C. Borgs, J. De Conninck, R. Kotecky
An equilibrium lattice model of wetting on rough substrates
(1656K, Postscript)
ABSTRACT. We consider a semi-infinite 3-dimensional Ising system with
a rough wall to describe the effect of the roughness $r$ of
the substrate on wetting. We show that the difference of wall
free energies $\Delta \tau (r)=\tau_{AW}(r)-\tau_{BW}(r)$ of the
two phases behaves like $\Delta \tau(r) \sim r \Delta \tau(1)$,
where $r=1$ characterizes a purely flat surface, confirming thus,
at low enough temperature and small roughness, the validity of
the Wenzel's law $\cos \theta (r) \approx r \cos \theta (1)$ which
relates the contact angle $\theta $ of a sessile droplet with the roughness of the substrate.