Interfacial boundary conditions between a free domain and thin porous layers for non-Newtonian fluid flows

Abstract

A non-Newtonian fluid flows in a free domain and in a periodically perforated thin layer which are connected through a permeable interface. Two scales are present in the porous layer: one associated to the periodicity of the distribution of the channels which is associated to the thinness of the layer and the other to the diameter of these channels. Using Γ-convergence and two-scale convergence methods, we derive boundary conditions of Beavers–Joseph–Saffman type on the permeable interface between the free domain and the thin layer.