De Coninck J., Miracle--Sol\'{e} S., Ruiz J.
Wetting of Heterogeneous Surfaces at the Mesoscopic Scale
(91K, LATeX 2e)

ABSTRACT.  We consider the problem of
wetting on a heterogeneous wall with mesoscopic defects: i.e.\
defects of order $L^{\varepsilon}$, $0<\varepsilon<1$, where $L$ is
some typical length--scale of the system. In this framework, we
extend several former rigorous results which were shown for walls
with microscopic defects \cite{DMR,DMR2}. Namely, using
statistical techniques applied to a suitably defined semi-infinite
Ising-model, we derive a generalization of Young's law for rough
and heterogeneous surfaces, which is known as the generalized
Cassie-Wenzel's equation. In the homogeneous case, we also show
that for a particular geometry of the wall, the model can exhibit
a surface phase transition between  two regimes which are either
governed by Wenzel's or by Cassie's law.