## 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

**Chifu**

Polytechnic Institute of Cluj-Napoca

C.I. **Gheorghiu**

Tiberiu Popoviciu Institute of Numerical Analysis

**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;

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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

[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.