  We show that energy dissipation partition between a liquid and a solid
controls the shape and stability of droplets sliding on viscoelastic gels. When
both phases dissipate energy equally, droplet dynamics is similar to that on
rigid solids. When only the solid dissipate, we observe an apparent contact
angle hysteresis, of viscoelastic origin. We find excellent agreement between
our data and a non-linear model of the wetting of gels of our own that also
indicates the presence of significant slip. Our work opens general questions on
the dynamics of curved contact lines on compliant substrates.
