Development of a field-space corresponding-states method for fluids and fluid mixtures

Abstract

A field-space corresponding-states transformation is one in which the properties of a fluid, or fluid mixture, are related to the properties of a reference fluid, or fluid mixture, by equations which are analytic in the field variables (i.e., the pressure, temperature and chemical potentials). Such transformations are radically different from traditional corresponding states methods. The most useful of these differences is that the presence of phase coexistence in the target system is a direct reflection of phase coexistence in the reference system and never the result of the transformation itself. An immediate consequence of technical interest is that, if the phase transitions of the reference system are tabulated or known analytically, transforming these states maps all of the phase transitions of the target system directly. We introduce the underlying concepts of field-space transformations by implementing the simplest useful forms of the theory and illustrating their utility through application to the van der Waals equation of state for pure fluids. For mixtures we introduce a one-fluid type of system by reinterpreting and then transforming the same pure fluid van der Waals equation.