Interfaeial mass-transfer rates

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

This form is partieularly appropriate when the gas is of low solubility in the liquid and "liquid film resistanee" eontrols the rate of transfer. More eomplex forms whieh use an overall mass transfer eoeffieient whieh ineludes the effeets of gas film resistanee must be used otherwise. Also, if ehemieal reaetions are involved, they are not rate limiting. The approaeh given here, however, illustrates the required ealeulation steps. The nature of the mixing or agitation primarily affeets the interfaeial area per unit volume, a. The liquid phase mass transfer eoeffieient, kL, is primarily a funetion of the physieal properties of the fluid. The interfaeial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dj, whieh is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraetion of the total fluid volume (gas plus liquid) whieh is oeeupied by gas bubbles. 

The rate of mass transfer is a funetion, among other variables, of the drop size distribution or interfaeial area between the phases. The drop size is governed by the surface tension, and densities of the two phases and the type of agitation and design of the eontaetor. Up to a point, the smaller the drop, the greater the rate of mass transfer. 

Step 1 [Eq. (18)] describes the competitive extraction reaction of reactant and product anions between the aqueous and organic phases in the presence of a catalyst cation. The rate constants and k i include the effects of mass transfer across the interfaeial region and depend on the change in the interfacial area, i.e., on the agitation rate. Step 2 [Eq. (19)] describes an irreversible displaeement reaction in the organic phase to produee the product RX and the produet ion pair (Q Y )oj.g, which subsequently exchanges with (Q X )aq by repeating Step 1. It should be emphasized that Step 2 need not be irreversible, the kineties of the reaetion will be more complicated, and the extent of reaction will decrease. If Step 2 is irreversible, the rate equation can be expressed as... 

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