  Liquid drops on soft solids generate strong deformations below the contact
line, resulting from a balance of capillary and elastic forces. The movement of
these drops may cause strong, potentially singular dissipation in the soft
solid. Here we show that a drop on a soft substrate moves by surfing a ridge:
the initially flat solid surface is deformed into a sharp ridge whose
orientation angle depends on the contact line velocity. We measure this angle
for water on a silicone gel and develop a theory based on the substrate
rheology. We quantitatively recover the dynamic contact angle and provide a
mechanism for stick-slip motion when a drop is forced strongly: the contact
line depins and slides down the wetting ridge, forming a new one after a
transient. We anticipate that our theory will have implications in problems
such as self-organization of cell tissues or the design of capillarity-based
microrheometers.
