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A note on surface film driven convection
Published online by Cambridge University Press: 18 May 2009
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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].
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- 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
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
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
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