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Boundary conditions at a planar fluid–porous interface for a Poiseuille flow |
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| Affiliation: | 1. Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD, UK;2. Department of Engineering Science, University of Oxford, Oxford, OX2 0ES, UK;3. Karlsruhe Institute of Technology, Institute for Technical Physics, Campus North, Karlsruhe 76344, Germany;4. Mechanical Engineering Department, University of Idaho, Idaho Falls, Idaho, 83401, USA;5. Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, Arizona, 85721, USA |
| Abstract: | The velocity boundary condition that must be imposed at an interface between a porous medium and a free fluid is investigated. A heterogeneous transition zone characterized by rapidly varying properties is introduced between the two homogeneous porous and free fluid regions. The problem is solved using the method of matched asymptotic expansions and boundary conditions between the two homogeneous regions are obtained. The continuity of the velocity is recovered and a jump in the stress built using the viscosity (and not the effective viscosity) appears. This result also provides an explicit dependence of the stress jump coefficient to the internal structure of the transition zone and its sensitivity to this microstructure is recovered. |
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