Mass transfer coefficients drops

Values of the mass-transfer coefficient k have been obtained for single drops rising (or falling) through a continuous immiscible Hquid phase. Extensive Hterature data have been summarized (40,42). The mass-transfer coefficient is often expressed in dimensionless form as the Sherwood number ... 

The values of k and hence Sb depend on whether the phase under consideration is the continuous phase, c, surrounding the drop, or the dispersed phase, d, comprising the drop. The notations and Sh are used for the respective mass-transfer coefficients and Sherwood numbers. 

Although the adsorption of surfactants tends to reduce mass-transfer coefficients by suppressing drop circulation, a sharp increase in mass transfer... 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

A well-substantiated correlation for air-water systems taken from the trickle bed literature (Morsi and Charpentier, 1981) was used for the volumetric mass transfer coefficients in the / , and (Rewap)i terms in the model. The hi term was taken from a correlation of Kirillov et al. (1983), while the liquid hold-up term a, in Eqs. (70), (71), (74), (77), and (79) were estimated from a hold-up model of Specchia and Baldi (1977). All of these correlations require the pressure drop per unit bed length. The correlation of Rao and Drinkenburg (1985) was employed for this purpose. Liquid static hold-up was assumed invariate and a literature value was used. Gas hold-up was obtained by difference using the bed porosity. 

Assuming plug flow of both phases in the trickle bed, a volumetric mass transfer coefficient, kL a, was calculated from the measurements. The same plug flow model was then used to estimate bed depth necessary for 95% S02 removal from the simulated stack gas. Conversion to sulfuric acid was handled in the same way, by calculating an apparent first-order rate constant and then estimating conversion to acid at the bed depth needed for 95% S02 removal. Pressure drop was predicted for this bed depth by multiplying... 

The intensity of mass transfer shown by the mass transfer coefficient depends on the flow processes inside the drop or in its surroundings and, thereby, on the various life stages of the drops. During the drop formation, new interfaces and high concentration gradients are produced near the interface. The contact times between liquid elements of the drop and the surroundings that are near the surface are then extremely short. According to Pick s second law for unsteady diffusion, it follows that for the phase mass transfer coefficient [19] ... 

For the mass transfer coefficient on the outside of the drop kc, Eq. (9.34), according to the penetration theory by Highbie [19], obtains the contact time t as the quotient between the rising distance between two stages and the rising velocity. 

Interfacial tension is the parameter in equations influencing the drop size, as discussed in preceding sections. The smaller the value of a, the smaller are the resulting drops, if all the other conditions are the same, and the larger is the transfer area per unit volume. On the other hand, small drops may show little or no internal circulation, which implies equivalent consequences for the mass transfer coefficient and a lower rising velocity and, accordingly, a lower flow rate at the flooding point. 

Considerable interest has been generated in turbulence promoters for both RO and UF. Equations 4 and 5 show considerable improvements in the mass-transfer coefficient when operating UF in turbulent flow. Of course the penalty in pressure drop incurred in a turbulent flow system is much higher than in laminar flow. Another way to increase the mass-transfer is by introducing turbulence promoters in laminar flow. This procedure is practiced extensively in enhanced heat-exchanger design and is now exploited in membrane hardware design. 

The area between phases A is the surface area of the drops. It will clearly be a strong function of the stirring characteristics (we assume that stirring is always fast enough to mix both phases). The presence of surfactants, drop size distributions, stirrer design, and circulation patterns. Interfacial area is frequently an unknown in emulsion reactors, but the above formulation should be applicable. Another complication in emulsion reactors is the fact that mass transfer coefficients depend strongly on drop size and stirring rate. The relevant parameter in an emulsion reactor is A km wilh neither factor known very well. 

Mass transfer rates from drops are obtained by measuring the concentration change in either or both of the phases after passage of one or more drops through a reservoir of the continuous phase. This method yields the average transfer rate over the time of drop rise or fall, but not instantaneous values. For measurements of the resistance external to the drop this is no drawback, because this resistance is nearly constant, but the resistance within the drop frequently varies with time. The fractional approach to equilibrium, F, is calculated from the compositions and is then related to the product of the overall mass transfer coefficient and the surface area ... 

Many investigators base mass transfer coefficients upon the area of the volume-equivalent sphere, especially for oscillating drops ... 

The second section presents a review of studies concerning counter-currently and co-currently down-flow conditions in fixed bed gas-liquid-solid reactors operating at elevated pressures. The various consequences induced by the presence of elevated pressures are detailed for Trickle Bed Reactors (TBR). Hydrodynamic parameters including flow regimes, two-phase pressure drop and liquid hold-up are examined. The scarce mass transfer data such gas-liquid interfacial area, liquid-side and gas-side mass transfer coefficients are reported. 

It will be assumed that the reaction A + B takes place only in the dispersed phase, the reactant A is assumed to be insoluble in the continuous phase, but the reactant B will diffuse into the drops. Further it is assumed that inside the drops there is no mixing but only pure molecular diffusion. The diffusivity of B in the dispersed phase is 33b while the mass transfer coefficient outside the drops is m. The partition coefficient of B is Hb and equals the ratio of the concentration of B in the dispersed phase at the interface over the concentration of B in the continuous phase at the interface. 

As shown in Section II,B,1, zero-order drop conversion will occur when the drop conversion rate is limited by a relatively low outside mass transfer coefficient. It was derived that then... 

The mass transfer coefficient kL of oxygen transfer in fermenters is a function of Sauter mean diameter D32, diffusivity DAB, and density p, viscosity pc of continuous phase (liquid phase). Sauter-mean diameter D32 can be calculated from measured drop-size distribution from the following relationship,... 

When two phases are mixed together (gas-liquid, immiscible liquid-liquid), a fine dispersion of bubbles or drops and a high specific interfacial area are produced because of the intensive turbulence and shear. For this reason, resistance to interphase mass transfer is considerably smaller than in conventional equipment. In addition, a wide range of gas-liquid flow ratios can be handled, whereas in stirred tanks the gas-flow rate is often limited by the onset of flooding. Mass transfer coefficients (kLa) can be 10-100 times higher than in a stirred tank. 

The CFD simulations should be linked with the rate-based process simulator, providing important information on the process hydrodynamics in the form of correlations for mass transfer coefficients, specific contact area, liquid holdup, residence time distribution, and pressure drop. An ability to obtain these correlation via the purely theoretical way rather than by the traditional experimental one should be considered a significant advantage, because this brings a principal opportunity to virtually prototyping of new optimized internals for reactive separations. 

Slater M. A combined model of mass transfer coefficient for contaminated drop liquid- liquid systems. Can J Chem Eng 1995 73 462 4-69. 

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