Application of the Kirkwood-Buff theory of solutions to dilute supercritical mixtures

Abstract

Kirkwood-Buff (KB) solution theory has been used to develop a rigorous and general theory for the solubility of a nonvolatile solute in a supercritical solvent. The theory leads to expressions in terms of the Kirkwood fluctuation integrals, G mn, in a fluid mixture at equilibrium with a second (condensed) phase. The general theoretical framework presented in this work allows application of various molecular solution theories such as conformal solution models. A solution theory, based on a scaled distribution function approach, is introduced which leads to particularly simple results in the KB formalism. For dilute solutions this leads to an expression for the solubility which involves only the solvent properties plus characterization parameters for the solute. Predictions of solubility over the full range of densities, from dilute gas to dense fluid, are made for a sample supercritical mixture with satisfactory results. Predictions are sensitive to the model parameters which, in the simple formalism used, are assumed to be independent of state and are estimated from the critical properties. Less stringent assumptions may be introduced by use of other molecular solution theories.