Homogenization of a convection-diffusion equation in perforated domains with a weak adsorption

The aim of this paper is to study the asymptotic behavior of the solution of a convection-diffusion equation in perforated domains with oscillating velocity and a Robin boundary condition which describes the adsorption on the bord of the obstacles. Without any periodicity assumption, for a large range of perforated media and by mean of variational homogenization, we find the global behavior when the characteristic size E of the perforations tends to zero. The homogenized model, is a convection-diffusion equation but with an extra term coming from the weak adsorption boundary condition. An example is presented to illustrate the methodology.