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

  • María Anguiano
  • Francisco Javier Suárez-GrauEmail author
Article

Abstract

In this paper, we consider a non-Newtonian flow in a thin porous medium \(\Omega _{\varepsilon }\) of thickness \(\varepsilon \) which is perforated by periodically solid cylinders of size \(a_{\varepsilon }\). 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 \(1<p<+\infty \). We consider the limit when domain thickness tends to zero, and we obtain different models depending on the magnitude \(a_{\varepsilon }\) with respect to \(\varepsilon \).

Keywords

Non-Newtonian flow Stokes equation Darcy’s law Porous medium Thin fluid films 

Mathematics Subject Classification

76A05 76A20 76M50 35B27 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • María Anguiano
    • 1
  • Francisco Javier Suárez-Grau
    • 2
    Email author
  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de MatemáticasUniversidad de SevillaSevillaSpain

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