Paper
Modeling of a non-Newtonian thin film passing a thin porous medium
Authors
María Anguiano, Francisco J. Suárez-Grau
Abstract
This theoretical study deals with asymptotic behavior of a coupling between a thin film of fluid and an adjacent thin porous medium. We assume that the size of the microstructure of the porous medium is given by a small parameter , the thickness of the thin porous medium is defined by a parameter , and the thickness of the thin film is defined by a small parameter , where and are devoted to tend to zero when . In this paper, we consider the case of a non-Newtonian fluid governed by the incompressible Stokes equations with power law viscosity of flow index , and we prove that there exists a critical regime, which depends on , between , and . More precisely, in this critical regime given by , we prove that the effective flow when is described by a 1D Darcy law coupled with a 1D Reynolds law.