Ind. Eng. Chem. Res. 1990,29, 2258-2267
2258
SEPARATIONS Mechanism of Continuous-PhaseMass Transfer in Agitated Liquid-Liquid Systems A. H. P. Skelland* and L. T. Moeti School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
New data are reported on 180 area-free, continuous-phase mass-transfer coefficients for 9 turbine-agitated liquid-liquid systems in baffled vessels. Criteria are established that identify the prevailing class of mass-transfer mechanisms for systems of intermediate or high interfacial tension with low 4-namely, k, 0: D2/3p;1/3N3/2,It is also deduced that k, a d,O for the combined ranges of d , Ap, and p, investigated. A subsidiary result is the correlation of the k , values obtained, on the gasis of local isotropic turbulence theory for the inertial subrange of eddy sizes.
Introduction Liquid-liquid extraction is an industrial process for the separation of components of a solution. The rate of mass transfer across the interface between two liquids brought into intimate contact in a mixing vessel is dependent upon the concentration difference, the interfacial area between the two liquids, and the mass-transfer coefficient. Mixer-settlers are widely used in liquid-liquid operations performed either in batch fashion or with continuous flow. The merits of batch experimentation, as used in the paper by Skelland and Lee (1981) and in the present study, have not perhaps been fully appreciated. Thus, droplet breakdown into successively smaller drops persists for several minutes after injection of the disperse phase (Skelland and Lee, 1981; Bapat et al., 1983; Bapat and Tavlarides, 1985; Hong and Lee, 1985), whereas mass transfer is usually complete after a minute or two (Rushton et al., 1964; Treybal, 1980, p 524; Skelland and Lee, 1981). Batch experimentation, as described below, enables this behavior to be quantitatively followed with time by measurement of k, drop size, and surface area from moment to moment for a single injected element of disperse phase. In contrast, experiments with continuous-flow-through operation give only average transfer conditions corresponding to many different elements of disperse phase that simultaneously occupy the vessel but which entered it at different times and are therefore in different stages of mass transfer and drop breakup at any given instant. The time history of a given element of disperse phase in the vessel cannot then be followed in the manner necessary to properly model the process. Schindler and Treybal(1968), Mok and Treybd (1971), and Keey and Glen (1969) have studied liquid-liquid mass-transfer rates in continuous-flow agitated vessels. These investigations were confined to single systems, so that comprehensive correlations over a range of physical properties were not established. In the batch study by Skelland and Lee (1981),five systems were used, although the difisivity varied only 1.5-fold, to develop more general correlations for mass-transfer coefficients. The principal objectives of the present research are to determine the influence of diffusivity on the continuous-
* Author to whom correspondence
should be directed.
0888-5885/90/2629-2258$02.50/0
phase mass-transfer coefficient, in order to identify the class of mechanisms of liquid-liquid extraction prevailing in agitated vessels, and to determine whether small drops behave as rigid spheres with immobile interfaces, as stated by Harriott (1962) and Calderbank (1967), or as spheres with mobile interfaces, as claimed by Treybal (1963,p 416; 1980, p 523) and Glen (1965). As a subsidiary objective, a semitheoretical correlation of the experimental data will be attempted, on a basis not previously used for liquidliquid systems.
Theoretical Background Central to the question of which transport mechanism is prevalent for the situation at hand is the influence of the diffusivity on the mass-transfer coefficient. Thus, in the expression
k, a D,”
(1)
the exponent n has a value of unity according to the film theory, whereas for the film-penetration theory of Toor and Marchello (1958) and Dobbins (1956) n has values between 1/2 and 1. n values between 1/2 and 1also follow from our film-penetration theory with periodically varying rate of surface renewal-details of the development are given by Moeti (1986). Other theoretical mechanisms, including some that permit n to approach zero, are reviewed by Kozinski and King (1966). For fully mobile interfaces an n of 1/2 is indicated by the eddy cell model (Lamont and Scott, 1970), by boundary layer theory (Calderbank, 1967), by the large-eddy model (Fortesque and Pearson, 1967),by turbulent boundary layer and slip velocity theory (Keey and Glen, 1969), by potential flow theory (Calderbank, 1967), and by the theory of periodically varying rate of surface renewal (Skelland and Lee, 1981). For immobile interfaces, on the other hand, n equals 2/3 according to the eddy cell model (Lamont and Scott, 19701, to boundary layer theory (Calderbank, 19671, and to slip velocity theory for “large” particles (Harriott, 1962). When attention is restricted to mass transfer in twophase suspensions in agitated vessels, the experimental findings are often conflicting and at variance with theory. Thus, it was contended by Barker and Treybal(l960) that n equals zero. This was reiterated in two subsequent 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 11, 1990 2259 publications by Treybal (1961; 1963, p 417). For mass transfer from solid particles freely suspended in agitated liquids (Le., immobile interfaces), an n of 2/3 was obtained by Calderbank and Moo-Young (1961). This contrasts with n values of 1/2 found by Hixson and Baum (1941), Bieber (1962), Barker and Treybal (1960), and Sykes and Gomezplata (1967). In the work of Barker and Treybal, a 17-fold range of D, was used to establish a value of 1 / 2 for n by graphical means. Sykes and Gomezplata specifically showed that an n of 1 / 2 satisfactorily represented their results, whereas 2/3 did not. They observed that “the over-correction for the effect of system Schmidt number (and therefore of D,) ...by the fixed particle correlations (i.e., by use of n = 2/3) has been noted by Miller (1964).” Unfortunately their conclusions are undermined by their invalid “finding” that k, increases with increasing continuous-phase viscosity, p,. Both Harriott (1962) and Calderbank (1967) state that small drops and bubbles behave as rigid spheres when suspended in agitated liquids. The resulting immobile interface would suggest that n equals 2/3, according to some of the above theories. Thus, Calderbank‘s (1967) correlation of measurements for small bubbles in aqueous electrolytes uses n = 2/3. Both Treybal(1963, p 416; 1980, p 523) and Glen (1965), on the other hand, say that the surface of such liquid drops is mobile. This is consistent with Prasher and Wills’ (1973) use of n = 1 / 2 to correlate mass transfer from gas bubbles in agitated liquids. Humphrey and Van Ness (1957) and Miller (1971) arbitrarily assigned values of 1 / 2 and 2/3, respectively, to n,even though they each studied only one system of solid particles dissolving in an agitated liquid. Clearly D, and N s C cwere not variables in their experiments. Much of the work on mass transfer in agitated vessels has used sucrose in the continuous phase to increase viscosity and hence the range of the Schmidt group. This has been avoided here for two reasons. First, sucrose undergoes acidic hydrolysis to yield an equimolar mixture of glucose and fructose (Streitwieser and Heathcock, 1973). Second, hydrogen bonding between sucrose and acids has been well documented by Pimentel and McClellan (1960) and Gordy and Stanford (1940). These effects can reduce the apparent diffusivity of the acid and lead to erroneous conclusions regarding the exponents on both the diffusivity and the viscosity. It is perhaps relevant that most of the solid-liquid mass-transfer studies that report k, as proportional to DC1/* have involved the use of sucrose. Hixson and Baum (1941), Barker and Treybal (1960), and Sykes and Gomezplata (1967) all used it in aqueous solution to increase the range of the Schmidt number and found k, 0: D,’12. This conflicts with an exponent on D, of 2/3 found by Calderbank and Moo-Young (1961) from sucrose-free data and can perhaps be attributed to its use. Similarly, the larger effect of viscosity on the mass-transfer coefficient in the presence of sucrose, compared to sucrose-free effects of p, on k,, may be due to interaction between the sucrose and acids or other solutes. The wide variety of differing models and observations outlined above, together with conflicting statements on whether drops in agitated liquid-liquid systems are internally circulating or stagnant, requires experimental resolution. A definitive answer will be sought here by experimental determination of the dependence of k, on p, and on D,, thereby eliminating a large class of models from further consideration, while providing guidance for future modeling. Mixer-settler units in liquid-liquid extraction are more commonly applied to systems with high interfacial tension, u. Accordingly, attention will be confined
Table I. Interfacial Tensions of Liquids with Water interfacial tension, N/m o-xylene benzaldehyde temp, O C chlorobenzene 0.0348 0.0164 5 0.0345 12 0.0343 0.0342 0.0160 19 0.0340 0.0339 0.0159 26 0.0338 0.0335 0.0152 0.0148 33 0.0334 0.0331 40 0.0325 0.0318 0.0142 0.0306 0.0137 47 0.0315 0.0278 0.0128 54 0.0289 0.0263 0.0116 61 0.0274 70 0.0268 0.0259 0.0108
to systems of intermediate and high u (Le., for u L 0.015 N/m).
Experimental Work Choice of Materials. The influence of trace amounts of surface-active impurities in reducing or eliminating internal circulation currents in drops moving in liquid-liquid systems has long been known (e.g., Garner and Skelland, 1955, 1956). These effects are well summarized in more quantitative terms by Davies (1972, pp 304-308) and by Clift et al. (1978, pp 35-41). In work of the present kind, therefore, it is important to specify the nature of the materials used with some care, as follows. Solvents. Deionized water was employed as the continuous phase throughout. It was produced by passing Atlanta city water through beds packed with beads of mixed cation- and anion-exchange resins for the elimination of dissolved minerals. The beads were supplied by Rohm and Haas. Chlorobenzene and o-xylene were used as the disperse phase for our high interfacial tension systems, with benzaldehyde as the disperse phase for intermediate interfacial tension. The chlorobenzene and benzaldehyde were “Certified grade,” and the o-xylene was “Reagent grade”. All were supplied by Fisher Scientific Company. Solutes. Nonanoic, heptanoic, and benzoic acids provided an extended range of D, in association with temperature variation ranging from 5 to 70 “C. These solutes had slow rates of transfer so that concentration changes could be readily measured with time. Their distribution ratios greatly favored the disperse phase, so as to yield continuous-phase controlled systems. The nonanoic and heptanoic acids were both “Practical grade” and were supplied by Eastman Kodak Company. The benzoic acid was Certified grade and came from Fisher Scientific Company. Measurement of Physical and Transport Properties. All physical and transport properties were measured experimentally over a range of temperatures by immersing the interfacial tension beakers, viscometers, density beakers, and diffusion cells in a constant temperature bath to increase the range of diffusivities. Interfacial tension was obtained by using the Fisher surface tensiometer Model 21. The force necessary to pull a platinum-iridium duNuoy ring through the liquid-liquid interface was measured. Table I shows the interfacial tension values of the dispersed-phase liquids with water at the temperatures used here. Viscosity was determined by using Cannon-Fenske viscometers. Table I1 shows the viscosities of the liquids used at the various temperatures. Density was measured with a Troemner specific gravity chain balance Model S-101. Values of densities for the liquids employed are shown in Table I11 for our range of temperatures. Diffusivity was determined by using a diaphragm diffusion cell as described by Wilke and Chang (1955) and Bidstrup and Geankoplis (1963). The diffusion
2260 Ind. Eng. Chem. Res., Vol. 29, No. 11, 1990 Table 11. Dynamic Viscosities of Liquids dynamic viscosity, N s/mZ temp, O C chlorobenzene o-xylene benzaldehyde 5 0.000 95 0.000 94 0.002 14 12 0.00185 0.000 92 0.000 85 19 0.001 61 0.000 87 0.000 73 26 0.00142 0.000 73 0.000 71 33 0.001 31 0.000 72 0.000 59 40 0.001 19 0.00066 0.OOO 53 47 0.00107 0.000 63 0.000 50 54 0.000 98 0.000 59 0.000 47 61 0.000 56 0.000 42 0.000 90 70 0.00048 0.00081 0.OOO 39 Table 111. Densities of Liauids densities, kg/m3 temp, O C chlorobenzene o-xylene benzaldehyde 5 1091 858 1049 12 1091 1049 858 19 857 1088 1049 26 1083 856 1026 33 1083 796 1026 40 1082 786 1025 47 1082 786 1025 54 1079 778 1023 61 1078 778 1021 70 1077 1021 778 Table
40
water 0.001 52 0.001 24 0.001 03 0.000 87 0.000 75 0.000 65 0.000 58 0.000 51 0,00046 0.000 40
30
D,(m 2 / s ) x 1010
water 1000 1000 998 998 995 992 990 986 983 978
2o Hep t a n o i c Nonanoic
10
IV. Diffusivities of Solutes in Water 7 ooc
?C 26*C
temp, "C 5 12 19 26 33 40 47 54 61 70
nonanoic acid 4.20 4.80 5.80 6.80 8.OOn 9.40b 11.ooc 12.40 14.00d 16.20e
heptanoic acid 5.20 5.80 7.10 8.1P 9.50b ll.lOC
12.80 14.30d 16.20e 18.50'
benzoic acid 8.30. 9.40b 11.7OC 13.60d 16.10e 18.80' 22.10 24.90 28.30 32.70
0 0.153
0.553
T?,, x
0.953
( o K ~ ~ P . )
Figure 1. Diffusivities of acid solutes in water.
Superscripts identify temperatures at which the three (or two) solute diffusivities are approximately the same. Since, considering superscript b, for example, the aqueous phase viscosities at 40, 33, and 12 "C were 0.00065,0.00075, and 0.001 24 N s/m*, respectively, from Table 11, this facilitates evaluation of x in kc = p:, because variations in u and pc over this temperature range were slight, as shown by Tables I and 111.
coefficients of the three solutes are shown in Figure 1. Table IV lists the diffusion coefficients of each solute for the temperatures used in this study. Values in Table IV are interpolated from Figure 1. Apparatus. Details of the apparatus are described by Skelland and Lee (1981),although some modifications are noted below. Briefly, a cylindrical glass vessel with a flat bottom, fitted with four equally spaced, radial, vertical wall baffles, was used for mixing. A Neslab Model RTE-8DD temperature circulation bath waa used to vary the temperature of the mixing liquids to increase the range of diffusivity. A Model ELB experimental agitator kit manufactured by the Bench Scale Equipment Co. was used for mixing the liquids. It is equipped with a llrl-hp motor and provides a continuously variable output speed of 0-18 rps. The speed control dial is calibrated directly in rps by a tachometer system. The impeller studied was a stainless steel six-flat-blade turbine, since this type of impeller showed the best dispersion performance for uniform mixing (Skelland and Lee, 1978, 1981). Uniform mixing is defined to occur at the impeller speed at which the mixing index reaches 98%
1.353
B-
I E
I
I
I
w
I
A
Figure 2. Schematic diagram of the apparatus. A cylindricalglass vessel. B: baffle. C: six-flat-blade turbine. D: conductivity cell. E: temperature bath. Table V. Apparatus Dimensions internal diameter of vessel, T height of vessel liquid height in vessel, H diameter of impeller, dI diameter of shaft baffle length baffle width baffle thickness
0.2135 m 0.2500 m 0.2135 m 0.1000 m 0.0140 m 0.2300 m 0.0190 m 0.0031 m
Ind. Eng. Chem. Res., Vol. 29, No. 11, 1990 2261 (Skelland and Lee, 1978), and this was applied to determine the impeller speeds used. The dimensions of the apparatus are listed in Table V, and a sketch appears in Figure 2. The total interfacial area, found from drop-size distributions, of the liquid-liquid systems during mixing was determined from photographs of the dispersion taken through the flat glass temperature bath, thus eliminating the optical distortion caused by the cylindrical glass vessel. Other techniques for determining interfacial area, including light scattering, anti-coalescing surface-active agents, and refractive index, do not provide as absolute a drop-size distribution as the photographic technique (McLaughlin and Rushton, 1973) and therefore were not used in the study. Illumination was provided by a Hedler "Jet-Lux 1250" tungsten-halogen lamp mounted beside the temperature bath in which the vessel was placed. The camera used was a Nikon F-2 with 55 mm f/3.5 MicroNikkor-P lens and MD-2 motor drive. An M2 ring was inserted between the camera and the Micro-Nikkor-P for pictures with reproduction ratio 1:l (actual size). Kodak Tri-X Pan film with ASA-400 was used with a shutter speed of 1/2000 s and aperture setting of f/3.5. A conductivity cell made by sealing two tungsten wires in a poly(methy1methacrylate) rod was used for measuring the change of solute concentration by monitoring electrical conductivity as recommended by Rushton et al. (1964). The cell was connected to a Yellow Springs Instrument conductivity meter. The output of this meter was recorded simultaneously by a Fisher Recordall Series 5OOO recorder. For this study the conductivity varied linearly with the small concentrations of solute used (about 3% by mass initially in the dispersed phase throughout). This enabled the solute content of the continuous phase to be known from the corresponding conductivity a t any instant from previous calibration. Experimental Procedure. The continuous and dispersed phases of each system were prepared separately by presaturating each liquid with the other. All liquids were used only once. A certain amount of solute was dissolved in the material for the dispersed phase. The continuous phase was placed in the mixing vessel, and the agitation was started. The impeller speed, N, was always above the minimum value for 98% uniformity (Skelland and Lee, 1978). The conductivity cell was placed in the impeller stream, and the conductivity meter and recorder were turned on. The prepared solution of the dispersed phase, which was at the same temperature as the continuous phase, was poured rapidly from a beaker into the center of the vessel (i.e., near the impeller shaft). The conductivity was measured and recorded from the moment the dispersed phase was added until no further increase was observed. It took 3-12 s to obtain total distribution of the organic phase throughout the vessel, depending on the impeller speed, although much more time would be needed for the drops to reach equilibrium size. In this research the dispersion became cloudy after short times, such that drop sizes could only be determined until about one-third of the possible mass transfer had occurred. About 6-10 photographs (reproduction ratio 1:l)were taken a t intervals of 2-4 s during each run. The lamp illuminating the vessel was turned on only when pictures were taken, to prevent raising the temperature of the liquids during experiments. After each run the apparatus was taken apart, washed with detergent, and then rinsed repeatedly with hot water followed by deionized water, to eliminate any detergent residue.
Figure 3. Typical photograph of the drops seen in this work. Here the disperse phase is chlorobenzene containing heptanoic acid transferring into the continuous water phase in run 5. The equipment dimensions are as in Table V, the impeller speed N is 4.17 rps, 6 is 0.01, and dB2is 0.188 mm a t 26 "C.
The photographic film was developed, and the negatives, with reproduction ratio 1:l (actual size), were projected onto the screen of a microfilm reader having known magnification ratio for drop size measurement. This enabled estimation of the drop size spectrum by counting about 150 drops. A typical photograph is shown in Figure 3. The Sauter-mean diameter was calculated as follows: CnIdp: Cnidpi2 '32
= magnification ratio
This method was useful only for small volume fractions of the dispersed phase; 4 had a constant value of 0.01 in this study, not only to avoid cloudiness and obscured photography but also to avoid significant contributions by drop breakage and coalescence to the total transfer (see Boyadzhiev and Elenkov, 1966). I t may be remarked that the reason for confining the direction of mass transfer to that from the organic to the aqueous phase was to avoid interference from hydrogenbonding effects of the sort detailed by Licht and Conway (1950), Garner et al. (1955), and Skelland (1985, pp 424-425). Preliminary observations were made by using the suspended or pendant drop method to detect the presence or absence of any gross Marangoni effects (twitching,rippling, periodic pulsations of the drop, etc.), as described by Skelland (1985, pp 289-291). Such gross effects were entirely absent, perhaps because the low solute concentrations used here were below what Davies (1972, p 332) describes as "...the critical concentration of solute required just to produce surface turbulence." As another consequence of hydrogen bonding, many carboxylic acids exist as dimers in organic solvents (excluding alcohols) and as monomers in water (Skelland, 1985, p 58). Concern may therefore arise about the possibility of some interfacial resistance to transfer in the present work, associated with the "dedimerization" of the acid solutes when leaving the organic drops to enter the water. The following considerations may provide some reassurance in this regard. Skelland and Hemler (1969) correlated continuous-phase mass-transfer coefficients (approximated by K, values) for acetic acid crossing the interface in the dimerizing direction
2262 Ind. Eng. Chem. Res., Vol. 29, No. 11, 1990 1.0
0.4
I
I
I
I
10.0
1
I
I
4
i
i
6.0
1
VS
I
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1
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0 Chlorobenzene r
A
i
O-Xy:ene
L
4
0B e n z a l d e h y d e
e
7-
C-C,
I
6
(!CLI n s
1.0
0'8
0.5
1r
3.0
1 I
I
I
6.0
I
I
I
D,CIO1o)
I
10.0
I 20 0
30.c
m2's
Figure 5. k, versus D,at 33 O C .
In
P*A
- PA
P*A-PAl
k&
= --(t
- tl)
(4)
vc
which shows that a plot of In [ ( P * A - P A ) / ( P * A - PA1)I versus t - t , gives a straight line of slope -kJ/ V,, where V , is the volume of the continuous phase in the vessel and tl is the time at which the start-up disturbance has ceased; it ranged from 3-12 s depending upon the degree of turbulence in the mixing vessel. Consequently, k& has been obtained from this slope. The adequacy of this approach is demonstrated by the essential linearity of Figure 4, which presents a typical plot of In [ ( P * A - P A ) / ( P * A - PAI)] and In d,, versus t - t,. The Sauter-mean diameter whFn about 33% of the possible mass transfer had occurred, d,, [i.e., when ( P * ~- p A ) / ( p * A - pAI) = 0.671, was chosen and measured for the calculation of the interfacial area, A , as 64 A = a V = ---V 4 2
Correlations of the transient drop size in batch agitated liquid-liquid systems in the presence of mass transfer have not yet been established. It may be helpful to note, however, that our 180 values of d32 were correlated with an average absolute deviation of 45.2% by the Hong and Lee (1985) correlation for transient drop diameters without mass transfer. (The time recommended for use in this correlation is 8.9 s, with a standard deviation of 4.3 s. This is the average time when one-third of the possible mass transfer had occurred for the 180 runs in this study.) The liquid height, H, was always equal to the vessel diameter, T , and N was always above the minimum value needed for uniform dispersion, as defined by Skelland and Lee (1978). On the other hand, N could not be increased to high values, because the dispersion started emulsifying, making clear pictures difficult to obtain. Because of these considerations N varied somewhat throughout the study. Preliminary Estimates of the Effect of D , on k,. For each solvent-solvent system (e.g., chlorobenzenewater) at a given temperature, the three solute acids used provided roughly a 2-fold range of diffusivity in the continuous aqueous phase, with all other variables held constant. A typical example of the 10 plots obtained appears in Figure 5, which shows least-squares lines through the points. An average exponent of 213 on D, was found for both high and intermediate interfacial tension systems. Effect of N on k,. I t is reasonable to postulate that k, = f[(variable set I),(variable set II),@,N,dJ (6) where variable set I consists of all relevant equipment dimensions in Table V and variable set I1 comprises all relevant physical properties of the liquid-liquid system under consideration. Now the variables in set I and 6 all had respectively constant values throughout the present study. However, d, varies with N in agitated liquid-liquid systems. Thus, the exponential dependence of k, on N can be easily established from data on a given liquid-liquid system only if k, is not a function of d,, the drop diameter. In this regard, we first note that the preliminary estimate just obtained for the exponent on D, relates predominantly to that transfer mechanism associated with free travel of
Ind. Eng. Chem. Res., Vol. 29, No. 11, 1990 2263 10
4
+= 0 03
6
4
6, x'
0.06
11
0.1
2
G
4
N
(rps)
8
102
4
6
8 1 0
N (rps)
Figure 6. k, versus N for system 1 from Lee (1978) (2 cs silicone oil-heptanoic acid-water). dI = 0.078 or 0.106 m; T = 0.210 or 0.246 m.
discrete drops around the vessel. This follows from Boyadzhiev and Elenkov's (1966) finding in high interfacial tension systems for 0 5 4 50.06 that the breakup-coalescence process does not significantly affect the transfer mechanism in a turbulent isotropic flow field when the system is continuous phase controlled, as here (see also Davies, 1972, pp 231-232). Now the value of the exponent on D,-namely 213-indicates that these small drops were internally stagnant, resembling solid spheres in this respest. But for fully suspended solid spheres in our range of d3* (140-360 pm), Ap (0.05-0.12 g/cm3), and pc (for water), k, is practically independent of particle diameter according to Harriott (1962),in agreement with many other findings [i.e., Hixson and Baum (1941, 1942), Wilhelm (1949), Mack and Marriner (1949), Kneule (1956), Humphrey and Van Ness (1957), Barker and Treybal (1960), Calderbank and Moo-Young (1961), Calderbank (1967), Davies (1972, p 149), Nagata and Nishikawa (1972), Sherwood et al. (1975), etc.]. The effect of N on k, was therefore established in accordance with eq 6 and the above considerations from the work of Skelland and Lee (1981). Their equipment was the same as that used here, but their N variation was substantially greater for a given system. When attention is confined to their sucrose-free data, Figure 6 shows loglog plots of k, versus N for a system similar to those used in this research. The data in Figure 6 are from Lee's thesis (1978); his high interfacial tension system 1 (2 cs silicone oil-heptanoic acid-water) yields an exponent on N of 1.78. For Lee's intermediate u system 5 (benzaldehyde-heptanoic acid-water), the exponent on N is 1.30; averaging these results leads to an estimate for the exponent on N of 312. This exponent on N is about the same as that obtained earlier in liquid-liquid studies by Glen (1965), Schindler (1967), and Lee (1978). It is roughly twice the exponent found for the dissolution of solid particles in agitated systems [Barker and Treybal (1960), Brian et al. (1969), Levins and Glastonbury (1972), etc.]; the disparity was previously known and predicted (Davies, 1972, pp 239-240). Effect of pc on k,. The effect of the continuous-phase viscosity on the mass-transfer coefficient, k,, was determined as described at the foot of Table IV and illustrated by Figure 7, where least-squares lines are drawn through the data points, allowance for the effect of N appearing
I
0.2
I
1
I
0.a uc ( l o 3 )
Figure 7. k J N
I I I I I 0.6 0.8 1.0
2.0
~ s / d
versus pc for chlorobenzene drops.
Table VI. Effect of on the Mass-Transfer Coefficient" investigators x in k, a ~1.' Hixson and Baum (1941) s-1 -0.90' Barker and Treybal (1960) S-1 -0.83' Sykes and Gomezplata (1967) s-1 +0.12's Rushton et al. (1964) 1-1 -0.606 Skelland and Lee (1981) 1-1 -1.37'
Hixson and Baum (1941) Hixson and Baum (1942) Kneule (1956) Johnson et al. (1957) Harriott (1962) Harriott (1962) Levins and Glastonbury (1972) Calderbank and Moo-Young (1961) present research
5-1
S-1 S-1 S-1 9-1
s-1 S-1 g-1 1-1
-0.12 -0.50 -0.17 -0.42 -0.22 large d -0.06 small -0.26 -0.42 -0.30
8,
s-1, solid-liquid; g-1, gas-liquid; 1-1, liquid-liquid. In the presence of sucrose for viscosity variation. Directionally incorrect effect.
in the ordinate. For the high interfacial tension systems (chlorobenzene and o-xylene), an exponent on N of 1.78 was used. For the intermediate interfacial tension system (benzaldehyde),an exponent of 1.30 was employed. These were the exponents determined for systems 1 and 5 from Lee (1978) as discussed earlier. The average exponent on p, for the systems used in the present study was -0.30 (-0.35 for chlorobenzene, -0.24 for o-xylene, and -0.32 for benzaldehyde). Table VI shows the effect of pc on the mass-transfer coefficient reported by various investigators. It may be noted that when sucrose was used to increase viscosity, larger effects were found than in the absence of sucrose. Reasons for this were suggested earlier. General Effect of D , on k,. To generalize the effect of the diffusivity (which had a 7.8-fold range over the temperatures used in this research) on the mass-transfer coefficient, the effects of N and p, on k, were incorporated in Figures 8-10 for the three systems. The exponents on the impeller speed, N , and the continuous-phase viscosity, K,, are taken from the previous sections in association with either high or intermediate interfacial tension. All other variables were constant or had only slight variations with temperature. The exponents obtained on D, from regression analysis with the attendant 95% confidence intervals are as follows: chlorobenzene (0.70 f 0.037), oxylene (0.64 f 0.035), and benzaldehyde (0.63 f 0.053). Also included in Figures 8-10 are lines with slopes of 0.50, which demonstrate the lack of fit for mass-transfer mechanisms with exponents on D, of 0.50. These findings
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