  Consider a droplet of liquid on top of a grooved substrate. The wetting or
not of a groove implies the crossing of a potential barrier as the interface
has to distort, to hit the bottom of the groove. We start with computing the
free energies of the dry and wet states in the context of a simple
thermodynamical model before switching to a random microscopic version
pertaining to the Solid-on-Solid (SOS) model. For some range in parameter space
(Young angle, pressure difference, aspect ratio), the dry and wet states both
share the same free energy, which means coexistence. We compute these
coexistence lines together with the metastable regions. In the SOS case, we
describe the dynamic transition between coexisting states in wetting. We show
that the expected time to switch from one state to the other grows
exponentially with the free energy barrier between the stable states and the
saddle state, proportional to the groove's width. This random time appears to
have an exponential-like distribution.
