Homogenization of an incompressible non-Newtonian flow through a thin porous medium

Abstract

In this paper, we consider a non-Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically solid cylinders of size aε. The flow is described by the 3D incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index 1 < p < +∞. We consider the limit when domain thickness tends to zero and we obtain different models depending on the magnitude aε with respect to ε.