Díaz Díaz, Jesús Ildefonso and Martin, Sébastien
(2006)
*On the instantaneous formation of cavitation in hydrodynamic lubrication.*
Comptes rendus. Mécanique, 334
(11).
pp. 645-650.
ISSN 1631-0721

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Official URL: http://www.sciencedirect.com/science/article/pii/S1631072106001458

## Abstract

We consider the Elrod-Adams model extending the classical lubrication Reynolds equation to the case of the possible presence of a cavitation region. We show that the behaviour of the pressure and saturation depends crucially on the behaviour of the separation h (t, x, y) among the two surfaces. In particular, we exhibit some simple formulations for which we prove (rigorously) that a cavitation region is formed instantaneously (even for initially saturated flows). Some numerical experiences are also given.

Item Type: | Article |
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Uncontrolled Keywords: | lubrication; cavitation; Elrod-Adams model; Reynolds equation; free-boundary problems |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15356 |

References: | O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil, Phil. Trans. Roy. Soc. A 117 (1886) 157–234. H.G. Elrod, M.L. Adams, A computer program for cavitation, in: Cavitation and Related Phenomena in Lubrication—Proceedings, Mech. Eng. Publ. Ltd, 1975, pp. 37–42. S.J. Alvarez, R. Oujja, On the uniqueness of the solution of an evolution free boundary problem in theory of lubrication, Nonlinear Anal. 54 (5) (2003) 845–872. J.I. Díaz, On the mathematical analysis of transient cavitation problems in hydrodynamics lubrification, in: G. Bayada, M. Chambat, J. Durany (Eds.), Mathematical Modelling Lubrification, Univ. de Vigo, 1991, pp. 37–49. S.J. Alvarez, J. Carrillo, A free boundary problem in theory of lubrication, Comm. Partial Differential Equations 19 (11–12) (1994) 1743–1761. J. Carrillo, J.I. Díaz, G. Gilardi, The propagation of the free boundary of the solution of the dam problem and related problems, Appl. Anal. 4 (1993) 255–276. S.N. Antontsev, J.I. Díaz, S.I. Shmarev, Energy methods for free boundary problems, in: Applications to Nonlinear PDEs and Fluid Mechanics, in: Series Progress in Nonlinear Differential Equations and Their Applications, vol. 48, Birkhäuser, Boston, 2002. J.I. Díaz, Nonlinear Partial Differential Equations and Free Boundaries, vol. I. Elliptic Equations, Research Notes in Mathematics, vol. 106, Pitman, Londres, 1985. G. Bayada, M. Chambat, C. Vázquez, Characteristics method for the formulation and computation of a free boundary cavitation problem, J. Comput. Appl. Math. 98 (2) (1998) 191–212. |

Deposited On: | 24 May 2012 08:00 |

Last Modified: | 06 Feb 2014 10:22 |

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