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Homogenization of a two‐phase incompressible fluid in crossflow filtration through a porous medium
Author(s) -
El Jarroudi Mustapha,
ErRiani Mustapha
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4613
Subject(s) - homogenization (climate) , porous medium , compressibility , mechanics , no slip condition , capillary action , porosity , fluid dynamics , incompressible flow , materials science , mathematics , physics , boundary layer , boundary layer thickness , composite material , biodiversity , ecology , biology
We study the homogenization of a slow viscous two‐phase incompressible flow in a domain consisting of a free fluid domain, a porous medium, and the interface between them. We take into account the capillary forces on the fluid‐fluid interfaces. We construct boundary layers describing the flow at the interface between the free fluid and the porous medium. We derive a macroscopic model with a viscous two‐phase fluid in the free domain, a coupled Darcy law connecting two‐phase velocities in the porous medium, and boundary conditions at the permeable interface between the free fluid domain and the porous medium.