The statistical mechanics of wetting

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Abstract
The wetting of a rigid solid by a simple fluid is studied. Using the methods of statistical mechanics an exact expression is obtained for the work of adhesion W A (and hence the contact angle). It is found that W A consists of two terms W A(1) and W A(2). W A(1) depends directly on the solid-fluid interaction potential and the fluid one-particle distribution function, and corresponds to the direct interaction between fluid and solid. W A(2) depends directly on the fluid-fluid interaction potential and the fluid two-particle distribution function, and corresponds to the relaxation of the fluid density profile to its free surface form when the liquid is pulled away from the solid. The existence of W A(2) is the novel feature of this theory. Comparisons with existing theories are made. Calculations based on the theory are presented for the case of Lennard-Jones interactions and a flat smooth solid, using parameters corresponding to liquid methane on a variety of solids. The main result is that the new term W A(2) is comparable in magnitude to the term W A(1) to which previous studies have been confined.