Filling transitions on rough surfaces: Inadequacy of Gaussian surface models

We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory, except that we find critical end points within the physical parameter range. As predicted, Gaussian random surfaces are found to behave qualitatively different from non-Gaussian topographies. This shows that Gaussian random processes as models for rough surfaces must be used with great care, if at all, in the context of wetting phenomena.