A statistical mechanical framework is developed for generating exact results describing patterned inhomogeneous fluid phenomena. Generic models of patterning and corrugation are discussed, with specific choices of the pattern field invoked to provide a set of illustrative examples. Virial theorems are derived and complications inherent in the virial route to the surface tension of patterned interfaces are highlighted. A variety of compressibility sum rules describe new physics arising from the extended phase space available to patterned fluids. Applications include the wetting of patterned substrates and the solvation of patterned porous media.
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J. Henderson (1999) studied this question.
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