Simple fluids near rigid solids: statistical mechanics of density and contact angle

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Abstract
By making a simple approximation for the two-particle distribution function in a fluid, an approximate formula is obtained for the fluid density n(r) throughout the liquid-vapour region near an arbitrary rigid solid which exerts forces on the fluid. The density formula is based on a 'surface of tension' Sigma which curves in from infinity towards the solid. For a 'flat smooth solid', it is shown that only one asymptotic slope results in a surface Sigma corresponding to stable contact with the solid. This gives simple formulae for the angle of contact and the work of adhesion, in terms of intermolecular potentials and the bulk liquid radial distribution function. Solids which are not flat or smooth are discussed. The effects of large and rapidly-varying curvatures of Sigma are estimated, leading to the result that the formulae should become more accurate as the contact angle increases.

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