1780
Ind. Eng. Chem. Res. 1994,33, 1780-1785
Aspects of Drop Behavior in a Rotating Disk Contactor Zhong-Qiang Mao and Michael J. Slater' Department of Chemical Engineering, University of Bradford, Bradford, West Yorkshire, BD7 IDP, U.K.
The motion of single liquid drops in a swarm of other drops in a rotating disk contactor has been observed by employinga (viscous)matched refractive index system (odanoYaqueous sucrose solution). The breakage probabilities of drops in a swarm have been observed and compared with those of single drops. Single drop velocity is different above and below rotors. The ratio of characteristic velocity (over the whole compartment) and terminal velocity a t first decreases with increasing continuous-phase viscosity and then increases above 1.0, probably due to shape and drop orientation changes under the influence of agitation. Single drops in a swarm obey slip velocity relationships similar in form to that for the swarm, but the relationship between them is not yet clear. Single drop breakage probability in a swarm decreases as dispersed-phase flow rate increases and continuousphase flow rate decreases if rotor speed exceeds the critical value for breakage, but the behavior is more complex if this is not the case. Table 1. Physical Properties of Systems Used (at 20 "C)
Introduction Improvementsin the design procedures for liquid-liquid extraction equipment are much needed since present methods are based on a limited understanding of the phenomena involved and do not give reliable predictions of behavior. The starting point concerns drop sizes and distributions changing along a column because of drop breakage under the influence of agitation or contact with internal fittings or packings and because of drop coalescence. The present practice is to use empiricalcorrelations to give a Sauter mean size independent of position in the column. The quantitative influence of mass transfer and ita direction are not usually known. Further calculations of throughput and mass transfer depend strongly on drop size distribution and drop velocities so errors in column height and diameter will be incurred if mean drop sizes are assumed (Chartres and Korchinsky, 1975;Korchinsky and Azimzadeh-Khatayloo, 1976). The rotating disk contactor (RDC) is widely used industrially and has been very thoroughly investigated (Chartres and Korchinsky, 1975; Korchinsky, 1991; KOrchinsky et al., 1976,1979,1982). Our own studies on the RDC have been made on drop sizes (Chang-Kakotiet al., 1985), drop breakage (Cauwenberg et al., 19931, drop characteristic velocities (Bahmanyar et al., 19901, slip velocity relationships (Fei and Slater, 1984; Godfrey and Slater, 1991), and enhancement of mass transfer coefficients (Bahmanyar et al., 1990). Much of this work has been done with single drops as advocated by Fan et al. (1987),so questionsimmediatelyarise about the influence of dispersed-phase holdup on all these factors. Recently Abid and Godfrey (1993)have used a matched refractiveindex systemof OCtanoVaqueoussucrosesolution for studies of drop behavior in a stirred tank; this system has been used in this worktogether with other nonmatched systemsto examine drop motion in more detail in an RDC. The octanol/sucrose system is viscous and not representative of most industrial practice; however, little is known about viscosity effecta in columns so it was considered that exaggeration of any effects obtained using high viscosity could be helpful. The motion of a single drop through a compartment of the RDC is not simple as previously noted, there being a distribution of residence times of passage even for drops of the same size (Fan et al., 1987). A better knowledge of local drop rise velocitieswas soughtbecause of the influence on drop mass transfer coefficients.
octanoVwater octanoV15 w t 5% sucrose octanoV30 wt 5% sucrose octanou36 wt 5% sucrose octanou49wt % sucro88 octanov55 w t % sucrose octanoU59 wt % sucrose octanol/60 wt % sucrose octanou62wt 5% sucrose octanoV64 wt % sucrose
100 1060 1120 1160 1200 1260 1280 1280 1300 1310
o.Oo0 95 0.001 68
0.002 86 0.00496 0.009 41 0.032 1 0.044 8 0.062 6 0.082 6 0.120 0
819 819 819 819 819 819 819 819 819 819
0.00893 0.00893 0.00893 0.00893 0.00893 0.00893 0.00899 0.00893 0.00893 0.00893
8.67 8.80
9.10 8.80 8.40 8.60 9.30 10.0 10.2 10.4
In developing more accurate descriptions of column performance, it is necessary to know the velocity of drops of different sizes within a swarm of drops. Normally the motion of the swarm is characterized by an overall slip velocity correlated with a function of holdup, x , and an averagecharacteristicvelocity, VK. We chooseto correlate with the expression
vslip= V,(l-
x p
subsbtiated by earlier work (Godfrey and Slater, 1991; Fei and Slater, 1984). The exponent m has been correlated tentatively with a drop Reynolds number (based on VK). In our work we wish to apply this equation to all drop sizes di with characteristic velocities V s and exponent mi at a certain value of x in one compartment. One purpose of this work was to test the validity of this approach by measuring individual drop velocities for (colored) drops of known size in a swarm of drops with known drop size distribution and known average parameters VK and m. Observations of single drop shape were made using systemsof various viscosities. The influence of rotational speed is reported; the shape change noted can be considered responsible for the observed effect of continuousphase viscosity on drop characteristic velocity. Equipment and Procedures The properties of the phases used (at about 15-20 "C) are listed in Table 1. Experiments on single drops were made using a column of five stages with a 375-mm-high working section and 152-mm diameter containing stationary continuous aqueous phase (Figure 1). The internals were made of stainless steel and the shell was of glass. Dimensions are given in Table 2. The base was a steel plate through which were
Q888-5885/94/2633-1780~Q~.50/00 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No.7, 1994 1781 Discmcc ( m m )
SOLVENTPEASE
80.00 B
I
SCALED GLASS TUBE
RDC COLUMN
n Tim ( a)
Figure 3. S i l e drop moving in a compartmentof RDC (N= 1.03 8-', 62 w t 7% sucrose solution). OB, terminal velocity; OA, eharacteristic velocity; OC. DA, lower and upper velocities.
VALVE
U
NEEDLE Figure 1. Five-stage RDC column.
Figure 2. h o p poaition in compartment of RDC. Table 2. Column Dimensions
column diameter rotor diameter stator diameter shaft diameter compartmentheight rotor and stator thickness three vertical spacer rods free area at stator level
152 mm 102 mm 111 mm 15 mm 16 mm 3 mm 6.4 m m 52 %
passed several glass needles of different tip sizes. These needles could be twisted to make drops rise from different radial positions in the column, but normally they were positioned so that drops just missed the first rotor edge when the rotor was stationary (Figure 2). Solvent phase was held in a glass vessel high above the equipment to give near constant head and was passed via a rotameter to a needle. All valves and tubing were of glass or Teflon. Dropswere formed at a rate which could be easilycounted by eye, and equivalent drop diameter could be calculated (within about f 2 % ) knowing the solvent flow rate. A
video camera incorporating a timer was used to record drop motion within one compartment or several compartmenta. Drop size was checked before and after each experiment. Drop shape was determined from the still video frames using the rotor thickness as a reference. The shape is that projected along a radius line between the shaft and the camera; high precision of measurement was not sought. Terminal velocities were measured in a separate glass vessel of 75- or 152-mmdiameter using the video camera over a distance of typically 0.4-1.0 m and allowing time for drops to reach a steady velocity. Drops of 1.5-5-mm diameter were observed;the larger drops were not spheriml. The column of identical internal construction but of 23 stages, 1.75m working height,was used for countercurrent flow testa with the matched refractive index system (described by Bailes et al., 1986). A glass head tank contained octanol coloured with Oil Red 0 dye (whichhas noeffect onterminalvelocity)which flowed viaarotameter to a small-bore stainless steel tube passing through the column wall into the bottom stage. The tip of this tube was directed upward, and the tip was 20 mm below the edge of the rotor and in line with the edge. Colored drops were formed a t the tip and could he seen easily through the swarm of other drops formed at the distributor at the base of the column. It was very difficult to see the other drops even though refractive index matching was not perfect because of lack of close temperature control. The motion of colored drops-in the taller column was followedwiththevideocameramountedonavertical track with a motor to drive the camera at a controlled rate. Dropsize distributionswere measured photographically throughtheglasawallofthecolumn (asdescribedby Bailen et al. (1986))in the third stage above the distributor, and dispersed phase holdup was measured by shutting down all flows simultaneously (Bailes et al., 1986). Characteristic Velocities: Single Drops in the Five-Stage Column Forthe highlyviscous(matched refractive index)system it was found that drops moved upwards under all circumstances investigated (a limit on rotor speed being imposed by breakage of a drop). There was little sign of accelerative motion at drop entry to a compartment at stator level (Figure 3). At zero rotor speed drops moved a t terminal velocity throughout the stage, but as speed was increased thevelocitydecreased and thevelocity below the rotor was less than that above the rotor (Table 3).
1782 Ind. Eng. Chem. Res., Vol. 33,No. 7,1994 ExperimentalV W t
200
I
Tots1 time
T above 1.20
T below
u.0
0.80
0.2
0.4 0.8 ROTOR SPEED,
0.8
1.0
11s
rotor speed, N, s-l 0 0.17 0.33 0.50
0.67 0.83
drop velocity, V,mm/s above rotor below rotor 27.4 27.9 28.5 27.2 28.7 27.3 33.9 30.5 40.9 32.7 40.8 34.9
These observations in the lowest stage were followed by measurementsmade over three stagesbecause it was found that at higher rotor speeds drops could be trapped for a while under the edge of the stator and the drop entry position is fixed for the first stage but not for higher stages. The characteristic velocities for one stage ( V K ~and ) three ) slightly different. The situation is shown stages ( V K ~are in terms of time spent in differentregionsof a compartment on Figure 4. (Note that the distances used in calculations of velocity are not identical above and below the rotor). The time spent in the rotor and stator regionscould amount to 25-40% of the total residence time in a compartment. This highlights the difficulty of predicting hydrodynamic behavior and mass transfer coefficientssince drop velocity and residencetime are not uniform within a compartment. The cause of velocity differences above and below a rotor might be considered due to circulation patterns in the continuous phase; drops in the 1ower.regioncould be slowed if they are moving against a downcurrent of continuousphase and could move faster in the upper region if moving with an upcurrent. These two effects would compensateeach other to some degree so that the average velocity in the stage would not be much affected if drops rise at a near uniform distance from the shaft as is typically the case; drops do not noticeably move toward the shaft in the lower region and toward the wall in the upper region as might be expected. The effectof continuous-phaseviscosity provides further evidence to be considered. The sucrose content of the water phase was varied so that viscosity varied from 1.0 to about 120 g/(m 8). Experiments on drops in a single compartment showed that the ratio of characteristic velocity relative to terminal velocity (at zero agitation) at first decreased as viscosity increased but then increased markedly; VK can exceed VT and variation in drop size from 1.3 to 3.1 mm had little discernible effect on V ~ V T (Figure 5). An explanation based on circulating flow patterns as given above is not sustainable, and changing drop shape was thought to be mainly responsible. Drops in the region below the rotor appear to be stable in shape and near spherical. Above the rotor drops are recovering froma distorted shape caused by interaction with the rotor
0.12
0.14
0
0.60 0.00
Figure 4. Effect of rotor speed on drop residence time (d = 2.1 mm). Table 3. Single Drop Velocity within a Stage (Fivestage RDC; Drop Diameter 2.1 mm;80 wt % Sucrose)
1
0
7
T 8tator T rotor V
I
63
(D
1.40
@
0.02
0.06
0.04
0.08
0.10
Conti~~uluour pbsse VbDOrlty
kghnr
Figure 6. Effect of continuowphaseviecosityon Vd VT(rotorspeed 1 s-’, d = 1.3-3.1 mm).
N
200
r
Lines for eq(2)
[
2E
,
100
/
I
/ **
*
//
Vlscosltv 0.0005 kg/m
8
0.045 kg/m 8 0.063 to 0.083 kg/m 8 0.120 kg/m
8
nI 0
1
2
3
4
5
Drop diameter, mm
Figure 6. Terminal velocities.
and the major axis is inclined to the horizontal. A reduced projected plan view area of a distorted drop compared to the equivalent spherical drop could allow such drops to have a higher vertical velocity component. This point is discussed again below.
Terminal Velocities Terminal velocity data were best fitted by Misek’s type of equation modified here with an extra viscosity ratio term of viscosity relative to that of water (Misek, 1970);
(ReT 0.4-327)with the coefficient 0.289 being larger than the value 0.249proposed by Misek (Figure6). Drop shape is nonspherical for larger drops.
Drop Shape Drop eccentricity (e = major/minor axis) was measured from video camera still frames using the rotor thickness as reference. For very viscous continuous phase and/or high rotor speeds, drops were severely distorted at the rotor. In the absence of agitation e values reached 1.5, and with agitation values up to 20 were found in the rotor edge region. Wellek et al. (1966) have summarized much data obtained in the absenceof agitation and show how difficult it is to find an unequivocal correlation of data because of the large number of variables playing some part in determining drop shape. The simplest of the equations with adequate accuracy are e = 1 + 0.129EB
and
(3)
Ind. Eng. Chem. Res., Vol. 33, No. 7, 1994 1783 e=1
+ o.~lwe,o.86
(4)
Sicedrop breakage probability has been correlatedusing the laminar rotor Weber number derived by Schlichting (see Cauwenberget al. (1993)), we propose the correlation e=1
+ 0.1'BEo + 29.71We.
-a"
(5)
(37 data points, correlation coefficient R = 0.82, absolute error f47%) for laminar agitation conditions (Figure 7). The large scatter is in part due to the inadequacy of understanding of the situation, as indicated by Wellek (1966). Resolvingforcesin the vertical direction (Eo)and horizontal direction (We.) gives the equation e=1
+ [(30.73We:) + (0.129E6)*1"
(6) 5
0
which gives results identical to eq 5 but which might be preferred. Drops in the RDC alter their inclination as rotor speed increases so that the plan view of the projeded area of a drop decreases by up to 2-fold compared with the area of the equivalent sphere (Figure 8). The drag is affected, and drops can therefore rise faster than if they were still spherical in shape. Drop shape relaxes back to an oblate spheroid with the major axis horizontal or to a sphere as the drop moves in the upper region of a compartment. This observation helps to explain why VK/ V ~ c a nincrease as continuous-phase viscosity increases.
10
15
Eccentriclly, e expertmental Figure 7. Conelation of eccentricity. I
..
'disc
Countercurrent Flow Experiments were done with the viscous matched refractive index system. Holdup measurementscould not he correlated with any existing equations (which were developed for low viscosities). The dependenceof holdup on the only variables can be expressed as
Figure 8. Drop deformation. 1.8
(30 data points, R = 0.93). The ranges of the variables were N 0.83-1.67 s-', V, 0-3.67 mm/s, v d 0.55-1.84 mm/s, and x 0.042-0.36. The slip velocity can be expressed in terms of eq 1 with theexponent varyingfrom-13 atverylowagitationspeeds to 1.3 at more sensible speeds (Figure 9 and Table 4). Operation of the column was confined to low ReD and power consumption conditions under which undesirable intensivebreakup ofdropsleadingtomassiveentrainment did not occur. Godfrey and Slate? (1991) show that this typeof slipvelocitybehavior is not unusual;largenegative exponents at low agitation mean that drops are not uniformly distributed across the column so that the slip velocity definition is no longer valid. In this previous work an equation for calculating the exponent was given,
m = 0.19ReK
(8)
for water continuous phase and is valid only when m is positive and decreases as agitation increases, which is not the case here. In this work we appear therefore to be operatingat agitation intensitieswhich donotgiveuniform distribution across the column cross section. Thus, in operating with highly viscous continuous phases, hydrodynamic conditions are atypical and existing correlations of performance parameters based on low-viscositysystems cannot be expected to apply. Table 4 shows the Sauter mean drop size measured and extrapolated values of VKB(23-stage column) to compare
r
/
N
= o to N
d.
1.2
N
-
0.50 1/a
0.61 1Ia
= 0.03
.
and 1.0 11s
1.0
a -0 0.0
I
1.33 1la
0.0
0.4
u.0
0.1
-
0.2
log
0.3
(%X)
Figure 9. Slip velocities.
with values of vK3 (bstage, single drops) for that mean size. The values of VK, and m are of course averaged over the whole column; VG and m;are for specific drop sizes. The agreementof characteristic velocities V Kfor ~ d32 and v K 3 is only approximate. We have observed the rise velocity of colored drops of 2.1-, 2.4-, and 2.5-mm diameter (d;) within the swarm a t rotor speeds of 0.67-1.33 s-l and a t different disperaedphase holdup varied by changing both flow rates to the column,although in most cases the continuous-phase flow rate was kept at zero. Unfortunately it was too difficult to follow drops at higher speeds. Figure 10 shows the "single drop" slip velocity plots from which VG and m;are derived, and results are summarizedin Table 4. Measured values of V K (single ~ drops) were used to find the value
1784 Ind. Eng. Chem. Res., Vol. 33,No. 7, 1994 Table 4. Cornparinon of Characterintic Velocitien and Exponentn. N,s-I d = , m m V ~ ~ , m m / s V~g,b11139/s V T , " ~ S m 0 23 -13 0.17 23 -13 0.33 23 -13 0.50 2.60 23 32 35 -13 0.67 2.00 15 22 27 -6 1.60 13 14 22 1.2 0.83 1.00 1.30 14 10 18 1.3
( T w e n t y - T h - S t a g e Column; 60 wt % Sucrone) ReK di,mm V~i,'mm/s V~g,mm/s mi V~,'11139/~
1.64 1.21 0.46 0.41
2.1 28 39 -6.5 28 2.4 56 32 4.3 32 2.1 35 23 -3.1 28 2.5 55 25 -1.3 34 1.33 9 (0.2) 2.1 42 -2.8 28 a V m is obtained from Figure 9 at x = 0; m is found from Figure 9; Vm is obtained from single drop experiment data over three stages in the short column; Vu is obtained from Figure 10 at x = 0; mi is found from Figure 10.b Based on d a . Based on di. 0.6
N11.33; 612.1
r
d
=
2.1 mrn
0.4
0.3
N10.83; de2.4 0.2
1'5&10.67 1.4' 0.00
"
0.02
l l s ; dr2.1 mm '
I
0.04
'
I
0.06
0.1 '
I
0.08
- log (1-x)
.
' 0.10
;ob
"
0.12
0.0 0.0
I
1
I
I
0.1
0.2
0.3
0.4
Figure 10. Slip velocities of single drops in swarm.
appropriate for di. Again it is found that V Kand ~ VKSfor di are only roughly similar. The values of VK~ for the same di increase as rotor speed increases, which is not expected behavior; the assumption that holdup is uniform along the column as well as radially in a stage (giving false calculation of slip velocities V&fi) is the probable cause of this observation. The wide divergence of the values of m and mi may similarly be due to the fact that m is based on the whole column and that mi is measured near the distributor. In future work holdup in individual stages will be required to be measured since longitudinally nonuniform holdup is probably the cause of the discrepancies. The data in Table 4 showthat a clear pattern of behavior is not evident in terms of either VE or mi values, and therefore the only conclusion so far is that we cannot confidently assume that eq 1 can be applied to individual drops in a swarm with values of mi derived from a correlation of m values for a swarm. The operating conditions are far from normal with the viscous system used, so there is a need to repeat the work with a lowviscosity matched refractive index system.
Drop Breakage
A study of single drop breakage has been made and reported by Cauwenberget al. (1993). Data were correlated in terms of number fraction breaking at a rotor for the condition that rising drops just missed the edge of the rotor at zero rotor speed. For a fixed drop size there was a criticalrotor speed Naat which dropsjust failed to break. In this work we have observed the breakage of single colored drops in a swarmof drops. The dropswere released at the same radial position into the fiist compartment above the distributor in the 23-stage column. The results are shown as a function of holdup in Figure 11 for two rotor speeds. The holdup used is an average value for the
..
0.3
n
$
ec s
0.2
*
-
:
.L
02
n
0.1
.
2
u.0
1.33 11s
4.0 umln
t
-
V.V
I
Continuous phssa flow rata
2.4 Umln
m
I
P
n
N
2.0 Umin 0.5
1.0
1.5
2.0
Dispersed phase llow rate, Figure 12. Single drop breakage in a swarm.
2.5
3.0
Umln
column, and the local value is probably smaller as judged from work on slip velocities described above. The rotor speed of 1 s-l is below the measured critical speed for the single colored drop size used (for initial drop position just under the rotor edge),so breakage should be near zero until holdup rises to some value which affects the breakage process. Since the initial position of drop release affects the critical rotor speed, it is considered that the single drop path to the rotor is changed by the flows and breakage is then initially enhanced. At N i= 1.33 s-1 the critical rotor speed is exceeded for drops of 2.1 mm so colored drops break at zero holdup. Figure 12 shows some of the same results as a function of flow rates for a single drop of 2.1 mm; increase in flow rate of dispersed phase or decrease in continuous-phase flow rate decreases the breakage fraction significantly. This plot avoids using the uncertain assumption that local and column average holdup values are the same. Drop breakage frequencyis therefore a complex function of flow rates which seriously complicates the calculation of drop size distributions along a column.
Ind. Eng. Chem. Res., Vol. 33, No. 7,
Conclusions Single drop velocities in a compartment of an RDC are near uniform above and below the rotor, but not equal, in a viscous continuous-phase system. The ratio of characteristic velocity to terminal velocity first decreases and then increases substantially above 1.0 as continuous-phaseviscosity increases. Circulating flow patterns may have some influence, but changing drop shape and inclination are probably the cause of this behavior. Drop delay times at the rotor and stator have a large effect on single drop overall residence time and so affect the characteristic velocity in a complex manner. Drop eccentricity is marked in the viscous system used and can be correlated with E&& and laminar Schlichting rotor Weber numbers. Operation of a countercurrent RDC with a viscous system in a region which does not give undesirableintensive breakup of drops leads to nonuniform holdup conditions; existing correlations of RDC performance are not valid. Single drop velocities in a swarm can be correlated by slip velocity equations of the type adequate for a swarm of drops but not with values of characteristic velocity and exponent which can yet be related to those for the swarm. A low-viscosity matched refractive index system needs to be used in further studies and holdup measurements need to be made in individual stages. Single drop breakage in a swarm of drops is lower in extent than for single drops alone and is a complex function of flow rates.
Acknowledgment The authors wish to thank Separation Processes Service, AEA Technology, Harwell, for financing this and associated projecta. Z.-Q.M. acknowledges the leave of absence granted by Tsinghua University, Beijing, China, for him to work in Bradford. Nomenclature d = drop diameter = Sauter mean drop diameter di = single drop size in a swarm DR = rotor diameter d32
e = drop eccentricity (majodminor axis)
E8 = Eijtvijs number (gdzAply) g = gravitational acceleration m = exponent for swarm mi = exponent for single drop in swarm N = rotor speed ( 8 - 9
N, = critical rotor speed ( 8 - 9 p = drop breakage fraction R = correlation coefficient ReK = drop Reynolds number (pcdVK/pc) ReT = drop Reynolds number (pcdVT/pc) v K 1 = single drop characteristic velocity determined in one
stage V , = continuous-phase superficial velocity vd = dispersed-phase superficial velocity
V K = average drop characteristic velocity for swarm V K =~ single drop characteristic velocity v K 1=
single drop characteristic velocity determined in one stage V K =~ single drop characteristic velocity determined over three stages v K 2 3 = single drop characteristic velocity determined over 23 stages V,U,= slip velocity for swarm Vslipi= slip velocity for single drop in swarm
1994
1786
VT = terminal velocity Wed = drop Weber number (p$~~J3Wd1.67/y) We, = Schlichting laminar Weber number (pcO+5pc0.5D#6dl 7) x = dispersed-phase holdup
Greek Symbols
= interfacial tension = continuous-phase viscosity pd = dispersed-phase viscosity y
p,
clw = water viscosity
p , = continuous-phase density
= dispersed-phase density Ap = density difference
Pd
Literature Cited Abid, K. H.; Godfrey,J. C. Requirementa for liquid-liquid dispersion studies with a matched refractive index system. Proceedings ISEC'93, York, UK;Elsevier: London, 1993; pp 4 m 5 0 5 . Bahmanyar, H.; Chang-Kakoti,D. K.; Garro, L.; Liang, T.-B.; Slater, M. J. Mass transfer from singledrops in rotatingdisc, pulsed sieve plate and packed liquid/liquid extraction columns. Trans. Inst. Chem. Eng. 1990,68 (part A), 74-83. Bailee, P. J.; Gledhill, J.; Godfrey, J. C.; Slater, M. J. Hydrodynamic behaviour of packed, rotating disc and Kahni liquialiquid extraction columns. Chem. Eng. Res. Des. 1986,64,43-55. Cauwenberg, V.; Mao, Z.-Q.; van Rompay, P.; Slater, M. J. The breakage of drops in rotating disc contactors. Proceedings ZSEC'93, York U K Elsevier: London, 1993; pp 421-428. Chang-Kakoti,D. K.; Fei, W.-Y.; Godfrey, J. C.; Slater, M. J. Drop sizes and distributionsin rotating disc contactors used for liquidliquid extraction. J. Sep. Process Technol. 1985,6,4&48. Chartres, R. H.; Korchinsky, W. J. Modelling of liquid-liquid extraction columns: predicting the influence of drop size distribution. Trans. Inst. Chem. Eng. 1975,53,247-254. Fan, Z.; Oloidi, J. 0.;Slater, M. J. Liquid-liquid extraction column design data acquisition from short columns. Chem. Eng. Res. Des. 1987,65,243-250. Fei, W.-Y.; Slater, M. J. A new look at the hydrodynamic behaviour of rotating disc contactors. J. Sep. Process Technol. 1984,5,3944.
Godfrey, J. C.; Slater, M. J. Slip velocity relationships for liquid/ liquid extraction columns. Trans.Znst. Chem.Eng. 1991,69 (part A), 130-141. Korchinsky, W. J. Hydrodynamic and mass transfer parameter correlations for the rotating disc contactor. J. Chem. Technol. BiotechnoL 1991,50 239-256. Korchinsky, W. J.;Azimzadeh-Khatayloo,S. An improved stagewiee model of counter-currentflow liquid/liquid contactors. Chem. Eng. Sci. 1976, 31, 871-857. Korchinsky, W. J.; Cruz-Pinto, J. J. C. Mass transfer coefficientacalculation for rigid and oscillating drops in extraction columns. Chem. Eng. Sci. 1979,34,551-561. Korchinsky, W. J.; Loke, C. T.; Cruz-Pinto, J. J. C. Optimization of drop size in counter-current flow liquialiquid extraction columns. Chem. Eng. Sci. 1982.37, (5), 781-786. Misek, T.; Marek, J. Asymmetric rotating disc extractor. Br. Chem. Eng. 1970, 15 (2), 202-207. Wellek, R. M.; Agrawal, A. K.; Skelland, A. H. P. Shape of liquid drops in liquid media. Am. Inst. Chem. Eng. J. 1966,2 (5), 854862.
Received for review December 22, 1993 Revised manuscript received March 28, 1994 Accepted April 6, 1994.
* Abstractpublishedin Advance ACSAbstracts,May 16,1994.
