Contact line depinning from sharp edges

Abstract

With the aim of finding mathematical criteria for contact line depinning from sharp corners, we have studied the equilibrium and stability of a semi-infinite planar liquid layer pinned at the vertex of a wedge. Equilibrium is compatible with a fan of apparent contact angles θ0 bracketed by the equilibrium contact angles of both flanks of the wedge, so the contact line could remain pinned if θ0 is within this fan. However, the equilibrium becomes unstable at critical depinning advancing θa0 and receding θr0 contact angles, which are found as subcritical saddle-node bifurcations. Equilibrium is possible (stable) within the interval θr0<θ0<θa0, but the contact line depins from the vertex beyond these critical angles if they occur within the equilibrium fan.