Fluid adsorption at a non-planar wall: roughness induced first-order wetting

We study the problem of fluid adsorption at a non-planar wall with a view to understanding the influence of surface roughness on the wetting transition. Starting from an appropriate Landau-type free energy functional we develop a linear response theory relating the free energy of the non-planar system to the correlation functions in its planar counterpart. We generalize the well known graphical construction method used to study the planar surface phase diagram and derive analytical expressions for the shift in the phase boundary for first and second-order wetting transitions. Of particular interest is the influence of surface roughness on a second order wetting transition which is driven first order, even for small deviations from the plane.