  In the classic theory of solid adhesion, surface energy drives deformation to
increase contact area while bulk elasticity opposes it. Recently, solid surface
stress has been shown also to play an important role in opposing deformation of
soft materials. This suggests that the contact line in soft adhesion should
mimic that of a liquid droplet, with a contact angle determined by surface
tensions. Consistent with this hypothesis, we observe a contact angle of a soft
silicone substrate on rigid silica spheres that depends on the surface
functionalization but not the sphere size. However, to satisfy this wetting
condition without a divergent elastic stress, the gel separates from its
solvent near the contact line. This creates a four-phase contact zone with two
additional contact lines hidden below the surface of the substrate. While the
geometries of these contact lines are independent of the size of the sphere,
the volume of the phase-separated region is not, but rather depends on the
indentation volume. These results indicate that theories of adhesion of soft
gels need to account for both the compressibility of the gel network and a
non-zero surface stress between the gel and its solvent.
