Second order model in fluid film lubrication

Eduard Marušić-Paloka; Igor Pažanin; Sanja Marušić

doi:10.1016/j.crme.2012.05.004

Second order model in fluid film lubrication

Eduard Marušić-Paloka ¹ ; Igor Pažanin ¹; Sanja Marušić ²

¹ Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
² Faculty of Transport and Traffic Engineering, University of Zagreb, Vukelićeva 4, 10000 Zagreb, Croatia

Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 596-601.

Abstract

The goal of this Note is to derive the second order model correcting the standard Reynolds equation for fluid film lubrication. Starting from microscopic model described by the Stokes system, we compute an asymptotic expansion for the solution. Instead of computing only the first term, as in the standard Reynolds approximation, we keep first two terms leading to the corrected model. We obtain equations similar to the Brinkman model for porous medium flow.

Received: 2012-02-19
Accepted: 2012-05-31
Published online: 2012-06-22

DOI: 10.1016/j.crme.2012.05.004

Keywords: Lubrication, Fluid film lubrication, Asymptotic analysis, Second order model

Author's affiliations:

Eduard Marušić-Paloka ¹; Igor Pažanin ¹; Sanja Marušić ²

¹ Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
² Faculty of Transport and Traffic Engineering, University of Zagreb, Vukelićeva 4, 10000 Zagreb, Croatia

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     title = {Second order model in fluid film lubrication},
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Eduard Marušić-Paloka; Igor Pažanin; Sanja Marušić. Second order model in fluid film lubrication. Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 596-601. doi : 10.1016/j.crme.2012.05.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.05.004/

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