Mathematical models for mass transfer accompanied by reversible chemical reaction

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Abstract

Based on the film-penetration theory, the film theory, and the surface renewal theory, theoretical equations are obtained for the rate of interphase mass transfer accompanied by a first-order reversible reaction. The film-penetration theory is again found to be the more general concept and the other two theories are merely the limiting cases of the film-penetration theory. The rate equation based on the film-penetration theory can also be reduced to those obtained by other investigators on the basis of simpler postulations.

Contrary to the previous findings in other chemical mass transfer systems, it is found that the predicted effects of chemical reaction on the overall mass transfer rate are indeed sensitive to the theory or the model adopted in postulating the mechanism. One exception to this is when the diffusivities of the reactant and the product are nearly equal. For this special case, the three theories predict practically the same effects of a reversible reaction.

An approximate rate equation is proposed for mass transfer with a high order reversible reaction. When the forward reaction is very rapid, the reaction rate constants become insignificant variables and the mass transfer rate is a simple function of the diffusivity ratio, the concentration ratio, and the order of reaction.

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