The solubility of solids in mixtures composed of a supercritical fluid and an entrainer

The goal of this paper is to develop a predictive method for the solubility of a solid in a supercritical fluid containing an entrainer at any concentration. The main difficulty consists in the derivation of an expression for the fugacity coefficient of the solid solute in the binary solvent. A method based on the Kirkwood–Buff formalism was employed and expressions for the derivatives of the fugacity coefficient of the solute in a ternary mixture with respect to the mole fractions were obtained. On the basis of these expressions an algebraic equation was derived, which allowed one to predict the solubility of a solid solute in terms of its solubilities in the supercritical fluid and in the entrainer. The equation was compared with the experimental results available in the literature regarding the solubility in a mixture of supercritical fluids and good agreement was obtained.