Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-16T09:36:53.442Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on surface film driven convection

Published online by Cambridge University Press:  18 May 2009

Brian Straughan
Brian Straughan
Affiliation:
Department of Mathematics, University Gardens, Glasgow G12 8QW, Scotland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [6] McTaggart presented a nonlinear energy stability analysis of the problem of convection in the presence of a surface film overlying a non-shallow layer of fluid heated from below. In her work the film is regarded as a two-dimensional continuum and surface tension is then introduced naturally as a combination of a surface density and the derivative of a surface free energy. In fact, the model originated with work of Landau and Lifschitz [4] on the effect of adsorbed films on the motion of a liquid. The precise model she uses was developed from a continuum thermodynamic viewpoint by Lindsay and Straughan [5].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 155 - 158
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Hardy, G. H., Littlewood, J. E., and Polya, G., Inequalities. (Cambridge University Press, 1934).Google Scholar
2.Joseph, D. D., Stability of fluid motions I. (Springer-Verlag 1976).Google Scholar
3.Joseph, D. D., Two fluids heated from below. In, “Energy stability and convection: Proceedings of the Capri workshop”, pp. 364–382. Pitman Research Notes in Mathematics, vol. 168. (Longman, 1988).Google Scholar
4.Landau, L. D., and Lifschitz, E. M., Fluid mechanics. (Pergamon Press, 1959).Google Scholar
5.Lindsay, K. A., and Straughan, B., A thermodynamic viscous interface theory and associated stability problems. Arch. Rational Mech. Anal. 71 (1979), 307–326.CrossRefGoogle Scholar
6.McTaggart, C. L., On the stabilizing effect of surface films in Bénard convection. Physico Chemical Hydrodynamics 5 (1984), 321–331.Google Scholar