The wetting properties of solid substrates with customary (i.e., macroscopic)random roughness are considered as a function of the microscopic contact angleof the wetting liquid and its partial pressure in the surrounding gas phase.Analytic expressions are derived which allow for any given lateral correlationfunction and height distribution of the roughness to calculate the wettingphase diagram, the adsorption isotherms, and to locate the percolationtransition in the adsorbed liquid film. Most features turn out to depend onlyon a few key parameters of the roughness, which can be clearly identified. Itis shown that a first order transition in the adsorbed film thickness, which weterm 'Wenzel prewetting', occurs generically on typical roughness topographies,but is absent on purely Gaussian roughness. It is thereby shown that evensubtle deviations from Gaussian roughness characteristics may be essential forcorrectly predicting even qualitative aspects of wetting.
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