A nonanalytic model for the generic van der Waals equation of state and the critical behavior of simple fluids

Abstract

In this paper, we assume a phenomenological model for the generic van der Waals equation of state to study the subcritical behavior of fluids. In the present model each generic van der Waals parameter consists of the corresponding van der Waals parameter and nonanalytic contributions. By explicitly assuming nonanalytic functions of density for the generic van der Waals parameters, we show that critical exponents of thermodynamic variables near the critical point can be directly related to the nonanalyticity of the generic van der Waals parameters. The critical exponents can be determined in comparison with the experimental values. Thus the generic van der Waals equation of state is shown to be an economic way of phenomenologically relating the critical exponents to the nonanalyticity of the equation of state as functions of density and temperature.