Homogenisation of local colloid evolution induced by reaction and diffusion

TL;DR

This paper develops a homogenisation approach for a non-linear reaction-diffusion process in porous media with evolving microstructure, capturing the coupled effects of reactions and structural changes.

Contribution

It introduces a two-scale-transformation method to homogenise a highly non-linear, coupled reaction-diffusion and microstructure evolution problem.

Findings

Derivation of a homogenised reaction-diffusion equation with an internal variable

Effective modelling of pore structure evolution in porous media

Application of the method to complex non-linear microstructure dynamics

Abstract

We consider the homogenisation of a coupled reaction-diffusion process in a porous medium with evolving microstructure. A concentration-dependent reaction rate at the interface of the pores with the solid matrix induces a concentration-dependent evolution of the domain. Hence, the evolution is fully coupled with the reaction-diffusion process. In order to pass to the homogenisation limit, we employ the two-scale-transformation method. Thus, we homogenise a highly non-linear problem in a periodic and in time cylindrical domain instead. The homogenisation result is a reaction-diffusion equation, which is coupled with an internal variable, representing the local evolution of the pore structure.