On the Boundary Conditions at the Contact Interface between Two Porous Media

We consider an incompressible creeping flow through a 2D porous medium containing two different types of pores. The two parts are separated by the interface (0, L) × {0}. It is well-known that the effective flow in both parts is described by Darcy’s law, with different permeabilities. For the periodic porous medium we prove that at the interface, continuity of the effective pressure and the effective normal velocity hold true. The proof uses the boundary layers for the Stokes operator in a heterogeneous periodic porous medium.