On dewetting and concentration evolution of thin binary fluid films

Abstract

We study the stability and dewetting dynamics of a thin free-surface film composed of two miscible liquids placed on a solid substrate. Our study focuses on the development of a self-consistent model such that the mixture concentration influences both free-surface and wetting energies. By assuming a simple relation between these energies and the bulk and surface concentrations, we analyse their effect on the concentration distribution and dewetting down to the equilibrium film thickness determined by the fluid–solid interaction potential. The model, developed within the gradient dynamics formulation, includes the dependence of the free-surface energy on surface concentration leading to the Marangoni effect, while a composition-dependent Hamaker constant describes the wetting energy resulting from the fluid–solid interaction. We analyse the restrictions that must be fulfilled to ensure an equilibrium state for a flat film of a binary fluid. Then, we proceed by studying its linear stability. First, we consider the Marangoni effect while assuming that wetting energy depends only on the fluid thickness. Then, we include a dependence of wetting energy on concentration and study its effects. We find that the linear stability results compare very well with those of numerical simulations of the full nonlinear problem applied to the particular case of a binary melted metal alloy, even close to breakup times. Therefore, in practice, most of the evolution can be studied by using the linear theory, simplifying the problem considerably.