Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Authors: Nadia Benhaboucha, Michèle Chambat and Ionel Ciuperca
Journal: Quart. Appl. Math. 63 (2005), 369-400
MSC (2000): Primary 76D07, 76D08, 78M35, 78M40
DOI: https://doi.org/10.1090/S0033-569X-05-00963-3
Published electronically: May 4, 2005
MathSciNet review: 2150781
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

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

DOI: https://doi.org/10.1090/S0033-569X-05-00963-3
Keywords: Homogenization, rough boundary, Reynolds equation, asymptotic stresses
Received by editor(s): January 3, 2005
Published electronically: May 4, 2005
Article copyright: © Copyright 2005 Brown University


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