A note on surface film driven convection

Abstract

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].