Is there an Optimal Substrate Geometry for Wetting ?

We consider the problem of the Winterbottom's construction and Young's equation in the presence of a rough substate and establish their microscopic validity within a 1+1-dimensional SOS type model. We then present the low temperature expansion of the wall tension leading to the Wenzel's law for the wall tension and its corrections. Finally, for a fix roughness, we compare the influence of different geometries of the substrate on wetting properties. We show that there is an optimal geometry with a given roughness for a certain class of simple substrates. Our results are in agreement and explain recent numerical simulations.