Homogenization of Bingham flow in thin porous media

María Anguiano (1) , Renata Bunoiu (2)

1 Universidad de Sevilla = University of Seville
2 IECL - Institut Élie Cartan de Lorraine

By using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham fluid 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 ε tends to zero, following the ratio between the height ε of the porous medium and the relative dimension aε of its periodically distributed pores. We conclude with the interpretation of these limit problems, which all preserve the nonlinear character of the flow.

Keywords: thin domain; porous medium; Bingham fluid

Domains: Analysis of PDEs [math.AP]; Functional Analysis [math.FA]

María Anguiano, Renata Bunoiu. Homogenization of Bingham flow in thin porous media. 2019. ⟨hal-02059914v1⟩