Dynamic Contact Angle of a Soft Solid

The wetting motion of a liquid on a rigid solid is a multi-scale problem in which viscous effects at microscopic scales modify the macroscopic liquid contact angle. Here we show that a contact line moving on a soft elastic substrate also leads to a dynamic contact angle, but this time, in the solid: the initially flat solid surface is deformed elastically into a sharp ridge whose angle depends on the contact line velocity. We predict the dynamic solid contact angle for generic viscoelastic rheologies. The solid angle provides a mechanism for changing the liquid contact angle, which is corroborated by dynamic wetting experiments of water on silicone gels. Our dynamical theory for soft wetting also captures the growth or decay of the wetting ridge, as recently accessed experimentally.