Describing diffusion, reaction and convection on porous medium

Abstract

In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic medium diffuses until they react to the electrode surface and become part thereof. Our model consists in formulating convenient boundary conditions for the transport equation, that somewhat resembles the real system but is nevertheless simple enough to be solved, and then solve it. Similar approach was taken by Nicholson [1, 2], except that, to avoid the difficulties regarding the boundary conditions, he considered none whatsoever, and proposed a modified diffusion coefficient for the porous medium instead. Apropos, our model, with moving boundary condition pertain to the class of problems know as The Stefan problem [3].