Some remarks concerning the Marangoni flow on an inclined plane

Abstract

We consider a thin liquid layer of a transverse triangular section, situated on an inclined solid plane. On the liquid-gas interface a surface tension gradient acts along or against gravity. We simplify the equations of motion (Navier-Stokes and continuity) to obtain a linear diffusion equation supplied with mixed boundary conditions, i.e., a Dirichlet one on the solid walls of the section and a Robin boundary condition on the liquid-gas interface. A Galerkin finite element procedure along with a Crank-Nicolson finite difference scheme, in order to march in time, is used to solve this initial/boundary value problem. Some numerical experiments are carried out. They determine numerically the flow field for various values of tension gradients.

Authors

E. Chifu
Polytechnic Institute of Cluj-Napoca

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

I. Stan
Polytechnic Institute of Cluj-Napoca

Keywords

Marangoni flow; inclined plane; anti-parallel flow; unsteady diffusion equation; mixed boundary value problem; Galerkin finite element; Crank-Nicolson; velocity profile;

References

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Paper coordinates

E. Chifu, C.I. Gheorghiu, I. Stan, Some remarks concerning the Marangoni flow on an inclined plane, Proceedings of the VII-th International Tagung über Grenzflächenaktive Stoffe, 1985, Akad. Verlag, Berlin, 1987, pp. 211-217.

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Proceedings of the VI-th International Tagung über Grenzflächenaktive Stoffe

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References

[1] E. Chifu, et al. Studia  Univ. Babes-Bolyai, 6 (2), 19, 1961; 8 (1). 49 (1963); 9 (1), 95 (1964); 9 (1), 101 (1964); 10 (2), 85 (1965); 10 (2), 91 (1965); 10 (2), 99 (1965); Rev. Roumaine Chim., 11, 873 (1966).

[2] E. Chifu, I. Stan, Rev. Roumaine Chim., 27, 703 (1982)


[3] E. Chifu, C. I. Gheorghiu, I. Stan, Rev. Roumaine Chim., 29, 31 (1984)


[4] R. Van Den Bogaert and P. Joos, J. Colloid Interface Sci., 69, 301 (1979).


[5] E. Chifu, et. al., Rev. Roumaine Chim. (in press).


[6] L. Howarth,
Modern Developments in Fluid dynamics, High Speed Flow, vol. I, Oxford 1953

[7] L. E. Scriven, Chem. Eng. Sci., 12, 98 (1960); R. Aris,
Vectors Tensors and the Basic Equations of the Fluid Mechanics”,  Prentice Hall, New Jersey, 1962, Cap. X; E. Chifu, I. Stan, Z. Finta, E. Gavrila, J. Colloid Interface Sci., 93, 140 (1983).

[8] C. I. gheorghiu, Ph. D. Sissertation, The University of Bucharest, Faculty of Mathematica 1984.

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