Abstract
AbstractWe consider the flow of a generalized Newtonian fluid through a thin porous medium of thickness , perforated by periodically distributed solid cylinders of size . We assume that the fluid is described by the 3D incompressible Stokes system, with a non‐linear viscosity following the Carreau law of flow index , and scaled by a factor , where . Generalizing (Anguiano M.: et al. Q. J. Mech. Math., 75(1), 1–27 (2022)), where the particular case and was addressed, we perform a new and complete study on the asymptotic behavior of the fluid as goes to zero. Depending on and the flow index , using homogenization techniques, we derive and rigorously justify different effective linear and non‐linear lower‐dimensional Darcy's laws. Finally, using a finite element method, we study numerically the influence of the rheological parameters of the fluid and of the shape of the solid obstacles on the behavior of the effective systems.
Published Version
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