Comptes Rendus
On nano-scale hydrodynamic lubrication models
Comptes Rendus. Mécanique, Volume 333 (2005) no. 6, pp. 453-458.

Current magnetic head sliders and other micromechanisms involve gas lubrication flows with gap thicknesses in the nanometer range and stepped shapes fabricated by lithographic methods. In mechanical simulations, rarefaction effects are accounted for by models that propose Poiseuille flow factors which exhibit singularities as the pressure tends to zero or +∞. In this Note we show that these models are indeed mathematically well-posed, even in the case of discontinuous gap thickness functions. Our results cover popular models that were not previously analyzed in the literature, such as the Fukui–Kaneko model and the second-order model, among others.

Actuellement, de nombreux microdispositifs tels que les têtes de lecture magnétiques mettent en oeuvre des écoulements lubrifiés compressibles d'une épaisseur de film à l'échelle nanométrique. Leurs géométries, obtenues par des méthodes lithographiques, sont pratiquement discontinues. Dans les simulations, les effets de raréfaction sont incorporés dans des modèles, couramment utilisés en lubrification (modèle de Fukui–Kaneko, modèle de deuxième ordre, etc.) qui font intervenir les facteurs de Poiseuille qui deviennent singuliers quand la pression tend vers zero ou vers +∞. Dans cette Note nous montrons que ces modèles sont mathématiquement bien posés, même avec des fonctions d'épaisseur discontinues.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2005.04.006
Keywords: Computational fluid mechanics, Hydrodynamic lubrication models, Rarefaction effects, Numerical simulation, Magnetic storage
Mot clés : Mécanique des fluides numérique, Modèles de lubrification hydrodynamique, Effets de raréfaction, Simulation numérique, Enregistrement magnétique

Gustavo Buscaglia 1; Ionel S. Ciuperca 2; Mohammed Jai 3

1 Centro Atómico Bariloche and Instituto Balseiro, 8400, Bariloche, Argentina
2 CNRS-UMR 5208, université Lyon I, analyse numérique, bâtiment Doyen Jean-Braconnier, 69622 Villeurbanne cedex, France
3 CNRS-UMR 5208, INSA de LYON, centre de mathématiques, bâtiment Léonard de Vinci, 69621 Villeurbanne, France
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Gustavo Buscaglia; Ionel S. Ciuperca; Mohammed Jai. On nano-scale hydrodynamic lubrication models. Comptes Rendus. Mécanique, Volume 333 (2005) no. 6, pp. 453-458. doi : 10.1016/j.crme.2005.04.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.04.006/

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