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, are 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
Polytechnic Institute of Cluj-Napoca
C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis
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
See the expanding block below.
Paper coordinates
E. Chifu, C.I. Gheorghiu, I. Stan, Some remarks concerning the Marangoni flow on an inclined plane, Proceedings of the VI-th International Tagung über Grenzflächenaktive Stoffe, 1985, Akad. Verlag, Berlin, 1987, pp. 211-217.
About this paper
Journal
Proceedings of the VI-th International Tagung über Grenzflächenaktive Stoffe
Publisher Name
Paper on journal website
Print ISSN
Online ISSN
MR
?
ZBL
?
Google Scholar
?