Kinetics Regimes for Two-Film Model

We treat each of these three cases in turn to obtain, as far as possible, analytical or approximate analytical rate expressions, taking both mass transfer and reaction into account. Each of these cases gives rise to important subcases, some of which are developed further, and some of which are left to problems at the end of the chapter. In treating the cases in the order above, we are proceeding from special, relatively simple, situations to more general ones, the reverse of the approach taken in Section 9.1 for gas-solid systems. 

It is necessary to distinguish among three rate quantities. We use the symbol NA to represent the flux of A, in mol m-2 s-1, through gas and/or liquid film if reaction takes place in the liquid film, NA includes the effect of reaction (loss of A). We use the symbol (—rA), in mol m-2 s 1, to represent the intensive rate of reaction per unit interfacial area. Dimensionally, (—rA) corresponds to NA, but (— rA) and NA are equal only in the two special cases (1) and (2) above. In case (3), they are not equal, because reaction occurs in the bulk liquid (in which there is no flux) as well as in the liquid film. In this case, furthermore, we need to distinguish between the flux of A into the liquid film at the gas-liquid interface, NA(z = 0), and the flux from the liquid film to the bulk liquid, Na(z = 1), where z is the relative distance into the film from the interface these two fluxes differ because of the loss of A by reaction in the liquid film. The third rate quantity is ( rA)int in mol irT3 s-1, the intrinsic rate of reaction per unit volume of liquid in the bulk liquid. ( rA) and (- rA)int are related as shown in equation 9.2-17 below. 

2 Reaction in Bulk Liquid Only Relatively Slow Reaction 

If chemical reaction occurs only in the bulk liquid, but resistance to mass transfer of A through gas and liquid films is not negligible, the concentration profiles could be as 

We assume that the reaction is intrinsically second-order (first-order with respect to each reactant), so that 

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