A multi-phase, multi-component critical equation of state

Abstract

Realistic equations of state valid in the whole state space of a multi-component mixture should satisfy at least three important constraints: (i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial equation of state with the correct multicomponent structure. (iii) Close to critical points, plait points, and consolute points, the correct universality and scaling behavior is guaranteed. This paper discusses semiempirical equations of state for mixtures that express the pressure as an explicit function of temperature and the chemical potentials. In the first part, expressions are derived for the most important thermodynamic quantities. The main result of the second part is the construction of a large family of equations of state with the properties (i)-(iii).

Analytic Representation of Critical Equations of State

“…Standard thermodynamic stability considerations imply (cf. Neumaier [44]) that, for given T and µ, the stable phase is determined by finding all solutions P of the equations ( 34) for all phase groups g, and taking the one with largest P . In case of ties, several phases from different phase groups coexist.…”

“…The freedom remaining, namely the form of the analytic expressions for the scaling fields, must be determined from the known the behavior at low density (virial equation of state) and any experimental information available. For phenomenological purposes we may choose all scaling fields as low degree polynomials or rational functions of T , P , and µ (or, as argued in Neumaier [44], of a reduced temperature, a reduced pressure, and reduced activities), and fit the coefficients to match experimental data. Simple restrictions discussed in [44] guarantee that, at low densities, one can deduce a virial equation of state with the correct multi-component structure.…”

“…For phenomenological purposes we may choose all scaling fields as low degree polynomials or rational functions of T , P , and µ (or, as argued in Neumaier [44], of a reduced temperature, a reduced pressure, and reduced activities), and fit the coefficients to match experimental data. Simple restrictions discussed in [44] guarantee that, at low densities, one can deduce a virial equation of state with the correct multi-component structure.…”