On the Marangoni and gravity flow in an inclined channel of an arbitrary section


In this paper we use a lubrication approximation in order to investigate the flow of a thin layer of a viscous fluid (rivulet, trickle) confined to a channel of an arbitrary transverse section driven simultaneously by a constant surface tension gradient. The work extends some results of Wilson and Duffy (1998) of gravity-driven thin trickle of viscous fluid which include the effects of surface tension gradient. It acts on the free surface of the layer. At the same time we try an alternative analysis to our traditional approaches (Chifu, Gheorghiu, Stan 1984).  Numerical results concerning the free-surface profile are carried out.


E. Borsa 
-University of Oradea, Deparment of Mathematics

C. I. Gheorghiu
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy


slow viscous flow; thin film approximation; surface tension gradient; shear tangential stress; gravity-driven flow

Cite this paper as:

E. Borşa. C. I. Gheorghiu, On the Marangoni and gravity flow in an inclined channel of an arbitrary section, Rev. Roum. Sci Techn.-Mec. Appl., 45 (2000) 255-264.



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[1] Acheson, D. J.,  Elementary fluis dynamics,  Oxford University Press, United Kingdom, 1990, pp. 238-259.

[2] Allen, R. F., 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 analysis, Theory, Methods and Applications,  2, pp. 689-720, 1978.

[4] Amick, C. J., Fraenkel, L. E.,
 Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types,  Acta Mathematica, 144, 83-152, 1980.

[5] Aris, R.,
Vector, tensors and the basic equations of fluid mechanics,  New Jersey, Englewood Cliffs, 1962.

[6] Chifu, E., Gheorghiu, C.I., Stan, I.,
Surface mobility of surfanctant 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., Moffatt, H. K.,
Flow of a viscous trickle on a slowly varying. The chemical engineering Journal, 60, 141-146, 1995.

[8] Duffy, B. R. and Wilson, S. K.,
 A third-order differential equation arising in thin-film flows and relevant to Tanner’s law,  Appl. Math. Lett. 10, pp. 63, 1997.

[9] Gheorghiu, C. I.,
An  unified treatment of boundary layer and lubrication approximations in viscous fluid mechanics,  Cluj-Napoca submitted to Studia Univ. “Babes-Bolyai”.

[10] Levich, V. G.,
Physico-chemical hydrodynamics,  Englewood Cliffs. New Jersey, 1967.

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

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

[13] Wagner, A.,
Instationary Marangoni convection,  Heidelberg Preprint 94-42 (SFB 359), Univ. Heidelberg.

[14] Wilson, S. K., 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.

[15] Whitaker, S.,
 Effect of surface active agents on the stability of falling liquid films.  I and EC Fundamentals, 3, pp. 132-142, 1964.

[16] Young, G. W., Davis, S. H.,
 Rivulet instabilities,  J. Flujid Mech., 176, 1987.

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