  In this paper we propose an extension of the Cahn method to binary mixtures
and study the problem of wetting near a two-phase critical point without any
assumption on the form of intermolecular potentials. A comparison between
Cahn's method and later works by Sullivan, Evans et al is made. By using an
expression of the energy of interaction between solid surface and liquids
proposed recently by Gouin, we obtain the equations of density profiles and the
boundary conditions on a solid surface. In the case of a convex free energy, a
one-dimensional solution of a linear problem is proposed for the density
profiles between a bulk and on a solid wall. A non-linear model of binary
mixtures extending Cahn's results for simple fluids is also studied. For the
case of a purely attractive wall we have established a criterion of a first
order transition in terms of the structure of the level set of the homogeneous
part of the free energy. Additively, explicit expressions of density profiles
near the wall are proposed. They allow one to consider the adsorption of
mixture components by a solid wall.
