Quarterly of Applied Mathematics

Asymptotic behaviour of pressure and stresses in a thin film flow with a rough boundary

Author(s): Nadia Benhaboucha; Michèle Chambat; Ionel Ciuperca
Journal: Quart. Appl. Math. 63 (2005), 369-400.
MSC (2000): Primary 76D07, 76D08, 78M35, 78M40
Posted: May 4, 2005
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Abstract: We study the asymptotic behaviour of an incompressible viscous flow in a narrow gap with a thickness of order $\eta$ and a rough surface. The roughness is defined by a quasi-periodical function with period $\epsilon$ . In both cases, when $\eta$ is smaller or at the same order as $\epsilon$ , we obtain different Reynolds equations for the pressure. We have also studied the convergence of the stresses on the rough boundary and we discuss the different cases.

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Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 76D07, 76D08, 78M35, 78M40

Nadia Benhaboucha
Affiliation: CNRS UMR 5585, Maply, Bat J. Braconnier, Univ. Lyon1, 69622 Villeurbanne Cedex France
Email: Nadia.Benhaboucha@maply.univ-lyon1.fr

Michèle Chambat
Affiliation: CNRS UMR 5585, Maply, Bat J. Braconnier, Univ. Lyon1, 69622 Villeurbanne Cedex France
Email: chambat@maply.univ-lyon1.fr

Ionel Ciuperca
Affiliation: CNRS UMR 5585, Maply, Bat J. Braconnier, Univ. Lyon1, 69622 Villeurbanne Cedex France
Email: ciuperca@maply.univ-lyon1.fr

PII: S0033-569X-05-00963-3
Keywords: Homogenization, rough boundary, Reynolds equation, asymptotic stresses
Received by editor(s): January 3, 2005
Posted: May 4, 2005
Copyright of article: Copyright 2005, Brown University

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