Instabilities in thin-film binary mixtures

Binary mixtures of ultra-thin films are subject to both height and concentration fluctuations, either of which, under the appropriate conditions, can become unstable. We investigate a simple general thermodynamic model which shows that, due to the constraint imposed upon coupling between these fluctuations, a thin-film binary mixture will be less stable than if either height or concentration fluctuations are considered in isolation. We investigate the height dependence of the stability condition, discuss equilibrium conditions when higher-order contributions to the free energy are negligible, and predict the scaling behaviour.