall &deation rate. The nucleation rate due to crystakrystal collisions correlates with the product of a moment of crystal size dis~~butions with weight percent ice (22, 23). The contribution of crystal-crystal collisions to the overah nucieation rate, therefore, increases with an increase in VI;tght ?< ice and is estimated to be 9.10/Oand 16.77; at 4 and 8 weight % ice. t%qectively. The estimated decrease in the mean crystal size is small (4.59: if n = 3). The observation that the fixed crystal initiated growth and nucleation in the bat& crystallizer suggests that fluid shear is capable of inducing secondary nucieatiott. Aqther indication of the possible importance of this mechanism is that secondary nucleation &; significant in crystallizers agitated by an evaporating refrigerant in the absence of mechanicai agitation (4). it should be noted that this may also be expk.ined*by the collision of crystals with the vcahs.

5. COPXLUStONS

AND SIGNIFICANCE

The nucleation rate per crystal fl for ice has been determined as a function of refrigerant subcoohng, solution subcooling, degree of agitation, type of agitator and salt concentration. The avenge crystal size G&I was found to be most sensitive to the solution subcooling. but relatively insensitive to the refrigerant subcooling, degree of agitation and type of agitator over the operating conditions considered. If the crystallizer pr~ucti~ty is increased by reducing the average residence time the average crystal size is expected to decrease with the crystallizer productivity to the 0.43 power in 5.3 wt 7; salt solution and to the 0.28 power in tap water. These conclusions are supported by the reported resuhs obtained from continuous

crystallizers, The above conclusions, therefore, provide an adequate generalization of the nuclea~on data reported in past studies and in the present work. The correlation between the predicted and observed continuous erystahizer nucleation data demonstrates the vaiidity and utility of the method presented in this paper for predicting continuous crystafiizer performance from batch crystallizer nucieation data. _ It is presently believed that the new nuclei are the result of shearing dendrites or irregularities from the surface of the parent crystals. The results of this study suggest that collisions of crystals with the crystalker is a mechanism of nucleation, but it is also Possible that fluid shear is making a contribution_ Comribution of crystal-crystal coflisions is negligible at ice concentrations used in this’ study. Inasmuch as the se&-up criteria-for different mechanisms are different (23) and are not presently available for all of them, nucleation data should be applied with caution to conditions other than those under which they were obtained until a better understanding of the meehanism.is available.

KINETICS OF THJZSECONDARY NUCLEATION

Of ICE

15

ACKNOWLEDGEMENT

The authors gratefully acknowledge the financial support provided by the Ofice of Saline Water of the Department of the Interior and the many useful discussions with Dr. G. Margolis and A. Garcia. REFERENCES

I. G. hIAa(iOus. T’. K. SHERWOOV,P. L. T. BRIAX A.?~DA. F. SAROFIU, The Performance of a Continuous Well Stirred Ice Crystallizer, Ind Eng. Chem. Fundumenrafs, IO (1971) 439. 2. P. L. T. BRIAN. H. B. HALFS ASD T. K. SHERWOOD.Transport of Heat and Mass Between Ltquid and Spherical Rrticlc in an Agitated Tank. A,n. Ins?. Chzm. Eng. 1.. IS (1969) 727. 3. P. R. SPERRY, The Effst of Additives on the Kinetics of Crystalliza~lon of Supercooled Water, Sc.D_ Thesis in Chemical Enginrering, M.I.T., Cambndgc. Mass.. 1965. 4. S. S~DEK. Nucleation and Growth cf Ice in Saline Solutions, Sc.D. Thesis in Chenricul Engineering. &l_I.T., Cambridge, Mass., 1966. 5. H. A. C. THIJSSEX, cr nl.. Nu&ation and Growth of Ice Crystals in a Continuous Stirred Tank Crystallizer. Proc. Stmp. Indtts!riuI Cr.vsialIkarion, London. April 1969, p_ 69. 6. W. H. D~sro~, N. S. H. TAYLOR. J. T. KLASCHKA. M. J. S. SMITH, H. R. DIFFEY AND C. H. RUBBERY, Experimental Studies on the Immiscible Refrigerant Freezitig Process, Report AERE-R6IO& Chcm. Eng. Div.. Atomic Energy Research Est., Hatwell. U.K., 1970. 7. 1. ESTIUN, Fmal Report to Office of Saline Water. U S. Dept. of Interior under Grant No. 14-01-0001-971, August 1969. 8. G. R. ~&.X~S~IDER, P. R. NEWTONA%D D. F. SHEEHAN,Nucleation and Growth of Ice Crystals. Final Report to Oflice of Saline Water, U.S. Dept. of Interior under Grant No. 14-01-OOOl333. December 1968. 9. G. R. SCHNEIDER. Quarterly Report to Office of Saline Water, U.S. Dept. of Interior under Grant NO. 14-01-0001-2156. November 30. 1970. 10. S. G. KANE. Secondary Nucleation of Ice in a Stirred Batch Crystallizer, Sc.D. Thesis in Chemical Engineerin& M.I.T., Cambridge. Mass., April 1971. 11. S. G. KASE, T. W. EVA~X, P. L. T. BRIAN. A. F. SAROF~M,Methods for Determining Nucleation Kinetics in Batch Crystallizers. AICHE J., 20 (1974) 855. 12. T. P. hkLU AND W. P. Mom. Crystallization from Aqueous Solution, 1. Colfo&l Sri.. 19 (1964) 433. 13. T. P. hfnu AND W. P. MoF~. Secondary Nucleation from Aqueous Solution, Ind. Etw. Chem. Fundumentals, 3 (1964) 313. 14. S. C. HARDY AXD S. R. CORIFLL. Morphological Stability and the Ice-Water Interfacial Frc= Energy, /. Cr_sstai Growrh, 4 (1968) 569. 15. S. C. HARDY AWI S. R. Cottt~t~. Morphological Stability of Cylindrical Ice Crystals. J. Crystal Growth, 5 (1969) 329. 16. S. C. HARDY ASD S. R. CORIELL, Morpholo8ical Stability of Cylindrical Ice Crystals in Aqueous Solution, /. Cijxrul Growth, 7 (1970) 147. 17. H. E. C. PO\hlERS, Nucleation and Early Crystal Growth, Ind. Chem.. (July 1%3) 351. 18. D. P. LAI_ R. E. A. Mhsox AND R. F. STRICK~ND-COXS~~LE, Collision Breeding of Crystal Nuclei, /_ Crysful Grow//:. 5 (I%91 1. 19. N. A. Ctomz AND W. L. MCCABE, Contact Nucleation of Magnesium Sulfate Heptahydrale. presented at 62nd Annual Meeting, AICbE, Washington. DC.. November 1969. 20. R. T. JOHNSON. R. W. ROVSSEAUAND W. L. hfcClraE. Factors Affecting Contact Nucleation. presented at Third Joint Meeting. AIChE-I.M.I.Q., Denver. Cola., 1970. 21. T. W. Evq Mechanisms of Secondary Nucleation During the Crystallization of Ice, Ph.D. Thesis in Chemical Engineering, M.I.T., Cambridge, Mass., 1373. 22. T. W. Evms, G. MARGOU~ sm A. F. SAROFL~, Mechanisms of Secondary Nucleation in Agitated Qystallizers. AICHE 1.. 20 (1974) 950.

16

S. G. KANE et 01.

23. T. W. Evans, G. MARGOLIS AWJ A. F. SAROFIM. Models of !SecondaryNucleation Attributable to Crystat-Ciystallizxr and C~mM2-ySal Collisions, AICHE 1.. 20 (1974) 959.