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Complete Wetting on Rough Surfaces: Statics

We study the profile of a thin liquid film completely wetting a rough solid surface. The long-wavelength undulations of the liquid interface follow those of the solid surface, while short-wavelength undulations are strongly damped. There is Lorentzian damping of wavelengths smaller than the healing length ξ determined by a balance between surface tension and disjoining pressure. Undulations with wavelength smaller than the mean film thickness e are exponentially damped. We study in detail the case where the binary interactions between molecules may be described by an inverse power law potential such as the Van der Waals potential. These results are relevant for recent ellipsometry and grazing incidence x-ray scattering experiments.