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arXiv · 1401.6278

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

Thomas Carraro·Christian Goll·Anna Marciniak-Czochra·Andro Mikelić
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Abstract

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.

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Thomas Carraro, Christian Goll, Anna Marciniak-Czochra, Andro Mikelić. 2014-01-24. Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization. https://doi.org/10.1016/j.cma.2014.10.050

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