On the flow of a viscous thin layer on an inclined solid plane driven by a constant surface tension gradient

7 years ago

Abstract

Steady flow of a thin layer (trickle, rivulet) of viscous fluid down an inclined surface is considered, via a thin-film approximation. The work extends the study by Duffy and Moffatt [7] of gravity-driven thin trickle of viscous fluid to include the effects of a surface tension gradient. It acts on the free surface of the layer. At the same time the work tries an alternative analysis to our traditional approaches exposed in [6] and the papers quoted there. Asymptotic and numerical results for several values of volume flux and surface tension gradients are carried out.

Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Emilia Borşa

University of Oradea

Keywords

viscous flow; thin film approximation; surface tension gradien

References

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Cite this paper as

C.I. Gheorghiu, E. Borşa, On the flow of a viscous thin layer on an inclined solid plane driven by a constant surface tension gradient, Rev. Anal. Numér. Théor. Approx. 30 (2001) 127-134.

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https://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no2-art2/Borsa-Gheorghiu-pdf

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Journal

Rev. Anal. Numér. Théor. Approx.

Publisher Name

Editions de l’Academie Roumaine

Article on journal website

https://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no2-art2

Print ISSN

1222-9024

Online ISSN

2457-8126

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ZBL

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[1] Achenson, D. J., Elementary Fluid Dynamics, Oxford University Press, Oxford, United Kingdom, pp. 238–259, 1990.

[2] Allen, R. F. and Biggin, C. M., Longitudinal flow of a lenticular liquid filament down an inclined plane, Phys. Fluids, 17, pp. 287–291, 1974.

[3] Amick, C. J., Properties of steady Navier–Stokes solutions for certain unbounded channels and pipes, Nonlinear Anal., 2, pp. 689–720, 1978.

[4] Amick, C. J. and Fraenkel, L. E., Steady Solutions of the Navier–Stokes Equations Representing Plane Flow in Channels of Various Types , Acta Math., 144, pp. 83–152,1980.

[5] Aris, R., Vector, Tensors and the Basic Equations of Fluid Mechanics, Englewood Cliffs, New Jersey, 1962.

[6] Chifu, E., Gheorghiu, C. I. and Stan, I., Surface mobility of surfactant solutions XI. Numerical analysis for the Marangoni and gravity flow in a thin liquid layer of triangular section , Rev. Roumaine Chim., 29 no. 1, pp. 31 42, 1984.

[7] Duffy, B. R. and Moffatt, H. K., Flow of a viscous trickle on a slowly varying, The Chemical Engineering Journal, 60 , pp. 141–146, 1995.

[8] Georgescu, A., Asymptotic Analysis, Ed. Tehnicˇa, Bucharest, 1989.

[9] Gheorghiu, C. I., An unified treatment of boundary layer and lubrication approximations in viscous fluid mechanics, Rev. Anal. Numer. Theor. Approx., to appear.

[10] Levich, V. G., Physico-Chemical Hydrodynamics, Englewood Cliffs, New Jersey, 1967.

[11] Ockendon, H. and Ockendon, J. R., Viscous Flow, Cambridge, University Press, 1995.

[12] Sorensen, T. S., Hennenberg, M., Steinchen–Sanfeld, A. and Sanfeld, A., Surface chemical and hydrodynamic stability, Progr. Colloid and Polymer Sci.,61, pp. 64–70, 1976.

[13] Towell, G. D. and Rothfeld, L. B., Hydrodynamics of rivulet flow, AICHE. J., 12, p. 972, 1966.

[14] Wagner, A., Instationary Marangoni convection, Preprint, SFB 359, Univ. Heidelberg, pp. 94–42, 1994.

[15] Wilson, S. K. and Duffy, B. R., On the gravity-driven draining of a rivulet of viscous fluid down a slowly varying substrate with variation transverse to the direction of flow, Phys. Fluids, 10, pp.13-22, 1998.

[16] Whitaker, S., Effect of surface active agents on the stability of fal ling liquid films, I and EC Fundamentals, 3, pp. 132–142, 1964.

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On the flow of a viscous thin layer on an inclined solid plane driven by a constant surface tension gradient

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