Stokes theory of thin-film rupture

Abstract

The structure of the flow induced by the van der Waals destabilization of a non-wetting liquid film placed on a solid substrate is unraveled by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that lubrication theory, which yields $h_{\text{min}} \propto \tau^{1/5}$ where $h_{\text{min}}$ is the minimum film thickness and $\tau$ is the time until breakup, cannot be used to describe the local flow close to rupture. Instead, the slender lubrication solution is shown to experience a crossover to a universal self-similar solution of the Stokes equations that yields $h_{\text{min}} \propto \tau^{1/3}$, with an opening angle of $37^{\circ}$ off the solid.