The mechanical theory of fluid interfaces and Maxwell's rule

Abstract

By operating within a recently developed mechanical theory of fluid interfaces we find that Maxwell's equal area rule fails to hold unless certain molecular conditions are satisfied. In view of these conditions various statistical models for fluid interfaces which have previously been proposed need to be restricted if they are to be compatible with the equal area rule. We show that in both concept and fact the mechanical theory is more general than previous interfacial theories which as a rule assume the existence of thermodynamic functions and the validity of thermodynamic relations within the spinodal set. In particular, we list necessary and sufficient conditions for the reduction of the mechanical theory to the modified and original van der Waals theories of fluid interfaces. These conditions are also molecular in nature, the reduction being accomplished without the use of thermodynamic reasoning within the spinodal region. Finally, we consider three-dimensional interfaces and note that when the conditions for Maxwell's rule and van der Waals' theory are not satisfied, then the interfaces are generally planar, cylindrical, or spherical at equilibrium.