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Ind. Eng. Chem. Res. 1997, 36, 4928-4933
Measurement of Drop Rise Velocities within a Ku 1 hni Extraction Column Sandra E. Kentish, Geoff W. Stevens,*,† and H. R. C. Pratt Department of Chemical Engineering, University of Melbourne, Parkville, Australia 3052
A new method is presented for the determination of droplet rise velocities within liquid-liquid extraction columns. This method utilizes the difference between the static drop size distribution as measured by a photographic technique and the dynamic drop size distribution as measured by a capillary probe technique. The ratio of the two volume densities multiplied by the average flow velocity is then a direct measure of the individual drop velocity. Droplet velocities measured using this technique are consistent with single drop velocities measured by other workers at low holdups. However, at higher holdups the droplet velocities converge toward a single value rather than retaining a range of drop size dependent values. Introduction A new method is proposed here for the determination of droplet rise velocities within liquid-liquid extraction columns such as the rotating disk (RDC) and Ku¨hni columns. Such information is essential to the construction of an accurate model of the dispersed phase behavior within such columns. In this discussion, it will be assumed that the droplet phase has the lower density, i.e., that the drops rise. A significant amount of effort has been directed toward the determination of such rise velocities for single isolated drops. Thus, Haunold et al. (1990), Seikova et al. (1992), and Fang et al. (1995) all measured the velocity of single drops through a Ku¨hni column, while Fan et al. (1987) measured similar velocities in an RDC. Gourdon et al.(1991) used both a Ku¨hni and a pulsed sieve plate column. These authors related the experimental single drop value, us(d), to the terminal velocity, ut(d), by
us(d) ) Kvut(d)
(1)
For a Ku¨hni column, Fang et al. (1995) have provided an expression for the slowing coefficient, Kv, as
Kv ) 1 -
(1 - e)γ (1 + γ)
(2)
with γ ) 7.18 × 10-5ReI/e. The above authors all assumed that the rise velocity within a droplet swarm, ur(d), can be derived from the single drop velocity through an equation of the type
ur(d) ) Kvut(d)(1 - φ)m
(3)
However, there are very few direct experimental measurements of such swarm velocities. Further, much of the experimental work in this area has been confined to monodispersions (Barnea and Mizrahi, 1975; Pilhofer, 1979; Kumar et al.,1980; and Bao and Chen, 1993); that is, the hydrodynamic interactions between drops of identical size only were considered. Such work may not be applicable to polydispersions because, for example, small droplets can travel at a speed greater than their * Author to whom correspondence should be directed. † E-mail:
[email protected]. Fax: 61 3 9344 6 4153. S0888-5885(97)00269-8 CCC: $14.00
terminal velocity in such a dispersion as a result of being carried in the wake of larger drops (Jayaweera et al., 1964). Rise velocities have been measured experimentally within polydispersed swarms by Steiner et al. (1986) in a Ku¨hni column and by Mao and Slater (1994) in an RDC. The method employed in both cases was to dye a proportion of drops and follow their progress. Although the results exhibited a high degree of scatter, Steiner et al. (1986) were able to derive two equations for the drop rise velocity which are dependent upon the direction of mass transfer. Weiss et al. (1995) extracted droplet rise velocities for a Ku¨hni column from a large database of holdup (φ), slip velocity (Vs) and drop size distribution (f(d)) data. These velocities were determined indirectly from the constraining equation:
Vs )
d ur(d)f(d)γd ∫d)0 max
(4)
In the present work, an alternative method is presented for determining the range of droplet rise velocities within a polydispersion. The proposed method utilizes the difference between the results given by two commonly used experimental techniques for determining the drop size distribution within a liquid-liquid dispersion. Thus, the photographic technique involves the counting of all drops visible in a photograph taken of the relevant section of the dispersion. Conversely, the use of a capillary probe involves sucking a small sample of the dispersion through a fine capillary of a diameter generally less than 1 mm. The length and velocity of the resulting “slugs” of dispersed phase is then recorded through the use of photodiodes. By comparing the output from these two experimental techniques, it is possible to determine the range of droplet velocities present within the dispersion. This method is outlined in detail below, and a limited number of droplet velocities determined in this manner within a Ku¨hni column are presented. Experimental Techniques The current experimental work was carried out in a precision bore glass Ku¨hni column of 25 stages and 72.45 mm diameter, with a stator plate spacing of 50 mm. Details of the impeller and stator plates are shown in Figure 1. Measurements of drop size were taken on stages 15 and 17 from the bottom, well away from the © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4929
classified the drops, the volume fraction of each drop size interval was calculated from
fi )
nidi3 Ni
(5)
nidi3 ∑ i)1 The continuous density function was approximated by dividing through by the interval width (∆d ) 0.1 mm). Thus, the volume density is given by
f(d) )
Figure 1. Details of column internals: (a) stator plate; (b) impeller.
Figure 2. Setup for photographic and capillary probe measurements of the drop size distribution.
dispersed phase inlet. Full details of the equipment have been given by Kentish (1996). Distilled water formed the continuous phase while two grades of methyl isobutyl ketone were used as the dispersed phase. These two grades had the same interfacial tension (σ ) 0.0101 kg/s2) but gave slightly different holdup and drop size results as a consequence of different impurity levels resulting from activated carbon treatment in one case to remove added dye. For the photographic determination of the drop size distribution a Perspex box was fitted concentrically around the center of the column (see Figure 2). This box was filled with water in order to eliminate the distortion effects associated with the curved column wall. The box was then entirely covered with opaque black paper except for a thin slit (1-2 mm wide) on one surface for the light source and a rectangular window on the adjacent surface for photography. This enabled photographs to be taken of drops illuminated by the plane of light throughout the column cross section rather than simply those closest to the camera. The resulting photographic images were magnified by a factor of 10 using a slide projector. Each drop was classed into a size interval by placing a standard metric circle template over the magnified image. Having
fi ∆d
(6)
The drop size distribution was also determined by a capillary suction technique. This technique was initially developed by Pilhofer and Miller (1972) while the particular experimental setup used in this work was constructed by Weyrich (1992) and tested both by him and by Isselhard (1993). Drops were collected through a fine bore capillary tube of either 0.76 or 0.89 mm internal diameter, fitted with an entrance funnel of 5-7 mm in diameter and a 90° bend (see Figure 2). This entrance funnel was designed to lead drops into the capillary without breakage. Flow through the capillary was driven by gravity and was controlled by a needle valve in order to maintain a velocity within the capillary tube of between 0.2 and 0.7 m/s (Retube ) 156-640). As with the photographic equipment, the probe was used only in the central stages of the column to eliminate the effects of the inlet distributor, settling zone, etc. External to the column, the capillary tube was mounted in an optical frame. This frame contained two pairs of microlamps and photocells connected to a photodiode circuit. The output from each photocell was an analog voltage which was directed to a data logging system resident in a personal computer. This output appeared as a rectangular wave pattern with each rectangle representing the passage of a single drop. The time required for a drop to pass one photocell and the time required to traverse the distance between the photocells was extracted from this wave pattern and used to calculate the drop diameter. Drops counted by the above technique were also classified into size intervals of ∆d ) 0.1 mm in width, and the drop volume fractions, gi, and densities, g(d), were calculated in an manner identical to that for the photographic method. Method Development There is a fundamental difference between the two experimental techniques described above. Thus, the photographic method records all drops occupying a space at a single moment in time; this is known as the static volume distribution function, f(d). Conversely, the capillary records all drops passing a point over a period of time, i.e., the dynamic volume distribution function g(d). These two distributions are related by
u(d)f(d)γd g(d)γd )
dmax
(7)
∑ u(d)f(d)γd
d)0
where u(d) represents the vertical velocity of the drop relative to stationary co-ordinates. Given that the
4930 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
average dispersed phase velocity is given by
UD ) φ
d u(d)f(d)γd ∫d)0
(8)
φu(d)f(d)γd UD
(9)
max
then
g(d)γd )
It is apparent from eq 9 that the two drop size distributions, f(d) and g(d), are only equivalent when drop velocities are independent of drop size. Olney (1964), Rod and Misek (1971), and Pietzsch and Blass (1987) all comment on this distinction. The difference in the type of distribution has two implications. First, it is inappropriate to use one method to check the integrity of the other, unless the drop velocity distribution is known. Second, it should be possible to deduce the drop velocity profile within a dispersion by independently evaluating both distributions. Thus
u(d) )
UD g(d) φ f(d)
(10)
This velocity is that of the drops relative to stationary co-ordinates. The more usual rise velocity is quoted relative to the continuous phase; i.e.
ur(d) )
UC UD g(d) + φ f(d) 1 - φ
(11)
Such an approach provides a relatively simple means of measuring the drop velocity distribution within a dispersed phase medium. However, as a method it requires very careful experimental procedure as the errors in both the capillary and photographic techniques are cumulative. This approach is unsuitable if some drops move with a negative velocity relative to stationary co-ordinates, as the capillary probe cannot accurately record such drops. Jiricny and Prochazka (1980) argue that fine droplets can move backward as a result of entrainment by the continuous phase. However, this effect is proportional to the continuous phase flow rate. Throughout the present work, the continuous phase was maintained at a moderately low throughput (Uc ) 0.1 cm/s), so that the contribution of such fine droplets should be minimal. Sources of Error In order to use such a method, it must first be confirmed that the two methods produce comparable drop size distributions when there is no net velocity distribution. In the present instance, this objective was achieved by transferring the capillary and photographic equipment to a batch stirred tank containing two density-matched fluids (water and an n-decane-carbon tetrachloride mixture). Under these “velocity neutral” conditions, the two methods produced equivalent results for a broad range of drop sizes. Below a diameter of 0.6 mm the capillary probe was not capable of recording all drops; however, such small drop sizes contribute little to either the drop volume distribution or the Sauter mean diameter. Further, there was some evidence that the capillary technique was incapable of accurately measuring the largest drops in the distribution, leading to a trend toward this technique having a slightly smaller Sauter mean diameter at large average drop sizes. In spite of these differences, the Sauter mean diameters agreed to within (15%.
Having established that the two methods produce similar results when there is no velocity distribution, care must be taken that neither measurement process itself affects the drop velocity distribution when it is present. Thus, a light source projected through a plane of the column was used for the photographic technique to ensure that drops closest to the column wall, which might move with a different velocity from the bulk, were not preferentially recorded. Similarly, the suction velocity at the capillary mouth must be sufficiently low that there is no significant acceleration of drops toward the probe. In this work, a capillary mouth diameter of 5-7 mm was used, leading to an intake velocity of 1 cm/s or less. Given drop terminal velocities of 2.5-10 cm/s and experimental slip velocities of 1.5-8 cm/s, this intake velocity was sufficiently low as to substantially eliminate such flow disruption. The capillary method provides a localized measurement of drop size, whereas the photographic measurement covers a much larger area. If the drop velocity distribution is to be accurately determined, it is necessary to combine capillary measurements from a variety of local positions or, conversely, to select the capillary position such that it measures a drop population which is typical of the much larger area. In particular, the circulation pattern created by the rotor in each stage could result in a significant radial velocity profile, with drops being sucked into the rotor near the shaft and expelled near the column wall. To minimize the effects of these local velocity gradients and any accompanying variation in drop size, the capillary probe was maintained in a central radial position for all experiments (10-20 mm from the column wall). The probe was used at two vertical locations within a stage. In the first instance, the probe was located in the bottom section of the stage, immediately above a stator plate hole. In the second case, the probe was positioned in the top section of the stage, above the rotor. Ideally, capillary results taken from both these positions should also be combined in the analysis. However, little difference was found in dynamic drop size distributions between the top and bottom halves of a stage, so capillary results from both positions were used interchangeably. Laso (1986) suggested that a measured drop population of 300 drops is necessary to provide a reasonable degree of accuracy in the determination of the Sauter mean diameter (d32). In the present instance more than one parameter is sought, i.e., the function ur(d), so it would be prudent to count more than this number. Pacek et al. (1994), using a comparable video technique, found that if drop populations are in excess of 800 drops, then the volume density distributions virtually overlap. In this work, drop populations were a little smaller than this ideal, with an average of 777 drops. In order to gain accurate results, the local holdup at the point of measurement should be used in calculations. However, in the present work, these local holdup values differed little from the column average value. Hence in this work, column average holdup values, φ, as determined by the usual complete shut-off method were used. Comparison of Drop Size Distributions Average Sauter mean diameters as calculated by the two measurement techniques under a variety of conditions within the Ku¨hni column are compared in Figure 3.
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4931
distributions virtually overlap. Thus again, there is strong evidence for a velocity profile in the volume distributions at low holdup but much less evidence at high holdup.
Figure 3. Comparison of the Sauter mean diameters (d32) as measured by both photographic and capillary techniques (0.01 < φ < 0.15).
Figure 4. Comparison of drop volume densities at low holdup (run OCT1, QD ) 4.2 cm3/s, QC ) 4.1 cm3/s, N ) 80 rpm, φ ) 0.014, grade 1 MIBK).
Figure 5. Comparison of drop volume densities at high holdup (run DR9, QD ) 9.2 cm3/s, QC ) 4.1 cm3/s, N ) 160 rpm, φ ) 0.14, grade 2 MIBK).
As discussed above, the inability of the capillary probe to capture the largest drops in a distribution should result in a slight trend toward larger Sauter mean diameters in the photographic data if no velocity profile were present. However, results in the Ku¨hni column show a trend toward larger drop sizes in the capillary data. This is consistent with the larger drops moving faster and hence being recorded more often by the capillary probe. The trend away from identical drop sizes increases as the Sauter mean increases, that is, at lower dispersed phase holdup. This suggests a wide range of drop velocities at low holdup but less variation at high holdup. These trends are more apparent from graphs of the drop volume densities (Figures 4 and 5). At the lowest conditions of rotor speed and throughput (run OCT1, Figure 4) the two volume density curves are distinctly different, with the modal value for the photographic volume density 0.5-1 mm lower in magnitude. Conversely, at higher agitation levels and dispersed phase throughput (Run DR9, Figure 5) the volume density
Velocity Determination The next stage in this analysis is to deduce the actual velocity profiles through the use of eq 11. As discussed above, to achieve this objective with a high degree of accuracy requires drop populations larger than those available in the present work. Consequently only a limited data set was chosen for an assessment of the validity of this technique. These are as follows. (i) Only experimental series where both photographic and capillary drop size data were obtained simultaneously were analyzed. This eliminated variation in experimental conditions as a source of error but limited the analysis to nine pairs of volume distributions. (ii) Drops of size less than or equal to 0.65 mm were disregarded because of the problems with capillary probe accuracy described above. Drops of size greater than 3.05 mm were also disregarded since, while the drop volume contribution above this size limit can be large, the actual number of drops counted was very small and hence the drop volume distribution became quite variable. There are also some concerns with capillary probe accuracy at this end of the drop size distribution. (iii) The remaining drop sizes were divided into appropriate drop size intervals, thus averaging out some of the remaining variability in the distribution data. Hence, three drop diameter intervals each of width 0.8 mm were formed, with average diameters of 1.05, 1.85, and 2.65 mm. Equation 11 was then applied to each of the 27 data points. Results are presented in Table 1 and in Figure 6. While these results still exhibit some random variability due to the small size of the droplet populations, there is evidence that the drop velocity varies with both drop diameter, holdup, and dispersed phase throughput. At low holdup, there is a large variation of drop velocity with drop size. This is not unexpected as, under these conditions, the drops move fairly independently and their speed should be strongly correlated with the single drop terminal velocity. At higher holdup, the dependency of drop velocity upon drop size decays until it is independent of drop size. This convergence of drop velocities with increasing holdup was observed even when the capillary probe was positioned in the bottom half of a stage, directly above a hole in the stator plate (OCT series). This indicates that the exit frequency from the stage as well as the velocity within it is no longer dependent upon the drop size. Such a reduction in the dependence of droplet velocities upon drop diameter could be caused by a combination of four effects. (i) As the holdup increases, individual drops begin to associate with neighboring drops and this affects their net velocity. For example, Jayaweera et al. (1964) have shown experimentally with clusters of falling solid spheres that a small sphere will accelerate above its terminal velocity as it enters the wake of a larger one. Keh and Tseng (1992) use a combined analyticalnumerical method to examine such interactions. (ii) In the present work the impeller Reynolds number, ReIs ranged from 3430 to 6850, corresponding to an effectively constant value of the Power number of about 1.6, i.e., within the fully turbulent regime. Under such conditions, Tsouris et al. (1994) suggested that
4932 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 Table 1. Rise Velocities Calculated from Experimental Photographic and Capillary Probe Drop Size Distributions Using Eq 11 calculated rise velocity, ur(d) (cm/s) runa
MIBK flow rate,b QD (cm3/s)
OCT1 4.2 DR4 4.2 OCT2 4.2 DR5 6.6 DR7 4.2 OCT3 4.2 DR6 9.2 DR8 6.6 DR9 9.2 terminal velocity, ut(d)d
rotor speed, N (rpm)
estimated holdup,c φ
static sauter mean, d32 (mm)
slip velocity, Vs (cm/s)
d ) 1.05 mm
d ) 1.85 mm
d ) 2.65 mm
80 120 120 120 160 160 120 160 160
0.014 0.037 0.039 0.060 0.062 0.081 0.085 0.099 0.141
1.66 1.52 1.43 1.59 1.34 1.06 1.54 1.34 1.46
8.19 3.17 3.01 3.10 1.95 1.52 3.05 1.91 1.89
2.9 1.9 1.8 3.6 2.2 1.6 3.4 1.9 2.1 5.0
4.3 1.9 3.0 1.8 1.9 1.8 2.7 2.0 1.7 8.0
7.6 8.6 4.5 6.1 1.2 1.6 3.2 2.0 2.5 10.0
a OCT1-OCT3 used Grade 1 MIBK whereas DR4-DR9 used Grade 2 MIBK. b The continuous phase flow rate, Q ) 4.1 cm3/s, throughout C all experiments. c Holdup is calculated from correlations developed specifically for the system under study (Kentish, 1996). d Terminal velocities calculated from Grace et al. (1976) for contaminated systems.
Figure 6. Velocities calculated from eq 11: QD ) 4.2 cm3/s; QC ) 4.1 cm3/s.
drop movements through a column become a function of the number of circuits through the impeller that occur before escape, rather than being strongly linked to the buoyancy effects predicted by the terminal velocity. (iii) As the extent of agitation increases, this may also reduce the extent of internal circulation within a drop, as suggested by Misek (1963). In turn, this could result in oscillating droplet behavior being initiated at a smaller drop size. Such effects would result in a decline in the drop size dependence of the rise velocity. (iv) The law of conservation of momentum implies that droplets which undergo a breakage event will initially retain the velocity of the parent drop. There will be a finite time interval for deceleration to occur to the appropriate daughter drop velocity. Similarly two drops coalescing will initially move more slowly than appropriate for the new larger drop size. As the rates of such interaction events increase, so should the drop size dependency of the velocity parameter decrease. Comparison with Data of Other Workers In order to compare the present results with those obtained from single drop experiments, the corresponding slowing coefficient, Kv, was calculated from eq 3, using values of m derived from experimental slip velocity measurements. The magnitude of this slowing coefficient was consistent with the correlation of Fang et al. (1995) (see eq 2) at low rotor speeds. This indicates that, under conditions of low rotor speed and holdup, such single drop studies provide an accurate representation of drop behavior. However, as holdup and rotor speed increase, the present experimental database appears to show a mechanism shift from such divergent drop velocities to velocities which converge upon the system slip velocity.
These velocities thus become more dependent upon system properties such as rotor speed and holdup than upon individual drop charactersitics. A similar mechanism shift in an RDC is described by Laddha et al. (1978). Under these conditions, correlations such as eq 3 are inadequate, as they retain a constant dependency of drop velocity upon drop size. Hence, while drop velocities generally decrease with increasing holdup, they do not converge toward any value other than zero. Steiner and Hartland (1983), working with a spray column, and Mao and Slater (1994), working with an RDC, also found that single drop data cannot readily be applied to such swarm conditions. In the present case, equations are required which show an increasing dependence upon system parameters and less reliance upon drop terminal velocity. Thus, the work of Tsouris et al. (1994) includes the effect of turbulent flow structure through the impeller circulation frequency but does not explicitly consider holdup related effects. The equation presented by Weiss et al. (1995) predicts a drop velocity convergence with increasing rotor speed and in this respect is also consistent with the results presented above. Ultimately, the drop velocities measured in this work converge to the system slip velocity. Under conditions of high holdup, it is therefore most appropriate to utilize slip velocity correlations such as those of Gayler et al. (1953) and Bailes et al. (1986) to determine a single velocity for all drop sizes. Such a velocity represents the average velocity for each and every drop size. However, it must be noted that as the rotor speed and the continuuous phase flow rate increase beyond the range of the present experiments, backmixing effects will also become relevant. Such stochastic effects should not change the average velocity measured for each drop size, but they will increase the spread of values around this average. Conclusions While photographic measurement techniques determine the static drop size distribution within a dispersed phase, the capillary probe determines the dynamic drop size distribution. These distributions differ by the drop velocity profile. Given that both the static and dynamic drop size distributions have been measured, it is possible to deduce droplet velocities. Such calculations have been carried out on a very limited database of drop size distributions. The resulting drop velocities are consistent with the work of other authors at low holdup. However, contrary to much of this work, these velocities show a decreasing dependence upon drop size as holdup within the column increases. Under these conditions,
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4933
drop velocities need to be related to system properties such as rotor speed and holdup, rather than being considered as primarily related to single drop characteristics. Acknowledgment Assistance with the experiments presented in this work was provided by Todd Gallacher and Michael Dunn of the University of Melbourne and Stephan Isselhard of the Technischen Universita¨t Mu¨nchen, Munich, Germany. We would also like to acknowledge financial support from the Advanced Mineral Products Special Research Centre and the Australian Research Council. Nomenclature d ) droplet diameter, m d32 ) Sauter mean diameter, mm DI ) impeller diameter, m e ) fractional free area of stator plates f(d) ) static volume density of droplet size d, m-1 g(d) ) dynamic volume density of droplet size d, m-1 Kv ) slowing coefficient (eq 1) ni ) number of drops of size i Ni ) number of drop size classes N ) impeller speed, s-1 m ) empirical parameter defined in eq 3 QC ) continuous phase flow rate, m3/s QD ) dispersed phase flow rate, m3/s ReI ) impeller Reynolds number (FcNDI2/µc) Retube ) Reynolds number in a pipe or tube (Fdu/µ) u(d) ) mean drop velocity relative to stationary coordinates, m/s ur(d) ) mean drop rise velocity (relative to continuous phase), m/s us(d) ) single drop velocity, m/s ut(d) ) single drop terminal velocity in an unconfined space, m/s UC ) superficial velocity in the continuous phase, m/s UD ) superficial velocity in the dispersed phase, m/s Vs ) slip velocity, m/s γ ) parameter defining the slowing coefficient (see eq 2) µc ) continuous phase viscosity, kg/ms Fc ) continuous phase density, kg/m3 φ ) column average holdup
Literature Cited Bailes, P. J.; Gledhill, J.; Godfrey, G. C.; Slater M. J. Hydrodynamic Behaviour of Packed, Rotating Disc and KÅhni Liquid/ Liquid Extraction Columns. Chem. Eng. Res. Des. 1986, 64, 43. Bao, X.; Chen J. A Pseudo-Fluid Model for the Motion of Drop Swarms In Column Extractors. Proc. ISEC’93 1993, 1214. Barnea, E.; Mizrahi, J. A Generalised Approach to the Fluid Dynamics of Particulate SystemssPart 2: Sedmentation and Fluidisation of Clouds of Spherical Liquid Drops. Can. J. Chem. Eng. 1975, 53, 461. Fan, Z.; Oloidi, J. O.; Slater, M. J. Liquid-Liquid Extraction Column Design Data Acquisition from Short Columns. Chem. Eng. Res. Des. 1987, 65, 243. Fang, J.; Godfrey, J. C.; Mao, Z.-Q.; Slater, M. J.; Gourdon, C. Single Liquid Drop Breakage Probabilities and Characteristic Velocities in Ku¨hni Columns. Chem. Eng. Technol. 1995, 18, 41. Gayler, R.; Roberts, N. W.; Pratt, H. R. C. Liquid-Liquid Extraction: Part IV. A Further Study of Hold-up in Packed Columns. Trans. Inst. Chem. Eng. 1953, 31, 57. Gourdon, C.; Casamatta, G.; Angelino, H. Single Drop Experiments with Liquid Test Systems: A Way of Comparing Two Types of Mechanically Agitated Extraction Columns. Chem. Eng. J. 1991, 46, 137. Grace, J. R.; Wairegi, T.; Nguyen, T. H. Shapes and Velocities of Single Drops and Bubbles Moving Freely Through Immiscible Liquids. Trans. Inst. Chem. Engrs. 1976, 54, 167.
Haunold, C.; Cabassud, M.; Gourdon, C.; Casamatta, G. Drop Behaviour in a Ku¨hni Column for a Low Interfacial Tension System. Can. J. Chem. Eng. 1990, 68, 407. Isselhard, S. Drop Distribution in a Ku¨hni Liquid-Liquid Extraction Column. Diplomarbeit Thesis, University of Melbourne, Melbourne, Australia/Technischen Universita¨t Mu¨nchen, Munich, Germany, 1993. Jayaweera, K. O. L. F.; Mason, B. J.; Slack, G. W. The Behaviour of Clusters of Spheres Falling in a Viscous Fluid. J. Fluid Mech. 1964, 20, 121. Jiricny, V.; Prochazka, J. Measurement of Holdup Profiles and Particle Size Distributions in a Vibrating Plate Contactor, Chem. Eng. Sci. 1980, 35, 2237. Keh, H. J.; Tseng, Y. K. Slow Motion of Multiple Droplets In Arbitrary Three-Dimensional Configurations. AIChE J. 1992, 38, 1881. Kentish S. Forward Mixing in A Countercurrent Solvent Extraction Contactor. Ph.D. Thesis, University of Melbourne, Australia, 1996. Kumar, A.; Vohra, D. K.; Hartland, S. Sedimentation of Droplet Dispersions in Counter-current Spray Columns. Can. J. Chem. Eng. 1980, 58, 154. Laddha, G. S.; Degaleesan, T. E.; Kannappan, R. Hydrodynamics and Mass Transport in Rotary Disk Contactors. Can. J. Chem. Eng. 1978, 56, 137. Laso, M. A Model for the Dynamic Simulation of Liquid-Liquid Dispersions. Ph.D. Thesis, Diss. ETH No. 8041, Swiss Federal Institut of Technology, Zurich, Switzerland, 1986. Mao, Z-Q.; Slater, M. J. Aspects of Drop Behaviour In a Rotating Disc Contactor. Ind. Eng. Chem. Res. 1994, 33, 1780. Misek, T. Breakup of Drops by a Rotating Disc. Collect. Czech. Chem. Commun. 1963, 28, 426. Olney, R. B. Droplet Characteristics In A Countercurrent Contactor. AIChE J. 1964, 10, 827. Pacek, A. W.; Moore, I. T.; Nienow, A. W.; Calabrese, R. V. Video Technique for Measuring Dynamics of Liquid-Liquid Dispersion During Phase Inversion. AIChE J. 1994, 40, 1940. Pietzsch, W.; Blass, E. A New Method for The Prediction of Liquid Pulsed Sieve-tray Extractors. Chem. Eng. Technol. 1987, 10, 73. Pilhofer, T. Limiting Loads of Different Countercurrent Extraction Columns. Ger. Chem. Eng. 1979, 4, 200. Pilhofer, T.; Miller, H.-D. Photoelectric Method of Measuring Size Distribution of Moderately Dispersed Drops in an Immiscible Binary Liquid Mixture. Chem. Ing. Tech. 1972, 44, 295. Rod, V.; Misek, T. Residence Time Distribution of the Dispersed Phase in Agitated Extraction Columns. Proc. ISEC'71 1971, 738. Seikova, I.; Gourdon, C.; Casamatta, G. Single Drop Transport in a Ku¨hni Extraction Column. Chem. Eng. Sci. 1992, 47, 4141. Steiner, L.; Hartland, S. Hydrodynamics of Liquid-Liquid Spray Columns. Chapter 40 in Handbook of Fluids in Motion; Cheremisinoff, N. P., Gupta, R. Eds.; Butterworths/Ann Arbor Science Books: Stoneham, MA, 1960. Steiner, L.; Kumar, A.; Hartland, S. Application of Back- and Forward- Mixing Type Models in Simulation of Agitated LiquidLiquid Extraction Column Performance. World Congr. Chem. Eng. 1986, 739. Tsouris, C.; Kirou, V. I.; Tavlarides, L. L. Drop Size Distribution and Holdup Profiles in a Multistage Extraction Column. AIChE J. 1994, 40, 407. Weiss, J.; Steiner, L.; Hartland, S. Determination of Actual Drop Velocities in Agitated Extraction Columns. Chem. Eng. Sci. 1995, 50, 255. Weyrich, P. Development of a New Method to Determine the Drop Size Distribution in a Ku¨hni Liquid Extraction Column. Diplomarbeit Thesis, University of Melbourne, Melbourne, Australia/ Rheinisch-Westfa¨lische Technische Hochschule, Aachen, Germany, 1992.
Received for review April 10, 1997 Revised manuscript received July 25, 1997 Accepted July 26, 1997X IE9702690
X Abstract published in Advance ACS Abstracts, September 15, 1997.
