Energy of interaction between solid surfaces and liquids

We consider the wetting transition on a planar surface in contact with a semi-infinite fluid. In the classical approach, the surface is assumed to be solid, and when interaction between solid and fluid is sufficiently short-range, the contribution of the fluid can be represented by a surface free energy with a density of the form Phi(rho_s), where rho_s is the limiting density of the fluid at the surface. In the present paper we propose a more precise representation of the surface energy that takes into account not only the value of rho_s but also the contribution from the whole density profile rho(z) of the fluid, where z is the coordinate normal to the surface. The specific value of the functional of rho_s at the surface is expressed in mean-field approximation through the potentials of intermolecular interaction and some other parameters of the fluid and the solid wall. An extension to the case of fluid mixtures in contact with a solid surface is proposed.