Stability of fluids with more than two components

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Abstract
A complete theoretical basis is presented for integral equation investigations on the phase stability of simple fluid mixtures with any number of components. Thermodynamic criteria for local stability in terms of the Helmholtz free energy are reviewed accurately and compared with those expressed through the Gibbs free energy. The equivalence of several forms of stability condition is proved by means of new thermodynamic identities. Each form of stability criterion consists of a set of inequalities, and the reducibility of each set to only one necessary condition, namely to the most restrictive inequality, is emphasized. As a main result of the paper, Kirkwood-Buff theory is used and thermodynamic stability criteria for an M component fluid are related to microscopic structural properties, namely to correlation functions which can be calculated from integral equation theories. To complete such an extension of known formulas for binary mixtures, a generalization S (M) CC(k) is proposed of the concentration-concentration structure factor S CC(k) introduced by Bhatia and Thornton for twocomponent systems. The divergence of its long wavelength limit, S CC/(M) (k = 0), signals phase instability.