Comptes Rendus
On nano-scale hydrodynamic lubrication models
[À propos de modèles de lubrification hydrodynamique à l'échelle nanométrique]
Comptes Rendus. Mécanique, Volume 333 (2005) no. 6, pp. 453-458.

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.

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.

Reçu le :
Accepté le :
Publié le :
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/

[1] L. Wu; D.B. Bogy Use of an upwind finite volume method to solve the air bearing problem of hard disk drives, Comput. Mech., Volume 26 (2000), pp. 592-600

[2] H. Hashimoto; Y. Hattori Improvement of the static and dynamic characteristics of magnetic head slidesr by optimum design, ASME J. Tribology, Volume 122 (2000), pp. 280-287

[3] Y. Hu; D.B. Bogy Dynamic stability and spacing modulation of sub-25 nm fly height sliders, ASME J. Tribology, Volume 119 (1997), pp. 646-652

[4] T. Veijola; H. Kuisma; J. Lahdenpera The influence of gas-surface interaction on gas-film damping in a silicon accelerometer, Sensors Actuat. A – Phys., Volume 66 (1998), pp. 83-92

[5] S.-J. Yoon; D.-H. Choi Adjoint design sensitivity analysis of molecular gas film lubrication sliders, ASME J. Tribology, Volume 125 (2003), pp. 145-151

[6] M. Chipot On the Reynolds lubrication equation, Nonlinear Anal., Volume 12 (1988) no. 7, pp. 699-718

[7] M. Chipot; M. Luskin Existence and uniqueness of solutions to the compressible Reynolds lubrication equation, SIAM J. Math. Anal., Volume 17 (1986) no. 6, pp. 1390-1399

[8] I. Ciuperca; M. Jai Existence, uniqueness and homogenization of the second order slip Reynolds equation, J. Math. Appl. Anal., Volume 286 (2003) no. 1, pp. 89-106

[9] B.S. Grigor'ev; S.V. Lupulyak; Yu.K. Shinder Solvability of the Reynolds equation of gas lubrication, J. Math. Sci., Volume 106 (2001) no. 3, pp. 2925-2928

[10] S. Fukui; R. Kaneko Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report-derivation of a generalized lubrication equation including thermal creep flow, ASME J. Tribology, Volume 110 (1988), pp. 253-262

[11] G. Karniadakis; A. Beskok Micro Flows: Fundamentals and Simulation, Springer-Verlag, New York, 2002

[12] Y. Peng; X. Lu; J. Luo Nanoscale effect on ultrathin gas film lubrication in hard disk drive, ASME J. Tribology, Volume 126 (2004), pp. 347-352

[13] D. Gilbarg; N.S. Trudinger Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983

[14] D. Kinderlehrer; G. Stampacchia An Introduction to Variational Inequalities and their Applications, Academic Press, Harcourt Brace Jovanovich, New York, 1980

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