Homogenization of bingham flow in thin porous media

Abstract

By using dimension reduction and homogenization techniques, we study the steady ow of an incompresible viscoplastic Bingham uid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham uid on the small parameters describing the geometry of the thin porous medium under consideration. Three different problems are obtained in the limit when the small parameter tends to zero, following the ratio between the height of the porous medium and the relative dimension a of its periodically distributed pores. We conclude with the interpretation of these limit problems, which all preserve the nonlinear character of the flow.