Effective interface conditions for the forced infiltration of a viscous   fluid into a porous medium using homogenization
  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. 
Thomas Carraro, Christian Goll, Anna Marciniak-Czochra and Andro   Mikeli\'c
math.AP