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.