Micropolar effects in the coupling of a thin film past a porous medium

Article type: Research Article

Authors: Bayada, G.^; | Chambat, M. | Gamouana, S.R.^;

Affiliations: UMR 5585‐5514, Insa de Lyon, Math., Bât. Léonard de Vinci, 69621 Villeurbanne cedex, France | CNRS UMR 5585, Université Lyon 1, Math., Bât 101, 69622 Villeurbanne cedex, France

Note: [] Corresponding author. E‐mail: Guy.Bayada@insa‐lyon.fr.

Abstract: We study the coupling of a porous medium and an adjacent thin film flow, taking account of non‐Newtonian effects induced by additives in the fluid. The starting point is the micropolar Stokes system. A critical relation between η, the thin gap height size and ε, the characteristic size of the pores in the porous medium is exhibited. Asymptotic equations are obtained including the continuity of the pressure at the interface. The influence of the rheological micropolar parameters is discussed and various asymptotic behaviours are identified: the micropolar effects are found to be significant in both media, or only in the porous medium, or can be neglected everywhere.

Journal: Asymptotic Analysis, vol. 30, no. 3-4, pp. 187-216, 2002