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With aim of finding mathematical criteria for contact line depinning fromsharp corners, we have studied the equilibrium and stability of a semi-infiniteplanar liquid layer pinned at the vertex of a wedge. Equilibrium is compatiblewith a fan of apparent contact angles $\theta_0$ bracketed by the equilibriumcontact angles of both flanks of the wedge, so the contact line could remainpinned if $\theta_0$ is within this fan. However, the analysis of the stabilityof these solutions, studied exploiting the variational structure of the problemthrough turning-point arguments, shows that the equilibrium becomes unstable atcritical depinning advancing $\theta_0^a$ and receding $\theta_0^r$ contactangles, which are found as subcritical saddle-node bifurcations. Equilibrium isthus possible (stable) within the interval $\theta_0^a < \theta_0 <\theta_0^a$but the contact line depins from the vertex beyond these critical angles ifthey occur within the equilibrium fan.

Contact line depinning from sharp edges