A unified treatment of boundary layer and lubrication approximations in viscous fluid mechanics

Abstract

It is a matter of every day experience to find the boundary layer and lubrication approximations exposed as if they had nothing in common.
It is the aim of this note to show that, in fact, they come from the Navier-Stokes system and that they correspond to some distinguished limits of the Reynolds number.

Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Keywords

boundary layer; lubrication; Reynolds number; distinguished limits

References

See the expanding block below.

Cite this paper as

C.I. Gheorghiu, A unified treatment of boundary layer and lubrication approximations in viscous fluid mechanics, Rev. Anal. Numér. Théor. Approx., 29 (2000) 135-138.

PDF

About this paper

Journal

Rev. Anal. Numér. Théor. Approx.

Publisher Name

Editions de l’Academie Roumaine

Print ISSN

1222-9024

Online ISSN

2457-8126

MR

?

ZBL

?

Google Scholar

?

[1] ASCHESON, D. J., Elementary Fluid, Dynamrics, Clarendon Press, Oxford, 1992.

[2] BENDER C. M., ORSZAG, S. A., Advances Mathematical-Methods for scientists and Engineers, Mc Graw-Hill, 1928.

[3] FOWKES, N.D., MAHONY, J. J., An Introduction to Mathematical Modelling, John Miley & Sons, 1994.

[4] FOWLER, a.c., Mathematical Models in the Appried, science, Cambridge Univ. Press, 1997.

[5] GHEORGHIU, C. I., KASA, Z., STAN, I., Effects of Surfactants on an Undeformable Drop Initially at Rest, Studia Univ. “Babeş-Bolyai” Mathematica, XXXVIII, 2, 1993, 113-126.

[6] GHEORGHIU, C.I., On the Behaviour of a Thin Liquid, Layer Flowing Due to Gravity and Surface Tension Gradient, I. Mathematical Aspects, Studia Univ. “Babeş-Bolyai”, Mathematica, XLI, no. 4, pp. 47-54, I996.

[7] LANDAU, L.D., LIFSHITZ, E.M., Fluid, Mechanics,2nd, Edition, Pergamon Press, 1989.

[8] LEVICH, Y. G., Physicochemical Hydrodynamics, Prentice Hall, Englewood Cliffs, N.J.,1962.

[9] LIN, C. C., SEGEL, L. A., Mathematics Applied, to Deterministic Problems in Natural Sciences, Macmillan, London, 1974.

[10] OCKENDON, I., OCKENDON, J, Viscous Flow, Cambridge Univ. Press, 1995.

[11] OROVEANU, T., Viscous Fluid, Mechanics, Romanian Academy Publishing House, 1967 (in Romanian).

[12] SCHLICHTING, H., Boundary Layer Theory, Mc Graw-Hill, 1960.

[13] WILSON, S. K., DAVIS, S. H., BANKOFF, S. G., The unsteady expansion and, contraction of a long two-dimensional vaspour bubble between superheated or subcooled, parallel plates, J. Fluid Mech., vol. 891, pp. 1-27, 1999.

?
2000

Related Posts