Diffusion through a composite structure with a high contrasting diffusivity
Ali Sili · Asymptotic Analysis · 2014
We consider the stationary diffusion equation in a periodic composite medium made of two components M ε and B ε having very different diffusivity, the ratio between the coefficients of the diffusion in that structure being 1/α ε 2 , where ε is the size of the period and α ε which represents the amplitude of the diffusion in the inclusions B ε is a decreasing sequence towards zero. We show that the inclusions B ε work on the macroscopic diffusion as holes. In particular for scalings 0<α ε �ε corresponding to very weak diffusion in B ε , the volume fraction of the material at the limit is the well known one in the case of holes.