On the perturbation solution of interface-reaction controlled diffusion in solids

Insertion of species A into species B forms a product P through two kinetic processes, namely, （1） the chemical reaction between A and B that occurs at the B-P interface, and （2） the diffusion of species A in product P. These two processes are symbiotic in that the chemical reaction provides the driving force for the diffusion, while the diffusion sustains the chemical reaction by providing sufficient reactant to the reactive interface. In this paper, a math- ematical framework is developed for the coupled reaction- diffusion processes. The resulting system of boundary and initial value problem is solved analytically for the case of interface-reaction controlled diffusion, i.e., the rate of diffu- sion is much faster than the rate of chemical reaction at the interface so that the final kinetics are limited by the interface chemical reaction. Asymptotic expressions are given for the velocity of the reactive interface and the concentration of diffusing species under two different boundary conditions.