Thin films dewetting with phase separation: Dependence of surface tension and Hamaker constant on concentration

We study the instability of a thin film composed of two miscible liquids (binary fluid) on top of a solid planar surface including the fact that both the free surface and wetting energies are dependent on the mixture concentration. By assuming a linear relationship between these energies and both the bulk and surface concentrations, we analyze their effect on the eventual phase separation of the constituent fluids. The problem is formulated within the gradient dynamics formulation applied to thin film limit of the Cahn-Hilliard Navier-Stokes equations. The dependence of the free surface energy on concentration leads to a Marangoni type of effect, while the wetting energy resulting from van der Waals type of interaction between the film and the substrate is described by a concentrations dependant Hamaker constant. The linear stability analysis uncovers that both real and imaginary growth rates are possible, suggesting oscillatory and/or traveling evolution of any small perturbations of either the film thickness or the concentration field. While our problem formulation applies to any binary mixture that can be consistently modeled via the presented approach, a particular interpretation of the results is provided for the case of liquid metal alloy films on nanoscale.