The contact line of an evaporating droplet over a solid wedge and the pinned-unpinned transition

Abstract

We compute the equilibrium contact angles for an evaporating droplet whose contact line lies over a solid wedge. The stability of the liquid interface is also considered and an integro-differential equation for small perturbations is deduced. The analysis of this equation yields criteria for stability and instability of the contact line, where the instability represents transition from the pinned to unpinned contact line representative of stick-slip motion.