  The spreading of a liquid over a solid material is a key process in a wide
range of applications. While this phenomenon is well understood when the solid
is undeformable, its "soft" counterpart is still ill-understood and no
consensus has been reached with regards to the physical mechanisms ruling the
spreading of liquid drops over soft deformable materials. In this work we show
that the motion of a triple line on a soft elastomer is opposed both by
nonlinear localized capillary and visco-elastic forces. We give an explicit
analytic formula relating the dynamic contact angle of a moving drop with its
velocity for arbitrary rheology. We then specialize this formula to the
experimentally relevant case of elastomers with Chasset-Thirion (power-law)
type of rheologies. The theoretical prediction are in very good agreement with
experimental data, without any adjustable parameters. Finally, we show that the
nonlinear force balance presented in this work can also be used to recover the
classical de Gennes model of wetting.
