Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 439319, 26 pages
Research Article

Influence of Multiscale Roughness Patterns in Cavitated Flows: Applications to Journal Bearings

Sébastien Martin

Laboratoire de Mathématiques, Université Paris-Sud XI, CNRS-UMR 8628, Bâtiment 425, 91405 Orsay Cedex, France

Received 2 November 2007; Accepted 19 March 2008

Academic Editor: Giuseppe Rega

Copyright © 2008 Sébastien Martin. 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.


This paper deals with the coupling of two major problems in lubrication theory: cavitation phenomena and roughness of the surfaces in relative motion. Cavitation is defined as the rupture of the continuous film due to the formation of air bubbles, leading to the presence of a liquid-gas mixture. For this, the Elrod-Adams model (which is a pressure-saturation model) is classically used to describe the behavior of a cavitated thin film flow. In addition, in practical situations, the surfaces of the devices are rough, due to manufacturing processes which induce defaults. Thus, we study the behavior of the solution, when highly oscillating roughness effects on the rigid surfaces occur. In particular, we deal with the reiterated homogenization of this Elrod-Adams problem, using periodic unfolding methods. A numerical simulation illustrates the behavior of the solution. Although the pressure tends to a smooth one, the saturation oscillations are not damped. This does not prevent us from defining an equivalent homogenized saturation and highlights the anisotropic effects on the saturation function in cavitated areas.