Dispersed drops

However, in a countercurrent column contactor as sketched in Figure 8, the holdup of the dispersed phase is considerably less than this, because the dispersed drops travel quite fast through the continuous phase and therefore have a relatively short residence time in the equipment. The holdup is related to the superficial velocities U of each phase, defined as the flow rate per unit cross section of the contactor, and to a sHp velocity U (71,72) ... 

When an impeller is rotated in an agitated tank containing two immiscible Hquids, two processes take place. One consists of breakup of dispersed drops due to shearing near the impeller, and the other is coalescence of drops as they move to low shear zones. The drop size distribution (DSD) is decided when the two competing processes are in balance. During the transition, the DSD curve shifts to the left with time, as shown in Figure 18. Time required to reach the equiHbrium DSD depends on system properties and can sometimes be longer than the process time. 

Storage are the fresh and 75 h aged Pd ly TWCs (Cl and C2), and it is likely that rare earth oxides do contribute to oxygen up es in those catalysts. Interestingly, the C1 and C2 catalysts are the only pair which show a correlation between oxygen uptake and noble metal dispersion (i-e. the oxygen titrated by the first CO pulse drops from 35.5 to 27.2 /i-mol O/g-cat. as the dispersion drops from 10.8% (Cl) to 3.5% (C2)). 

Several factors contribute to the dual nature of silicone defoamers. For example, soluble silicones can concentrate at the air-oil interface to stabilize bubbles, while dispersed drops of silicone can accelerate the coalescence process by rapidly spreading at the gas-liquid interface of a bubble, causing film thinning by surface transport [1163]. 

Silicones exhibit an apparently low solubility in different oils. In fact, there is actually a slow rate of dissolution that depends on the viscosity of the oil and the concentration of the dispersed drops. The mechanisms of the critical bubble size and the reason a significantly faster coalescence occurs at a lower concentration of silicone can be explained in terms of the higher interfacial mobility, as can be measured by the bubble rise velocities. 

Mist flow, one component In a one-component system with finely dispersed drops in the mist flow, the mass transfer between phases over a large interfacial area has to be considered. For the compression wave the frozen state can be assumed to be subcooled liquid, superheated vapor conditions generated by the wave are fairly stable, and the expressions for the two-component system are valid (Henry, 1971) ... 

Unal, C K. Tuza, A. F. Cokmez-Tuzla, and J. C. Chen, 1991a, Vapor Generation Rate Model for Dispersed Drop Flow, Nuclear Eng. Design 725/161 -173. (4)... 

In order to prevent coalescence of the dispersed drops, van Duck(36) and others have devised methods of providing the whole of the continuous phase with a pulsed motion. This may be done, either by some mechanical device, or by the introduction of compressed air. 

Coulson, J. M. and Skinner, S. J. Chem. Eng. Sci. 1 (1952) 197. The mechanism of liquid-liquid extraction across stationary and moving interfaces. Part 1. Mass transfer into single dispersed drops. 

Suppose that a chemical reaction takes place in a dispersed system between the two reactants A and B, where A is dissolved in the dispersed phase and B in the continuous phase. Suppose further that at a certain place in the reactor the concentration of B is equal to b, while the dispersed drops at this place have different concentrations a of the reactant A caused by segregation. When the chemical conversion for each isolated drop can be described as being of the nth order in the reactant A, then the amount reacting per second in each drop of volume v equals2... 

In this chapter some effects of segregation on the kinetics of a chemical reaction between two liquid phases carried out in a continuous stirred tank reactor (CSTR) will be discussed. In the derivations of these effects it will be assumed that during the reaction the dispersed phase is maintained (e.g., in the case of extraction combined with chemical reaction) and that all dispersed drops have the same size. This means that when there is segregation it is only the age distribution which causes a concentration distribution in the dispersed phase. 

When both reactions are of the same order (rti = nf) the ratio of the amounts of C and W produced is independent of the time in each dispersed drop and equal to the ratio of the reaction constants. Hence, after integration over all drops, this same ratio is found and the selectivity, therefore, is equal to... 

Generally one must expect that in practice neither of these extreme cases will hold and that there is a finite interaction rate or partial segregation. This means that dispersed drops may have a certain period during which they keep their own identity, but after a shorter or longer time (which generally is spread statistically) they will coalesce with a neighboring drop, or with another part of the dispersed phase. After exchange of concentrations, new drops will be produced. 

Also, when the wall of the stirring vessel is preferently wetted by the dispersed phase, the wall may be covered with a thin stagnant layer of dispersed phase, which may act, more or less, as a dead corner in so far as the chemical reaction is slowed down by poor mass transfer. However, there still may occur a continuous coalescing of dispersed drops with these stagnant layers and corners, while on the other hand these dead corners will continuously lose new drops, which are taken up again in the living dispersed phase. In this way the dead corners act as a medium of interaction. 

As iB well known, in baffled, stirred tank reactors there is a strong circulation pattern, as shown in Fig. 22. The dispersed drops will move with this... 

Although this theory certainly explains many of the above-mentioned phenomena it does not account for the observed difference in coalescing rate when the dispersed drops are of an aqueous or of an organic phase, respectively (see Section IV,B). 

The most important emulsions are water-in-oil emulsions (W/O emulsions) and oil-inwater emulsions (O/W emulsions). Oil designates here any liquid not soluble in water. In an oil-in-water emulsion, water forms the continuous phase with dispersed drops of oil (Fig. 12.9). Milk is one example. In case oil is in the continuous phase, we have a water-in-oil emulsion. Introductions into emulsions are Refs. [4,538,540],... 

In these systems, the interface between two phases is located at the high-throughput membrane porous matrix level. Physicochemical, structural and geometrical properties of porous meso- and microporous membranes are exploited to facilitate mass transfer between two contacting immiscible phases, e.g., gas-liquid, vapor-liquid, liquid-liquid, liquid-supercritical fluid, etc., without dispersing one phase in the other (except for membrane emulsification, where two phases are contacted and then dispersed drop by drop one into another under precise controlled conditions). Separation depends primarily on phase equilibrium. Membrane-based absorbers and strippers, extractors and back extractors, supported gas membrane-based processes and osmotic distillation are examples of such processes that have already been in some cases commercialized. Membrane distillation, membrane... 

The range of volume fraction within which either of two immiscible liquids may be continuous is primarily a function of the viscosity ratio, but is only weakly dependent upon vessel characteristics or stirring speed. The coalescence frequency for the dispersed drops is, however, a strong function of impeller speed (i.e., frequency xN2,85). 

N, Number of theoretical stages Dimensionless Dimensionless dispersed drop ... 

The tension that exists between two liquid phases is called the interfacial tension. It is a measure of the energy or work required to increase the surface area of the liquid-liquid interface, and it affects the size of dispersed drops. Its value, in units of force per unit length or energy per unit area, reflects the compatibility of the two liquids. Systems that have low compatibility (low mutual solubility) exhibit high interfacial tension. Such a system tends to form relatively large dispersed drops and low interfacial area to minimize contact between the phases. Systems that are more compatible (with higher mutual solubility) exhibit lower interfacial tension and more easily form small dispersed droplets. 

Numerous studies have shown that mass transfer of solute from one phase to the other can alter the behavior of a liquid-liquid dispersion—because of interfacial tension gradients that form along the surface of a dispersed drop. For example, see Sawistowski and Goltz, Trans. Inst. Chem. Engrs., 41, p. 174 (1963) BaWcer, van Buytenen, and Beek, Chem Eng. Sci., 21(11), pp. 1039-1046 (1966) Rucken-stein and Berbente, Chem. Eng. Sci., 25(3), pp. 475—482 (1970) Lode and Heideger, Chem. Eng. Sci., 25(6), pp. 1081—1090 (1970) and Takeuchi and Numata, Int. Chem. Eng., 17(3), p. 468 (1977). These interfacial tension gradients can induce interfaci turbulence and circulation within drops. These effects, known as Marangoni instabilities, have been shown to enhance mass-transfer rates in certain cases. 

The mass-transfer coefficient in each film is expected to depend upon molecular diffusivity, and this behavior often is represented by a power-law function k . For two-film theory, n = 1 as discussed above [(Eq. (15-62)]. Subsequent theories introduced by Higbie [Trans. AIChE, 31, p. 365 (1935)] and by Dankwerts [Ind. Eng. Chem., 43, pp. 1460-1467 (1951)] allow for surface renewal or penetration of the stagnant film. These theories indicate a 0.5 power-law relationship. Numerous models have been developed since then where 0.5 < n < 1.0 the results depend upon such things as whether the dispersed drop is treated as a rigid sphere, as a sphere with internal circulation, or as oscillating drops. These theories are discussed by Skelland [ Tnterphase Mass Transfer, Chap. 2 in Science and Practice of Liquid-Liquid Extraction, vol. 1, Thornton, ed. (Oxford, 1992)]. 

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