Ind. Eng. Chem. Res. 1992,31, 25562563
2556
SEPARATIONS Transient Drop Size in Agitated Liquid-Liquid Systems, As Influenced by the Direction of Mass Transfer and Surfactant Concentration A. H.P.Skelland and Jeffrey S. Kanel* School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
The primary application of transient and equilibrium drop size correlations for agitated liquid-liquid systems is in extraction processes. Nevertheless, many previous investigations did not include the effect on the drop size of mass transfer and/or surface-active agents, commonly encountered industrially. Thus,the present work examinea the combined influence of surfactante and mass transfer in either direction on the variation in drop size with time throughout the duration of mass transfer. The variables that were studied in regard to their possible effects on the transient Sauter-mean drop diameter include the direction of mass transfer, the selection of the phase dispersed, and the concentration of surface-active agent in the eystem. Minor variables were the volume fraction of the dispersed phase and the impeller diameter and speed. Agitation was provided by a six-flat-bladed turbine in a batch-operated and baffled vessel. The prediction of transient and equilibrium drop size in agitated liquid-liquid dispersions is of primary importance to extraction processes. A vast literature has been developed to predict the steady-state mean drop size in agitated systems, as summarized by Coulaloglou and Tavlarides (1976)and Kumar (1983). Many of these investigations did not examine the effects of mass transfer and/or surfactants on the drop size-both of which are important to industrial extraction processes. However, studied transient drop Hoffer and Resick (1975,1979a,b) size and dispersed-phase holdup in the presence of solutes and surfactants in batch agitated liquid-liquid systems. Lee and Soong (1985)attempted to quantify the effect of surfactant type and concentration on the steady-state Sauter-mean drop diameter, d32*, by the correlation
with the correction factor for surfactants, C,, equivalent to 0.63 regardless of surfactant type. Hong and Lee (1985)developed an expression to predict the transient Sauter-mean drop diameter in a batch agitated liquid-liquid system free from surfactanta and mass transfer. In their experiments, either the dispersed phase was rapidly poured into the agitated continuous phase or both phases were charged into the vessel before mixing commenced. They n o d that d32 decreased exponentially during the initial period of mixing and asymptotically approached d32*, for which they also developed the correlation
with an average absolute deviation of 18.5% for 134 runs.
* Addresa correspondenceto this author a t Eastman Chemical Company, Kingsport, T N 37662.
Hong and Lee (1985)then determined that the d32(t) versus time curve could be linearized by plotting the dimensionless drop size, [(d32(t)- d32*)/d32*], versus dimensionless time, N t . The resulting expression was (3) where a! and @ were functions of physical properties and operating conditions, and d32* was calculated from eq 2. They found that B remained approximately constant at 4.70 for all of their experimental conditions, but a! varied with physical propertiea and operating conditions to give the general correlation for d32(t) as
with an absolute deviation of 11.1%. Here, new experimental data concerning the effects of mass transfer and surfactant concentration on the transient Sauter-meandrop size will be presented. Also, Hong and Lee’s (1985)correlation for the time-dependent Sautermean drop diameter will be augmented to incorporate the effects of mass transfer and surfactant concentration, at least for the water/tetrabutylammonium bromide/chlorobenzene/Triton X-100system. Experimental Work Material Selection. Tetrabutylammonium bromide, TBAB, was chosen as the solute for all of the experimental runs, since increasing ita concentration in both aqueous and some organic phases resulted in an increased electrical conductivity of the solution. In this manner the TBAB concentration in the continuous phase was both instantaneously and continuously monitored via electrical conductivity (Skelland and Kanel, 1992). The TBAB was purchased from the Sigma Chemical Company. Deionized water was obtained by passing Atlanta city water through several packed beds of mixed anionic and
0888-5885/92/2631-2556$03.00/00 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 2557 Table I. Physical and Transport Properties of Water and Chlorobenzene at 25 OC density, viscosity, diffusivity of liquid kg/m3 Ns/m2 TBA13,m2/s 0.00073 2.62 x 10-10 chlorobenzene 1083.0 water 997.1 0.00087 6.24 x 10-lo
...........................................................
00
05
10
15
20
25
30
. 35
40
niton X-100 concentration (g/1 H20)
Figure 1. Interfacial tension between water and chlorobenzene versus Triton X-100concentration at 25 O C .
cationic ion exchange resin beads. The latter were produced by the Rohm and Haas Company. Criteria for the organic solvent included the need for slight changes of TBAB concentration to produce measurable variations in electrical conductivity. The organic solvent chosen was chlorobenzene; it was "purified" grade supplied by the Fisher Scientific Company. Triton X-100 [CJ-117C6H4(OCH2CH2)eloOH], an octylphenoxypolyethoxyethanol supplied by the Sigma Chemical Company, was chosen as the surfactant because its nonionic nature eliminated electrical effects at the interface. Furthermore, Moeti (1984)claimed that Triton X-100 produced relatively clear dispersions in agitated liquid-liquid systems as opposed to anionic or cationic surfactants. The average number of OCH2CH2groups was 9.9,and the critical micelle concentration in water at 25 g-mol/L H20 from Brandup and O C was (7.5-9.0)X Immergut (1975,p 11-492). Physical and Transport Properties. All physical and transport properties were measured at 25 "C. Viscosity was determined by using a Cannon-Fenske routine viscometer, and the density was measured via a Troemner Specific Gravity Chain Balance Model S-101.Interfacial tension was determined by a Fisher Surface Tensiomat Model 20. The resulting interfacial tension versus surfactant concentration curve is presented in Figure 1. The effect of TBAB concentration on interfacial tension in the presence of Triton X-100 was then analyzed. Three different TBAB concentrations bracketing the range used in this study were prepared in an aqueous solution of 0.0782 g of Triton X-100/L of H20 (presaturated with chlorobenzene). The effect of TBAB concentration on interfacial tension in the presence of Triton X-100 was found to be negligible in the concentration range used here. The diffusivity of TBAB in various solvents was measured with diaphragm diffusion cella. The diaphragms were Ace Glass E-Type sintered glass filters with pore diameters between 4 and 8 Bm. The principles and techniques of this method have been described by Wilke and Chang (1955),Holmes (1966),Holmes et al. (1963),and Bidstrup and Geankoplis (1963). The equation for the diaphragm cell when the volumes on each side of the diaphragm are equal is given by
5)= BDt
log( ACf
which relatea the initial and finalconcentration differences in the cell to the time allowed for diffusion, t, and the diffusion coefficient, D. The cell constant, 8, was experimentally determined by using a 0.1 N KC1 aqueous so-
Table 11. Interfacial Tension between Chlorobenzene and Deionized Water Corresponding to a Given Concentration of Triton X-100at 25 OC solution concn of surfactant in corresp interfacial no. water, g of SAA/Lof water tension, dyn/cm 1 0.000 33.5 2 0.038 27.1 3 0.100 21.0 4 2.000 16.0 Table 111. Specifications of the Experimental Apparatus Where the Impeller Was Located at H / 2 dimension (all in m) internal diameter of vessel 2.135 x lo-' liquid height in vessel 2.135 X lo-' height of vessel 2.500 x lo-' diameter of shaft 1.4 x baffle width 1.9 x 10-2 baffle thickness 2.5 x 10-3 average diameter of six flat-blade impeller large 1.015 x lo-' small 6.314 x average width of flat-blade turbine large 1.262 x small 7.64 x 10-3 average thickness of impeller blade large 2.47 x 10-3 small 1.52 x 10-3
lution for which the integral diffusion coefficient of 1.87 X 106cm2/s at 25 OC has been reported. The final TBAB concentration in the aqueous phase was determined by the Mohr method [Fritz and Schenk (1979,pp 208-209)]. To determine the TBAB concentration in the organic phases, 25 or 50 mL of the TBAB solution from the concentrated side of the diaphragm cell was placed in a rotoevaporator. The organic solvent was stripped off leaving the TBAB salt which was rehydrated and titrated. It should be noted that small amounts of Triton X-100 in chlorobenzene did not significantly change the measured molecular diffusivity. A summary of the physical and transport properties of water and chlorobenzene is presented in Table I. Experimental Design. In the factorial experimental program, four surface active agent (SAA)concentrations were chosen to give the maximum interfacial tension (no surfactant), a minimal interfacial tension (2.0g of SAA/L of H20),and two equally spaced intermediate values (0.038 and 0.10 g of SAA/L of H20). The desired surfactant concentrations and reaultant interfacial tensions are given in Table 11. Two impeller diameters were selected, and their dimensions are given in the next section. Four impeller speeda were used for each impeller diameter. They were chosen to be below the speed at which air would be drawn into the continuous phase when it was being agitated alone and above the minimum impeller speed for complete dispersion as calculated from Skelland and Ramsay (1987). Two volume fractions of the dispersed phase were examined, namely 3 and 7 vol ?4. The latter was the maximum value that still allowed clear photographs of the dispersion to be obtained so that the interfacial area for mass transfer could be ascertained. Experimental Apparatus. A sketch of the experimental apparatus is shown in Figure 2, and the specifi-
2558 Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 Table IV. Concentrations of TBAB To Be Used for Various Directions of Dispersion and Maas Transfer continuous dispersed direction of z of TBAB/mL phase phase transfer Gf desired &e water water
chlorobenzene chlorobenzene
E
A Cyllndrlcal glass vessel B Barite C S I X flat-blade turbine D Conductlvlty c e l l E Temperature bath
Figure 2. Schematic diagram of the experimental apparatus
cations are given in Table III. A 7.64 X lW3 m3cylindrical, flabbottomed glass vessel was used to facilitate photographic determination of mean drop size. Four baffles of width equal to 0.0892' were placed at 90' intervals to prevent vortex formation. A six flabblade turbine impeller was centrally mounted in the vessel, since this type of impeller showed the best dispersion performance for uniform mixiing according to Lee (1978, p 60). The shaft, impeller, and baffles were all 316 stainless steel. The Experimental Agitator Model ELB manufactured by Bench Scale Equipment Company was used to mix the liquids. The unit was equipped with a 1/4 hp drive motor, and provided an infinitely-variable output speed of 0-18 rps. The speed control dial was calibrated directly in rpm by a tachometer. The Sauter-mean drop diameter was determined from photographs of the dispersion. A Nikon F-3 camera with an MD-4 motoredriveand a Micro-Nikkor 55-mm, f/2.8 lens was placed beside the vessel so that the focal plane was approximately 0.7 cm inside the vessel. The camera was located just below the impeller plane, so the photographic volume represented a region of mean drop size in the vessel as identified by Weinstein and Treybal(l973). The shutter speed was set to 1/2000 s and the ASA setting was 200. The lens was reversed by using a Nikon BR-2A macro adapter ring so that the depth of field was reduced, and approximatelyk1 reproduction ratio was obtained. The f stop was set to 2.8. Several fh were tried including Kodak Tri-X Pan ASA 400, Kodak Ektachrome Infrared 2236, and Kodak Technical Pan 2415. The latter, having near-infrared sensitivity and high contrast, was selected. The fh waa proceased in D-19 for 4 min for high contrast. Lighting was provided by a single Hedler Jet-Lux 1250 tungsten-halogen lamp mounted beside the vessel at an angle parallel to the focal plane. All other lighting in the Mom was extinguished to prevent stray light from reducing the contrast necessary for clear drop photos. Since the vessel was cylindrical, some optical distortion did occur, but it was minimal due to the relatively large diameter of the vessel with respect to the drops. From these photographs, transient drop size distributions were measured for each run by sizing approximately 500 drops on each frame using a Carl Zeiss Particle Size Analyzer TGZ-3. In this regard, Chen and Middleman (1967) have shown from
chlorobenzene chlorobenzene water water
--
D C C D D-C C-D
1.00 X lCr3 1.10 x 1V 4.00XlV 8.28~ lV
experiment that =a minimum count of 300 drops is necessary to obtain accurate results". The cylindrical glass vessel was placed in a constanttemperature bath with plane glass walls, and a Neslab Model RTEdDD temperature circulation bath was used to maintain a constant temperature of 25 "C for all experimental runs. Experimental Procedure. The following experimental procedure was followed. 1. Both organic and aqueous phases were presaturated with the other phase. 2. The desired concentrations of TBAB (given in Table IV) and Triton X-100 were mixed. 3. Both phases were allowed to reach thermal equilibrium at 25 OC by charging the continuous phase into the cylindrical glass mixing vessel (in the temperature bath) and placing the dispersed phase in ita beaker into the bath as well. 4. The camera was located so that the focal plane was approximately 0.7 em inside the vessel. 5. The baffles, impeller, and electrical conductance probe were placed in the vessel. 6. Agitation of the continuous phase was started 80 that the flow patterns became fully developed before the dispersed phase was added. 7. The strip chart recorder, Hedler light, and electrical conductance meter were turned on, and the room lights were extinguished. 8. The dispersed phase was rapidly poured from two beakers into opposite sides of the agitated continuous phase at a radial position equidistantbetween the impeller shaft and the vessel wall. 9. Photographs of the dispersion were taken at 3-s intervals for the first 15 s and then at 10-s incrementa for the next 40 s. 10. Mass transfer was allowed to near completion as determined when the electrical conductance versus time curve asymptotically approached a constant value. 11. The vessel, impellers, baffles, and conductance probe were thoroughly cleaned with hot soapy water followed by rinses with copious amounts of tap water and further rinsing with deionized water. The equipment was then air-dried. 12. The procedure was repeated with a new level of some variable.
Results and Discussion The qualitative effects of the experimental variables (DOD, DOT, surfactant concentration, $, dI, M on the transient Sauter-mean drop diameter are now examined. Figures simiiar to those below for different experimental runs are given by Kanel(1990). Figure 3, for two impeller diameters in systems without surfactant, shows the effect of $ upon the transient Sauter-mean drop diameter to be slight in the range explored. The effect of impeller speed in the a h n c e of surfactanta upon the transient d,, is illustrated in Figure 4. The inverse relationship between N and dS2was also found by Hong and Lee (1985) in their correlation for the transient Sauter-mean drop diameter.
2
s
0
0
m = R102 di=s, phk.03
d -
F2 w01E s ga 0
d
e
TZ ES - o
0
x-
o
01
a rns
e
d 1
I
I
t
0
m
0
gA
d -
-0
e
'
I
0 0
c I
m I
'
I
a 2-
0
d -
-
-0
01 m
s
*
m O o
' m
-
a2&
" 6 I
8
1
0 I
1
I
0 I
I
b
m = R240 dils, phi=.03
0
EEs Z-
o
0
."o
m
= R120 di=s phi=.03 = R l l B di-, phi=.(n 0 = R l l O d i 4 phi=.03 = R108 dW. phi=.O? N = 220 or 480rpm
d - e
= R99 di-, phi=.O? o ~ R 9 2di4,phi=.O3 = R89 did,phi=.07 N = 220 or 480rpm 0
o
3
0
= R243 di-, phi=.O? = R186 di=l, phi=.03
e = R201 di=l, phi=.O'i'
N = 220 or 480rpm e m o
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
time (sec) C
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
time (sec)
d
Figure 3. Effect of Q, on the transient d a in the absence of surfactant (,R" means run, and N for the small ( 8 ) and large (1) diameter impellers (di) are 480 and 220 rpm,respectively): (a) for transfer of TBAB from chlorobenzene drops; (b)for transfer of TBAB to chlorobenzene drops; (c) for transfer of TBAB from water drops; (d) for transfer of TBAB to water drops.
Figure 5 depicta the effect of reversing the direction of diffusion and dispersion upon the time-dependent Sauter-mean drop diameter at four different surfactant concentrations. From Figure 5a, the d32 versus time curve appeared to be slightly higher when water was the continuous phase than when water was the dispersed phase. Also, the Sauter-mean drop diameter versus time curve for solute transfer from the dispersed phase was consistently above the curve for the opposite direction of transfer (to the dispersed phase). The probable explanation for this phenomenon was the enhancement in the coalescence rate due to solute transferring from the droplet phase as discussed by Geankoplis and Hixon (19501, Cavers and Ewanchyna (1957),Jeffreys and Lawson (19651, Smith et al. (19631, and Groothuis and Zuiderweg (1960). The effect of surfactant concentration upon the Sauter-mean drop diameter versus time curves is illustrated in Figure 6. In general as the surfactant concentration increases the da versus time curve is depressed. Since the mean drop size in an agitated liquid-liquid dispersion depends on the breakage and coalescence rates, effects of surfactanta on such rates may be reaponsible for these observations. First, increasing surfactant concentration decreased the interfacial tension which allowed the drops to break more easily, according to Hinze (1975). This would result in a reduction in mean drop diameter. Second, the influence of surfactanta on film drainage and
rupture has been inve&gat.edby Hartland (19681, Hodgson and Wood (1969), Nielsen et al. (1958), and Allan et al. (1961). The drainage time was significantly increased with added concentration of surfactant, thus retarding the coalescence process. Reduction in the coalescence rate would again tend to reduce the mean drop size. In summary, the qualitative effects of the experimental variables on the transient Sauter-meandrop diameter are as follows: 1. d32was essentially independent of 4 for 0.03 I4 5 0.07. 2. As the impeller speed increased, the transient d32was decreased. 3. The dS2versus time curve when solute transferred from the drops was consistently above that with diffusion in the opposite direction. 4. As the surfactant concentration increased, the transient dS2curve was decreased.
Effects of Surfactant Concentration and Transfer Direction on d , , ( t ) To determine whether the constant value for B (in eq 3) of 4.70,as proposed by Hong and Lee (1985), would be appropriate for various surfactant concentrations and both directions of maas transfer, the average experimental 6 values for each combination of direction of diffusion, direction of dispersion, and surfactant concentration were
2660 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992
2 2N
0 0 1 0
g3 -
O
0
xa2-
phi4.07, large di
Es
- 0 -
0
8 '
I
I
I
0
0
0
1
0
22
0 1
m
0 0
t _
0
0
8
g o
$3
m
1
0 I
I
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b
a
3-
0
m
2-
zE2s --
m
O 0
phi-0.07, large di
CQ
q2 -
x-
i!
phi-0.07, large di
Es
-0
-0
0
0
D 0
a
D
0
4
I
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
.-
0:l
I
I
I
I
I
I
'
'
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
time (sec)
time (sec)
C
d
Figure 4. Effect of impeller speed on the transient dS2in the absence of surfactant. The transfer of TBAB is (a) from chlorobenzene drops, (b) to chlorobenzene drops, (c) from water drops, and (d) to water drops. Table V. Average Experimental @ Values for Each Experimental Block direction of surfactant exptl transfer concn, g/LH20 dispersed phase block no. D-C 2.00 chlorobenzene 1 D-C 0.10 chlorobenzene 2 2.00 C-D water 3 C-D 0.10 4 water D-C chlorobenzene 0.00 5 C-D 0.00 chlorobenzene 6 D-C 2.00 water I D-C 0.10 water 8 0.00 D-C water 9 0.00 C-D water 10 0.038 C-D water 11 0.038 D-C water 12 D-C chlorobenzene 0.038 13 Table VI. ANOVA Table To Determine Whether the Average B Values for Each Experimental Block Are Statistically Different sum of degof mean source of error squares freedom square felp f l z , l ~ , ~ . ~ l between blocks 4.516 12 0.376 9.45 2.72 within blocks 7.288 183 0.040 totalcorrected 11.804 195
computed using dS2*from eq 2, and are listed in Table V. Since these @ values ranged from -0.5996 to -1.191 with an average value of -0.856, a comparison of means test was used to examine the null hypothesis that the mean @ value for each of the 13 blocks was equivalent within experi-
av fl value -0.5996 -0.1379 -0.7984 -0.8672 -0.9348 -0.9140 -0.7080 -0.7125 -0.8999 -1.018 -1.191 -1.011 -0.738
--
no. of data points 14 14 18 17 14
16 16 16 17 18 14 14 8
-
Table VII. Experimental Design T o Determine the Effect of Surfactant Concentration [l 0.000 g/L H 2 0 , 2 0.038 g/L H20.3 0.1000 g/L H * 0 , 4 2.000 g/L H20], Direction of Diffusion. and Direction of Dismrsion on Average B av fl value for treatment blocks, water(c) water(d) water(d) lSAAl D-C D-C C-D 1 -0.9348 -0.8999 -1.0183 -0.7383 -1.1906 2 -1.0113 -0.7125 -0.8672 3 -0.7379 -0.7080 -0.7984 4 -0.5996
-.
mental error. The resulting ANOVA table is given in Table VI, where it was found that the null hypothesis could
Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 2661
R201 D->C W
0
large di and phi, 220rpm
large di and phi, 220rpm
0
P
o
8 0
*
6
8 D 0
e
0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 4S
time (sec)
time (sec)
b
a
2,
2-
1
0
0
. = R e 1 W(D C->D Q=R155 W D->C o = R 3 8 W C D->C large di and phi, 220rpm
n
d -
-
$2 33 -
v
‘El,
0.0 6.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
d -
large di a n d phi, 220rpm 8 0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.C
time (sec)
time (sec)
C
d
Figure 8. Effects of reversing the direction of dispersion and diffusion on the transient dBZ for dl = 0.101 m and N = 220 rpm (“R“means run): (a) surfactant-free systems; (b) 0.038 g of SAA/L of HzO; (c) 0.10 g of SAA/L of H,O; (d) 2.00 g of SAA/L of HzO. Table VIII. ANOVA Table To Determine Whether the Surfactant Concentration, Direction of Dispersion, or Direction of Transfer Affects Average /3 Values source of error sum of squares deg of freedom mean square fe, ftable treatment (DOD, DOT) blocks (ISAAl) treatmeit and block interaction8 residual total corrected
1.1651 2.7566 0.5488
2 3 6
0.5825 0.9189 0.0915
15.035 23.715 2.3608
f2,168,0.001 f3,168,0.001
= 6.91 = 5*42
f6,leS,O.OS
2*10
f6,168,0.01
6.5094 10.9800
168 179
be rejected at the 0.001 probability level, or the probability that the null hypothesis was correct was 0.001. In conclusion, there is a statistically significant difference in j3 values between blocks at the 0.001 level. A second experimental design was then developed, as shown in Table VII, to test the null hypothesis that @ values were independent of surfactant concentration as well as the direction of dispersion, DOD, and the direction of transfer, DOT. Three ‘treatments” depending on the direction of dispersion and transfer were examined with four ‘blocks” of different surfactant concentrations. The resulting ANOVA table appears in Table VIII, which shows that the direction of dispersion and transfer along with the surfactant concentration had statistically significant effects on 8. Thus the null hypothesis was rejected at the 0.001 level. Furthermore, the interaction effects between [SAA], DOD, and DOT were also found to be
0.0387
= 2*80
statistically significant at the 0.05 level. Now that the effects of DOD, DOT, and [SAA]on j3 have been shown to be statistically significant, these effects will be quantified. Plotting the average j3 values against the diminished interfacial tension due to the presence of surfactants, as illustrated in Figure 7, shows a roughly linear relationship. Thus, linear regression was used to develop expressions of the form (6) j3 = Cl,O* + c,, where Cl,and C2 are constants with values that appear in Table IX. T i e quantity u* is the dimensionless interfacial tension defined as
Q* =
Q
‘Jm,
where u,,
- Qmin - Qmin
(7)
is the surfactant-free interfacial tension and
2562 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 I
I
large di and phi, 220rpm
I
I
1
1
1
0.0 6.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
la' sigma(dynes/cm)
time (sec)
Figure Effect of interfacial tension resulting from sur...ctanta on block average 9, values.
a 9,
1
I
2I 24
/
id
large di and phi, 220rpm
0 0
s
m
g o
8 8
e
0
c -2.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
time (sec)
S
%C
iI
Y
large di and phi, 220rpm
I
8
d
-1.5
-1.0
0.0
-0.5
Beta exp Figure 8. Experimental block average and predicted fl values for the chlorobenzene/TBAB/water/Triton X-100system.
b
E"
c
Table IX. Average 9, Values and Their Corresponding Dimensionlees Interfacial Tension average fi value for [SAA], water(c) water(d) water(d) g/L D-C D-C C-D U* 0.000 -0.9348 -0,8999 -1.0183 1.000 0.038 -1.0113 -0.7383 -1.1906 0.638 0.100 -0.7379 -0.7125 -0.8672 0.294 2.000 -0.5996 -0.7080 -0.7984 0.011 ~
r2 Cl% C2%
-0.8032 -0.2829 -0.6554
-0.8032 -0.2829 -0.6554
~~~
-0.7135 -0.2904 -0.8276
TBAB transfer from water drops; (c) for TBAB transfer from chlorobenzene drops.
A plot of Bd, versus Berp is given in Figure 8, and the absolute deviation for eqs 8 and 9, computed as Be, )/j3expl,are 6.97% and 8.52%, respectively. 'fherefore, the effects of reversing the direction of transfer and varying the surfactant concentration on transient Sauter-mean drop diameter in agitated liquidliquid dispersions can be accounted for by inserting eq 8 or 9-in conjunction with the d32* and a expressions developed by Hong and Lee (1985)-into eq 3, at least for the system studied here.
uminis the asymptotically approached u at high surfactant concentrations. The resulting expressions for j3 that account for the effects of surfactant and direction of mass transfer are B = -0.28~*- 0.66 (8) j3 -0.296 - 0.83 (9) for transfer to and from the continuousphase, respectively.
Nomenclature C, = correction factor in eq 1, dimensionless C1, C2 = constants in eq 6, dimensionless A&, = initial and final concentxation differences between the two compartments in the diffusion cell, kg-mol/m3 D = molecular diffusivity, m2/s DOD = direction of dispersion, dimensionless DOT = direction of transfer, dimensionless
0.0 6.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
time (sec) C Figure 6. Effect of Triton X-100concentration on the transient dS2 V"" means run): (a) for TBAB transfer to water drops; (b) for
Atf
Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 2563
dI = impeller diameter, m d32,d,* = Sauter-mean drop diameter, equilibrium value, m 8 = grawtational acceleration, m/s2 H = height of fluid in vessel, m N = impeller speed, l/s NFr,= impeller Froude number, p&W/ApHg, dimensionless Nh = impeller Reynolds number, p c d t N / p c ,dimensionless Nwe,= impeller Weber number, W d t p c / u , dimensionless R = run number r2 = correlation coefficient, dimensionless SAA = surface-active agent, dimensionless [SAA] = concentration of surface-active agent, kg/L T * tank diameter, m TBAB = tetrabutylammonium bromide t = time, s a,fi = constants in the transient d32 expression, dimensionless BdC, &, = calculated and experimental fi values, dimensionless = diffusion cell constant, m2 pc = continuous-phase viscosity, kg/(ms) pc = continuous-phase density, kg/m3 Ap = density difference between phases, kg/m3 u, u,,, umh = interfacial tension, surfactant free value, asymptotically approached interfacial tension at large surfactant concentrations, N/m u* * dimensionless interfacial tension t#~ = volume fraction of dispersed phase, dimensionless
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Received for review June 22, 1992 Accepted July 22, 1992
