On the Marangoni flow on an inclined plane

Abstract

We consider the flow of a uniform thin layer (rivulet, trickle) of viscous fluid down an inclined plane driven simultaneously by a surface tension gradient. Using a lubrication approximation we determine the rates of flow due to various tension gradients.

Authors

E. Borsa,

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Keywords

viscous flow; thin film approximation; surface tension gradient; asymptotic analysis; rate of flow

References

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Cite this paper as

E. Borşa, C.I. Gheorghiu, On the Marangoni flow on an inclined plane, Bul. Inst. Politehnic din Iaşi, Supliment Mecanica Fluidelor, XLVI(L) (2000) suppl., pp. 61-64.

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Journal

Buletinul Institutului Politehnic Iași

Publisher Name

Universitatea Tehnica ”Gh. Asachi”, Iași

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1011-2855

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References

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References

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

[2] Amick, C.J.,  Properties of steady Navier-Stokes solutions for certain unbounded channels and pipes, nonlinear analysis, Theory, Methods and Applications, 2, 686-720, 1978.
[3] Duffy, B.R., Moffatt, H.K., Flow of a viscous trickle on a slowly varying,  The Chemical Engineering Journal 60, 141-146, 1995.

[4] Gheorghiu, C. I., An unified treatment of boundary layer and lubrication approximation in viscous fluid mechanics,  accepted to Rev. D’Analyse Numer et de Theorie de l’Approximation, Cluj-Napoca.

[5] Ockendon H, Ockendon J.R., Viscous flow, Cambridge, University Press, 1995.

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

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