On the depinning of a driven drop on a heterogeneous substrate

Abstract

We study the depinning of driven drops on a heterogeneous substrate using a long-wave evolution equation for the film thickness profile. The heterogeneity is incorporated into an additional pressure term describing the interaction of the liquid with the substrate or with an external field. A drop may be pinned by a hydrophilic defect at the back or a hydrophobic defect at the front. Two types of depinning occur depending on the strength of the driving. The first occurs via a saddle-node (sniper) bifurcation, while the second involves a Hopf bifurcation. The parameter dependence of the depinning process is studied using linear stability theory, and direct numerical simulations are used to explore the dynamical properties of the stick-slip motion of the drop after depinning.