Interfacial density profiles of a binary van der Waals fluid

Abstract

The van der Waals theory of the interface between coexisting fluid phases of a binary mixture is studied. The theory can be solved analytically on making certain assumptions about the nature of the intermolecular attractive forces, most importantly, the assumption that the cross interaction parameter a12 appearing in van der Waals’ equation of state satisfies the geometric-mean combining rule. In this case, it is found that the interfacial tensions between pairs of phases coexisting under three-phase equilibrium conditions satisfy Antonow’s rule. The theory is not, however, a ’’one-density’’ theory in the sense of Widom, and consequently the interfacial density profile of the more volatile component can be nonmonotonic. At three-phase equilibrium, the location and magnitude of the nonmonotonicity is related to the proximity of two of the phases to their upper critical end point (UCEP). Which pair of phases becomes critical at the UCEP is in turn related to the type of fluid–fluid equilibrium exhibited by the system, according to the classification scheme of van Konynenburg and Scott.