Abstract
The flow of a viscous fluid over a thin, deformable porous layer fixed to the solid wall of a channel is considered. The coupled equations for the fluid velocity and the infinitesimal deformation of the solid matrix within the porous layer are developed using binary mixture theory, Darcy's law and the assumption of linear elasticity. The case of pure shear is solved analytically for the displacement of the solid matrix, the fluid velocity both in the porous medium and the fluid above it. For a thin porous layer the boundary condition for the fluid velocity at the fluid-matrix interface is derived. This condition replaces the usual no slip condition and can be applied without solving for the flow in the porous layer.
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Barry, S.I., Parkerf, K.H. & Aldis, G.K. Fluid flow over a thin deformable porous layer. Z. angew. Math. Phys. 42, 633–648 (1991). https://doi.org/10.1007/BF00944763
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DOI: https://doi.org/10.1007/BF00944763