Homogenisation of local colloid evolution induced by reaction and diffusion
Analysis of PDEs
2022-06-01 v1
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.
Cite
@article{arxiv.2205.15845,
title = {Homogenisation of local colloid evolution induced by reaction and diffusion},
author = {David Wiedemann and Malte A. Peter},
journal= {arXiv preprint arXiv:2205.15845},
year = {2022}
}