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Journal Articles Mediterranean Journal of Mathematics Year : 2021

Lower-dimensional nonlinear Brinkman's law for non-Newtonian flows in a thin porous medium

Abstract

In this paper we study the stationary incompressible power law fluid flow in a thin porous medium. The media under consideration is a bounded perforated 3D domain confined between two parallel plates, where the distance between the plates is very small. The perforation consists in an array solid cylinders, which connect the plates in perpendicular direction, distributed periodically with diameters of small size compared to the period. For a specific choice of the thickness of the domain, we found that the homogenization of the power law Stokes system results a lower-dimensional nonlinear Brinkman type law.
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Dates and versions

hal-02902211 , version 1 (18-07-2020)
hal-02902211 , version 2 (19-01-2024)

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María Anguiano, Francisco J. Suárez-Grau. Lower-dimensional nonlinear Brinkman's law for non-Newtonian flows in a thin porous medium. Mediterranean Journal of Mathematics, 2021, 18 (175), ⟨10.1007/s00009-021-01814-5⟩. ⟨hal-02902211v2⟩

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