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Journal of Applied Mathematics
Volume 2014, Article ID 217174, 8 pages
http://dx.doi.org/10.1155/2014/217174
Research Article

Asymptotic Modeling of the Thin Film Flow with a Pressure-Dependent Viscosity

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Received 15 April 2014; Revised 19 June 2014; Accepted 26 June 2014; Published 16 July 2014

Academic Editor: Weiqing Liu

Copyright © 2014 Eduard Marušić-Paloka and Igor Pažanin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the lubrication process with incompressible fluid taking into account the dependence of the viscosity on the pressure. Assuming that the viscosity-pressure relation is given by the well-known Barus law, we derive an effective model using asymptotic analysis with respect to the film thickness. The key idea is to conveniently transform the governing system and then apply two-scale expansion technique.