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

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 ΓΓ-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.