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

• Published in: Computer methods in applied mechanics and engineering Vol. 292; pp. 195 - 220
• Main Authors: Carraro, Thomas, Goll, Christian, Marciniak-Czochra, Anna, Mikelić, Andro
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2015; Elsevier
• Subjects: Analysis of PDEs; Boundary layers; Homogenization; Interface conditions; Mathematics; Pore scale simulation; Pressure slip law; Slip velocity; 35B27; 65Z05; Slip velocity; 76D10; 35Q35; Homogenization; 76S05; Pressure slip law; Pore scale simulation; Interface conditions; Boundary layers
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2014.10.050

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. •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.