Rigorous interface properties for the van der Waals fluid mixture

A statistical mechanical treatment for the van der Waals fluid mixture is developed, based on Widom’s potential-distribution theory for nonuniform fluids. For the specific choice of Kac pair interactions, in the van der Waals limit, a set of coupled second-order differential equations determine the density profiles. The solution of these equations and the determination of the interfacial tension are discussed in terms of a mechanical analogy.