Homogenizing a critical binary structure of finite diffusivities

Abstract

We study the homogenization of a diffusion process which takes place in a binary structure formed by an ambient connected phase surrounding a suspension of very small spheres distributed in an ε-periodic network. We consider the critical radius case with finite diffusivities in both phases. The asymptotic distribution of the concentration is determined, as ε→0, assuming that the suspension has mass of unity order and vanishing volume. It appears that the ambient macroscopic concentration is satisfying a Volterra integro-differential equation and it is defining straightly the macroscopic concentration associated to the suspension.