On a wide class of nonlinear models for non-Newtonian fluids with mixed boundary conditions in thin domains

Article type: Research Article

Authors: Sac-Épée, J.-M. | Taous, K.

Affiliations: Laboratoire de Mathématiques, l'Université de Metz, Ile du Saulcy, 57045 Metz cedex 01, France E-mails: {jmse; taous}@poncelet.univ-metz.fr

Abstract: The behaviour of Newtonian and non-Newtonian flows through a thin three-dimensional domain are widely studied in the literature. Usually, authors deal with special models related to particular concrete fluids. In this work, our aim is to present a general model, governing the behaviour of a large class of Newtonian and non-Newtonian fluids. Moreover, we deal with mixed boundary conditions, which are not often studied in the literature related to flows in thin domains. We consider a nonlinear model of a flow in a thin three-dimensional domain, and we study its behaviour when the thickness in one direction tends to zero. At the limit, we obtain a quasilinear two-dimensional problem for the pressure, a nonlinear Reynolds's law for the velocity and a nonlinear Darcy's law for the averaged velocity. Finally, we check that our results hold for a large class of non-Newtonian fluids by producing concrete examples.

Journal: Asymptotic Analysis, vol. 44, no. 1-2, pp. 151-171, 2005