Flow near singular elastic interfaces: Lubrication, wetting \& cusps

Soft elastic surfaces exhibit intriguing similarities to liquid interfaces: they possess a surface tension and are susceptible to interfacial instabilities. The first part of this talk addresses why the wetting dynamics on such a very soft substrate is fundamentally different from the usual wetting hydrodynamics. The initially flat solid is deformed into a sharp ridge and the resulting contact line motion is governed by the rheology of the solid. We experimentally observe an irregular stick-slip motion of the drop, and explain this phenomenon by a viscoelastic theory for the dynamic contact angle. In the second part we address the morphology of sharp cusps that arise at elastic interfaces. Inspired by classical work on viscous cusps at liquid interfaces, we reveal the emergence of self-similar cusps in the regime of extremely nonlinear elasticity.