Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization

• A forced infiltration of a viscous fluid into a rigid porous medium.
• Novelty: Effective interface conditions are a pressure slip and a velocity jump.
• A long standing problem. Contradictory conditions in the literature.
• Rigorous multiscale tools: interface boundary layers, error estimates.
• Confirmation of the theoretical results using direct pore scale simulation.

It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers–Joseph slip law. To the contrary, in the case of a forced infiltration of a viscous fluid into a porous medium the interface law has been a subject of controversy. In this paper, we prove rigorously that the effective interface conditions are: (i) the continuity of the normal effective velocities; (ii) zero Darcy’s pressure and (iii) a given slip velocity. The effective tangential slip velocity is calculated from the boundary layer and depends only on the pore geometry. In the next order of approximation, we derive a pressure slip law. An independent confirmation of the analytical results using direct numerical simulation of the flow at the microscopic level is given, as well.