One-and-a-half-fluid theory: A new approach to conformal solutions

A theory is proposed that combines the most basic features of conformal solution theory and scaled particle theory (SPT) . The treatment in essence provides a means for evaluating mixture properties from pure fluid data; however, two intermediate substances-the “infinitely polydisperse” (IP) mixture and the “one-and-a-half fluid”-are used to implement the mapping. Associated with the IP mixture is a density-invariant surface onto which the properties of any mixture may be (approximately) mapped. This surface is itself evaluated through an inverse mapping of the properties of the 14 fluid. This substance is a particularly simple type of binary mixture. It contains particles of zero diameter in an otherwise pure fluid. For hard, purely repulsive potentials, the properties of such a mixture may be evaluated exactly, using an elementary argument from SPT. Thus, the IP mixture serves as a bridge between the one-and-a-half fluid reference and any mixture of interest. Independent of these hypothetical substances, a “principle of component corresponding states” is elaborated. The principle states that the fugacity coefficients are equal for components having the same (density) reduced diameter in different mixtures at the same reduced pressure. The one-and-ahalf-fluid theory is demonstrated for mixtures of hard rods in one dimension, where it is seen to be exact, and for hard spheres in three dimensions. The treatment is demonstrably superior to standard conformal solution approaches, particularly at high density and for mixtures of components widely differing in size.