Hydrodynamic Characteristics of Dispersed Phase Crystallizers. II. Coalescence in Three-phase Liquid-Liqu id-Solid Systems Samuel Sideman,* K. Shiloh,’ and William Resnick Department of Chemical Engineering, Technion, Israel Znstitute of Technology, Haifa, Israel
Three-phase dispersions contain “conglomerates” (C) (drops containing solids) and solid-free drops (D). The conglomerates are larger than the drops. The effect of drop and conglomerate sizes on the coalescence rate is analyzed, and possible mechanisms for homogeneous, C-C or D-D, and heterogeneous, C-D, coalescences are discussed. Overall coalescence rate data are used to calculate the specific coalescence rates. Solid content, hold-up ratio of the dispersed phase, and mixing intensity affect the size of conglomerates. The latter i s the most important parameter affecting coalescence. Depending on operating parameters, C-C coalescence rates are 2 to 13 times higher than D-D coalescence rates. Similarly, C-D coalescence rates are larger than D-D coalescence rates. The former i s smaller than C-C coalescence rates when crystals are large and uniform and approach C-C coalescence rates in the presence of small crystals.
Three-phase dispersions are anticipated in processes in which the active liquid (say, mother liquor) together with the solids (crystals or catalysts) are mechanically dispersed in a n immiscible liquid medium. This mode of operation has wide potential applications: for example, salt crystallization from aqueous solutions, solvent purification from dissolved salts, catalytic or liquid-solid reactions, and crystallization of reaction products in dispersed phases. It is particularly attractive for cases involving high solid to mother liquor ratio. The continuous liquid phase can be a reactant, carry a reactant, or else function as a selective solvent for a product of the dispersed phase reaction. It may also serve as a n inert heat transfer medium allowing better temperature control, efficient mixing, and a relatively convenient mode of transportation. Knowledge of the hydrodynamic behavior and the interaction between the dispersed particles is required for proper understanding, detailed evaluation, and future design of three-phase systems. The present work is devoted to the study of coalescence and complements a n earlier study (Shiloh, et al., 1971a) which deals with break-up mechanisms and the ensuing physical characteristics of such systems. Under intensive mixing conditions the three-phase system contains two kinds of “particles”: solid-free drops of the mother liquor similar in size to drops in liquid-liquid disconpersions (0.1-0.3 mm) and “conglomerates”-drops taining solids-which are a n order of magnitude larger than the solid-free drops (1-3 mm), The coexistence of conglomerates and free drops in the dispersion implies that three types of coalescence occur: homogeneous conglomerate-conglomerate (C-C) coalescences, homogeneous coalescence between the free drops (D-D), and heterogeneous coalescence between the conglomerates and free drops (C-D). Since these processes occur simultaneously, and most probably a t different rates, a technique to evaluate the specific coalescence rates is required. 1
Present address, A.E.C., Nahal Sorek, Yavne, Israel.
570 Ind.
Eng. Chem. Fundarn., Vol. 1 1 , No.
4, 1972
Once these rates are known, evaluation and efficient utilization of these three-phase “reactors” may be feasible. For instance, the C-D coalescence rate will dictate the crystallization rate, while the C-C Coalescence rate will dictate the degree of concentration segregation. Some related work on coalescence and breakup in threephase systems is of interest. Mizrahi and Barnea (1970) showed that a small amount of fine solids, such as graphite powder, greatly enhance emulsion breakup. I n the absence of mixing, the emulsion stability, or breakup by coalescence, depends strongly on the physical properties of the liquids and the solids employed. Of particular importance are the solid preferential wettability, the surface tensions, and the spreading coefficients. Granulation studies are also instructive. Here fine solids (up to 300 p ) are preferentially wetted by one fluid and granulated in another nonwetting continuous fluid. The final product is, usually, spheres 3-10 mm in diameter. Kapur and Fuerstenau (1969) developed a theoretical model for coalescence of wetted solid particles. Assuming that the probability for coalescence is identical for all granular sizes, they obtained a time-dependent size distribution of the conglomerates. The systems considered were not a t steady state since they neglected breakup and, theoretically, the granulars grow with time. Their calculated size distribution is, however, in good agreement with the first three moments of the experimental one. No steady state coalescence studies were reported for three-phase systems. However, earlier studies of two-phase systems are instructive. Utilizing various experimental techniques, most of the reported coalescence studies endeavor to determine coalescence rate dependence on the operating conditions rather than on drop size (Hielstad and Rushton, 1966; Rietema, 1964). The exceptions are Howarth (1964, 1966), Shinnar (1961), Shiloh (1970), and Shiloh, et al., (1971b). According to Howarth, coalescence between two “colliding” drops approaching one another depends on their velocity.
However, no connection is suggested between his quantitative conclusions and drop size. Shinnar suggests the limiting drop size for coalescence but does not relate coalescence to drop size below this critical size. Shiloh, et al., obtained steadystate dependence of coalescence rates on drop size. This was achieved by determining the coalescence rate dependence on hold-up ratio while simultaneously measuring drop sizes. Various coalescence mechanisms, depending on the controlling flow regime (viscous or kinetic) and the acting interparticle surface forces, were evaluated analytically. The phenomena encountered here are best understood in the light of these concepts and mechanisms. Theoretical Considerations
A. Homogeneous Coalescence (D-D and C-C). Random coalescence is a product of the collision rate and vl, the collision efficiency. Relating the drainage of the film between two drops in a collision course and the lifetime of the eddies pushing the drops together, Shiloh, et al. (1971b and unpublished work) suggested that
--
7 7
do
(viscous flow regime)
d’4/3
(kinetic flow regime)
(1) (2)
Combining eq 1 and 2 with the corresponding expressions for the collision rate and holdup #I yields ut
w,
-
@do
(viscous flow regime)
(3)
#Ia’/a
(kinetic flow regime)
(4)
-4s drop size increases, the efficiency indicated by eq 2 increases as the ratio of the drainage time to the eddy lifetime approaches unity. Also, large drops are carried by large eddies, and the inertial forces may overcome interparticle forces. Thus, with large drops and/or relatively small interparticle attraction forces, a coalescence prevention regime exists (Shinnar, 1961) and ut
-
#I~lo%) free-drop volumes are associated with large homogeneous crystals and low solid fractions. Obviously, reliable C-C coalescence rate data can be obtained under conditions giving a low, assumed negligible, free-drop volume. The effect of mixing on the characteristic coloring time and the average conglomerate diameter is presented in Figure 6, indicating that coalescence rate is proportional to the mixing intensity. As is to be expected, the average diameter of the conglomerates decreases with increased mixing intensity. Some typical coloring curves, ec us. 6, are shown in Figures 7 and 8. The characteristic coloring time decreases (coalescence rate increases) with 6. An apparent minimum is seen in the kerosene system whereas a n asymptotic level is noted in the kerosene-PCE system. The difference is due to segregation by gravity; the average density of the conglomerates varies between 1.3 and 1.35 and the dispersed phase tends, in the case of kerosene, to concentrate a t the bottom of the vessel as holdup (and conglomerate sizes) increases. Thus, the effective holdup in the kerosene system ( p c = 0.78) may be four times larger than the nominal one, and the characteristics exhibited by this system approach those of the kerosene-PCE system ( p c = 1.25). Figures 7 and 8 represent the combined, overall effect of all possible kinds of coalescences (C-C, C-D, and D-D) which simultaneously take place in the three-phase system. .41so included for comparison are the D-D Coalescence data obtained in the corresponding two-phase liquid-liquid system. However, it is important to note here that order of magnitude considerations (see dorivation of eq F in Appendix I) indicate that the contribution of D-D coalescence to the coloring of the free drops is negligible as compared with that of C-D
corn
400
m w x ) x X ) 4 w
aa,
R o t a l i m l 8P.d tRP.Ul
Figure 6. Influence of rotation speed on characteristic time and average conglomerate diameter
coalescences. Thus, the coloring data may be taken to represent the combined contribution of the C-C and C-D coalescences only. As seen from Figures 7 and 8, the three-phase overall coalescence rates are larger, a t the same 6, than those obtained with the comparable two-phase system. The coalescence rate is lower with the larger (0.8 mm) crystals (the effect of crystal sizes below 0.5 mm is undistinguished). Since large crystals are associated with a high free-drop volume, the O.&mm crystal size curve obviously represents the combined effect of C-C and C-D coalescence, whereas the curves obtained with small crystals-and very small free-drop volumes-are taken to represent C-C coalescence only. Data for C-C coalescence rates are presented in Figure 9.4 where the colored volume fraction a is plotted us. real time for various volumetric hold-up ratios. As seen from Figure 9B, the data for very low 6 can be “normalized” to yield a single dimensionless curve. This type of curve is characteristic of homogeneous coalescence and indicates the apparent geometric similarity between C-C and D-D coalescence. Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
573
8M) 500
-
-
__
056
025
\
C
d= 4 l c
a72 072 072 054
05
0 25
\
glomerates coalesce slower than wet ones. However, as can be seen from the data (curves IV-V in Figure 13), the limit of sensitivity to the liquor content decreases as crystal size increases. This is due to the fact that with small crystals the liquor tends to concentrate inwards, while the opposite is true with large crystals. The effect of crystal size, at constant holdup and liquor content, is shown in Figure 11. Crystal sizes here represent fine cuts obtained by careful screening. The characteristic time decreases (coalescence time increases) sharply with decreasing crystal size from 1 to 0.6 mm, then levels off. Comparison with Figures 4 and 5 shows that the apparent coalescence rate is affected by the rise of the free-drop volume with increased crystal size, synonymous with a larger fraction of C-D coalescence in the overall, apparent rate. It mag, therefore, be concluded that at low liquor content, where the C-C coalescence controls, the effect of crystal size seems minute. However, crystal size greatly affects the free-drop volume and thus affects the relative contribution of the C-D coalescence to the overall coalescence rate. B. The Coalescence Rates. Figures 12-14, representing typical coloring curves, illustrate the interrelated effects of crystal size, liquor content, and free-drop volume on the relative contribution of C-C and C-D coalescence to the overall coloring rate. With small, mixed crystals with a n average diameter of 0.25 mm (maximum 0.4 mm and minimum 0.05 mm), a family of geometricalIy simiIar curves is obtained (Figure 12). Thus, the C-C coalescence rate controls, regardless of liquor content. Otherwise stated: any C-D coalescence under those conditions is of the order of magnitude of the C-C coalescence rate. On the other hand, when uniform and large crystals (20-35 mesh) are present (Figure 13), unsimilar curves are obtained for different liquor contents, despite the relatively lower free-drop volumes. As seen from Figure 13, coloring is initially fast for all dispersions. The rate of coloring then decreases with the increase of the liquor content. Curves for 14-1 and 14-11] obtained a t low liquor content and low free-drops volume fraction in the dispersion, may be taken to represent C-C coalescence. The coloring curves in Figure 13 may be used to calculate w by utilizing eq 10 and the procedure outlined briefly in
i
dc[rnrnl
O.R08
\
*
I. 0.72 f.0.54
\
0
0
RPM=300
‘\
\
\ \
ai
02
0 5 07 IO
20
a2
so70
a507
Disponed Phase Holdup,
4
io
\
\
20
5070
%
Figure 7. Characteristic time vs. dispersed phase holdup for kerosene and perchloroethylene system: A, mixed crystals; 6,elongated small crystals
As the dispersed phase holdup increases, the geometric similarity of the curves exists no more. The conglomerates become nonspherical and less homogeneous. This is evident in Figure 9B where the (Y us. 8 (dotted) curve for the higher dispersed phase holdup departs from the normalized C-C curve. The theoretical curve obtained by eq 10 is included for comparison. The effect of liquor content in the conglomerates on the coalescence rate is easily understood by noting that when two relatively dry conglomerates collide, liquor coalescence may be limited to the point of contact. These conglomerates, being weakly bonded, may be pulled apart before complete coalescence occurs. As seen in Figure 10, the characteristic time decreases (or coalescence rate increases) rather sharply with liquor content for small, elongated crystals, but it levels off, or even increases, with relatively larger crystals. As already indicated, this increase or decrease in coalescence rate is due to C-D coalescence. Similar conclusions may be drawn from Figure 7B: with small crystals the coalescence rates are higher at higher liquor contents over the whole range of 4. This is also consistent with Figure 12, whereby drier con-
700 -\
- \
500-
200
\
-
\ \
g loo-
-
E
70 501
5
20-
Ir
0
c 0
\
\\
--
\
Q\\\\ I\
!I
\
-
5 43
IO
574
\
(I
: 10:7V
Free vdume cdourine, t a m rrporimtnt.
d 9 dlc
(2\
‘ I
n
\
-
1 - 072 Overall coloufing curve 0 - - - - - 8
0 o
f = 0.72 1 - 065
\
\
-B
n I
2
Ind. Eng. Chem. Fundom., Vol. 1 1 ,
I
I 1 1 1 1 1 1
5 7 1 0 0
No. 4, 1972
I
2
I
I
I I I I I
5 7 IO
\ I
2
I
4
,
I
\
/
/ I
4
6 8100
2
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6 OIOOO
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E
3
d
10
20
30
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l.Ot
10
40
20
70
10
40
20
70
IC0
Percent W o t n e a tY.1, ( 1 - f )
I 0
Figure 10. Characteristic time vs. fraction of mother liquor in conglomerates for kerosene and perchloroethylene system: A, plate crystals, screened; B, elongated crystals
-. ' 1 J
10
2.0 D i m e n s i o n l e u Tlme,
-6:
3.0
e
86-
I
Figure 9. Colored volume fraction vs. time a t various holdups for kerosene and perchloroethylene system
4 L
-
:
E
Appendix 11. The characteristic time (for 0.2 5 a1 5 O.8)8,1 = 10 sec O ( = O s ) , the coloring time of the free drops (essentially by C-D coalescence) from a = 0.2 to (Y = 0.5 is 20 sec. EquaLe., the C-C coalescence rate is 16 tion 10 yields w = times larger than the C-D coalescence rate. Figure 14 represents a n intermediate case, where the decrease in coloring rate is moderate, as compared with Figure 13. This is due to the fact that the crystals used in this run consisted of 80% uniform, 20-35 mesh, crystals and 20% small, elongated crystals (maximum size 0.4 mm). Here, 0,1 = 14 see (a1= 0.2 to 0.8),the free-drop coalescence time, corresponding to a2 = 0.2 to 0.5, is 10 sec, and w = 1 / 5 8 , Thus, the addition of small crystals to the uniform large crystals accelerates the C-D coalescence rate by, approximately, a factor of 2. It is interesting that Figure 14 represents data obtained with small crystals which were 1 week old. When fresh small crystals were used, the coloring curves (not shown here) were
h - 0.28 A -0.20 Q - 0.14 0-0.12 + - 0.07
f * 0.72 I
10 01
I
.2 Cryrtal
I
I
I
4 Diameter
I
L
8
I
I
10
dc [ m m l
Figure 1 1 . Characteristic time vs. crystal diameter for kerosene and perchloroethylene system
similar to the C-C coloring curves of low free-drop volume runs. Summarizing, it is noted that with homogeneous and relatively large crystals in the conglomerates the specific C-D coalescence rate is approximately '/le that of C-C. However, when small crystals are present even in moderate amounts the C-D coalescence rate is highly enhanced, approaching the C-C coalescence rate when the conglomerate contains a natural mixture of crystals of sizes equal to, or smaller than, the free drops.
-t 0.52 0.56 0.62
0
2-
0
c V
.
i c * 0 . 2 5 mm
+
1.5 K
320
0.65
RPM
0.71
* - 0.08
0.80
.9 .8 .? 6
5 4
.3 5
10
I5
20
Time t t e c l
Figure 12. Coloring curves a t various solid fractions for mixed crystals, kerosene and perchloroethylene system Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
575
-h
-1
,O.E
aeo
9=
1.5 7.
Q
0.71 0.62 0.56
N
320 RPM
0.14
t 0.18 A 0.28 0.32
. Cdculated
.
Calculatad
IO
9
dc = 20-35 Mesh
Q52
conglcmbrate8 colouring curva t r b a volume colouring curvb--;;4."
----
_././.
20
30
40
50
l i m a tracl
Figure 1 3. Experimental and calculated coloring curves of conglomerates and crystal-free drops; 20-35 mesh crystals, kerosene and perchloroethylene system
+' N
0
IO
20
30
1.s
74
320 R P M
40
50
Time taecl
Figure 14. Experimental and calculated coloring curves of conglomerates and crystal-free drops; cryslal size: 80% 20-35 mesh and 2070 small crystals; kerosene and perchloroethylene system
C, The Controlling Mechanism. The size of t h e smaller drops in the comparable two-phase liquid-liquid systems may be controlled by the viscous flow regime (Shiloh, et ai.,1971b) or as in other systems (Sprow, 1967a, b), by the kinetic flow regime. Coalescence rate increases strongly with drop size, as appears evident by the present results. However, the conglomerates are one order of magnitude larger than the drops in the two-phase system, and in this size range the inertial forces are quite large as compared with the interparticle forces (Shiloh, 1970). As seen from Figure 2 d
and, by Figure 7 wI a
-
eo-'
,pas
(11) Acknowledgment
40.2-0.43
(12)
Combining eq 11 and 12 reflects a decrease in the coalescence efficiency with increased conglomerate size. This is in accord with eq 5 representing the coalescence prevention regime, and consistent with the expectations above, based on the analysis of coalescence rate dependence on drop size. Conclusions
The three-phase liquid-solid-liquid dispersion constitutes a complicated multiparameter system with a number of inter576 Ind. Eng.
acting effects. Nevertheless, a number of conclusions may safely be drawn. 1. Coalescence rates in three-phase systems are 2-13 times higher than drop-drop coalescences in a comparable twophase system. The higher values are obtained when the conglomerates contain small crystals, as would be the case under normal operating conditions. 2. Conglomerate size, crystal size, and free-drop volume are the most important parameters affecting coalescence rates. 3. Higher liquor content in the conglomerates affects coalescence rate favorably when crystals are small, and negligibly when crystals are large and uniform. 4.Crystal size does not affect coalescence when conditions are such that C-C coalescence controls the overall coalescence rate. Crystal size affects the overall coalescehce rate through its effect on the volume of the free drops-the latter increasing as crystals size increases-and the correspondingly larger role played by the C-D coalescence. 5. Drop-conglomerate coalescence rates are 6-16 times smaller than C-C coalescence rates, when uniform larger crystals form the conglomerates. The C-D coalescence rates approach the C-C rates in the presence of small, 0.05-mm1 crystals. 6. Coalescence greatly increases with drop size, consistent with eq 2 and 4. However, in the range of sizes exhibited by the conglomerates in dynamic equilibrium, inertial forces are large and the coalescence prevention regime becomes important.
Chem. Fundom., Vol. 1 1 , No. 4, 1972
This work was sponsored by the Israel Council for Research and Development. The original version of this paper was written in the Department of Chemical Engineering, University of Houston, Houston, Texas, where one of the authors (S. S.) was on his sabbatical leave, 1970-1971. Appendix I
Assuming that all the conglomerates are, on the average, of equal size and that the free drops are also of a uniform size, the rate of coalescence, which affects the coloring of the
than the D-D coalescence rate. For the condition of Vz/V1 = 0.15, Kznz/Klnl is reduced to 0.03. The relative magnitude of the right-hand side terms of eq D is given by
conglomerates, is given by
Kznm 0.015~~~ 2Ktnlnl wff1
-m-
The rate of coalescence which causes the coloring of free drops is given by
Thus, for w = 0.06 and a ~ / a 1< 0.05, the error introduced by neglecting the first right-hand term in (D) is about 10%. Defining 7 =KlnlB, eq C and D reduce to
dai - - a1(1 dr
dnl/dO and dnp/do are the fractional increase of colored conglomerates and free drops, respectively; hence
- a11
d az - ‘v 2wa1(1 dr Dividing eq A and B by n1and n2,respectively, yields
ffd
Denoting a 1 , o as the “initial color fraction” (= 0.2 in this work) and integrating eq C yields ai = A/(e-’
+ A)
(G)
where
and
Introducing (G) into (F) and rearranging, yields The factor uz/ul is introduced since a coalescence between a drop containing FeC13 with a conglomerate containing KI[Fe(CN)8]will result with a color intensity V ~ / U Ismaller than that which would have been obtained had the drop been replaced by a conglomerate carrying the FeC13. ( u l / v z drops coalescing with one conglomerate give the color intensity obtained by one C-C coalescence). Equations C and D may be simplified by order of magnitude considerations. Since the conglomerate diameter is about 10 times that of the free drop, nz = 1000(Vz/Vl)n~.Let the total VZ, be 1 (unity), and volume of the dispersed phase, VI let h denote the liquor volume fraction of the free drops (from total volume of the dispersed liquor) and f be the solid fraction in the dispersed phase. The total free-drop volumetric fraction is given by V z = (1 - f)h, and the volume of the conglomerate is V1 = [[(I - f ) ( l- h ) f]. Hence
+
+
I n the worst case h = 0.30, f = 0.55, Vz/V1 = 0.15, nz ‘v 150n1, and V Z / V Z = l/1000 (1 - f) = l/450. The relative magnitude of the two right-hand terms of eq C, as given by their ratio, is then 2K3nza2 uz x - I Klnlal VI
2 3
- w
where w = K3/1a[r+ln
+
0.25 e-’ 1.25
]
--I
(J)
Equation J is transformed to real time by relating T = Klnle and ~~1 5 KlnlOcl, the characteristic dimensionless time for C-C coalescence. From eq G, ( W , O = 0.2 to a1 = 0.8), rC1 = 2.78, and introducing
into eq I yields eq 10. Thus, if Ocl , the characteristic coalescence time of homogeneous C-C coalescence, and a2us. 0 are known, w for the heterogeneous system may be calculated. Appendix II
The procedure used to evaluate the specific C-D coalescence rates is demonstrated with reference to Figure 14. Curve A represents the experimental overall coloring rate for a dispersion containing 33.5% free drops, by volume, or h = 0.335. Curve B, obtained with h = 0.05 is considered to represent C-C coalescence. Assuming that the specific C-C coalescence rate is identical for both curves (A and B) curve C is obtained by taking the C-C coalescence time in curve Ind. Eng. Cham. Fundam., Vol. 1 1 , No. 4, 1972
577
A, between ai = (0.665 X 0.2) = 0.133 and (0.655 x 0.8) = 0.542 as equal to the characteristic time ecl determined from curve B. Finally, the free-drop coloring curve, D, which is essentially due to C-D coalescences, is obtained by calculating the difference (in a ) between curves A and C a t identical times and normalizing this difference, Le., a ~=( a ~ =) (CYA ac)/O.335 at anyo. Nomenclature a
b
= =
d
= = = dc1 = = rlc dc
f
Hi
=
H2
=
h
k‘l
= = =
k‘z
=
K,
=
s
=
I
=
2’1 @2
X
= = = = =
exponent, collision rate dependence on diameter exponent, coalescence efficiency dependence on diameter part’icle, drop, or conglomerate, diameter charact’eristic crystal size average crystal size elongated small crystals solid fraction in dispersed phase, crystals to crystals mother liquor distances b e h e e n colliding drops, where drainage resistance st’arts distance between drops, where attraction forces dominat’ecoalescence free drop liquor, fraction of total liquor in dispersion light intensity average C-C coalescence rate of each conglomerate (with a concentration of one conglomerate per unit volume) average D-C coalescence rate of each drop (lvith drop concentration of one drop per unit volume) average C-D coalescence rate of each conglomerate with one free drop per unit volume (or, each drop with one conglomerate per unit volume) impeller rotational speed, rpm number of drops, or conglomerates, per unit volume volume fraction of conglomerates in dispersion volume fraction of free drops in dispersion liquor volume in one conglomerate liquor volume of one free drop exponent, coalescence rate dependence on diameter (= a + b )
+
GREEKLETTERS a1 = volume fraction of colored conglomerates a t a given time cy2 = volume fraction of colored drops a t a given time
578 Ind.
Eng. Chern. Fundarn., Vol. 1 1 , No.
4, 1972
ai,0 =
B Bc
= = BCl = 8d = Be = = pc = @ = 7 = = 7o w = wt = q =
e
initial value of a i (i = 1,2) time characteristic time, 0.2 6 CY 6 0.8 characteristic time of C-C coalescence, 0.2 6 drainage time lifet’ime of eddy dimensionless time (wit?) density of continuous phase dispersed phase holdup dimensionless time (E K1qlO), characteristic dimensionless tlme (5Kl?&) ratio, K3/K1 coalescence rate coalescence efficiency
CY
6 0.8
SUBSCRIPTS 1 = conglomerates (eq -1) 2 = drops (eq A) 3 = conglomerate drop (eq A) Literature Cited
Hielstad, J. G., Rushton, Y. H., International Symposium on Coalescence, AIChE 59th Kational Meeting, Columbus, Ohio, 1966. Howarth, W. J., Chem. Eng. Scz. 18, 33 (1964). Howarth, W. J., International Symposium on Coalescence, AIChE 59th National lIeeting, Columbus, Ohio, 1966. Kapur, P. C Fuerstenau, S. W.,Ind. Eng. Chern. Proc. Des. Develop. 8,’56 (1969). Kramer, H., as reported by Rietema, R., i l d v a n . Chem. Eng. 5 , 285 (1964). Mizrahi, J., Barnea, E., Brit. Chem. Eng. 15 (4), 497 (1970). Rietema, K., Advan. Chem. Eng. 5 , 280 (1964). Shiloh, K., “Crystallization in Dispersed Phases,” Ph.D. Thesis (in Hebrew), Technion-Israel Institute of Technology, 1970. Shiloh, K., Sideman, S.,Resnick, W., “Hydrodynamic Characteristics of Dilute Dispersed Phase Crystallizers,” AIChE 62nd Annual LIeeting, Washington, D. C., Nov 1969; Chem. Eng. Progr. Symp. Ser., 67, No. 110, 66 (1971a). Shiloh, K., Sideman, S., Resnick, W.,“Coalescence and Break-up in Dilute Polydispersions. Part 1. Coalescence Studies,” Preprint 79a, AIChE 68th National Meeting, Houston, Texas, 1971b. Shinnar, R. J., Fluzd Xech. 10 (2) 259 (1961). Sprow, F. B., Chem. Eng. Scz. 22 (3), 435 (1967a). Sprow, F. B., A.I.Ch.E.J. 13 (5), 995 (1967b). RECEIVED for review April 21, 1971 ACCEPTEDJuly 3, 1972
