Describing diffusion, reaction and convection on porous medium

TL;DR

This paper develops a mathematical model for electrochemical deposition in porous media, capturing diffusion, reaction, and convection processes to better understand inverse opal production.

Contribution

It introduces a simplified yet realistic boundary condition model for transport equations, extending previous approaches by incorporating a moving boundary akin to Stefan problems.

Findings

Model effectively describes ion transport in porous structures

Provides analytical solutions for electrochemical deposition processes

Enhances understanding of boundary conditions in porous media

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].