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