Leveling of thin films of colloidal suspensions

We present an analysis of leveling in thin films of colloidal suspensions. The colloidal particles are assumed to be much smaller than the film thickness and influence the film rheology through a concentration-dependent viscosity and bulk diffusivity. A system of coupled nonlinear partial differential equations based on lubrication theory is used to describe the film height and the particle concentrations in the bulk and at the film surface. Linear stability analysis is applied to develop expressions for leveling rates in a number of limiting cases. It is found that for soluble particles, there exist regimes where increasing the Marangoni number slows down leveling at both short and long times, in contrast to the case of insoluble particles. Nonlinear simulations show that the linear theory accurately predicts leveling times even for large amplitude disturbances, and that the presence of a concentration-dependent viscosity and bulk diffusivity speed up leveling. The results of this work should be useful for estimating leveling rates in coatings laden with colloidal particles, and also in coatings containing soluble surfactant.