Modeling of the three-phase equilibrium in systems of the type water + nonionic surfactant + alkane

Abstract

Liquid–liquid equilibria of systems water (A) + C i E j surfactant (B) + n-alkane (C) have been modeled by a mass-action law model previously developed and so far successfully applied to a series of binary water + C i E j systems and to the ternary system water + C 4E 1 + n-dodecane. These calculations provide the basis for the presented modeling. The aqueous systems give information about the association constants and the χ AB-parameter of the Flory–Huggins theory and the ternary C 4E 1-system provides universal temperature functions for the χ AC- and the χ BC-parameter. The three-phase equilibrium for seven ternary C i E j systems ( i = 6–12, j = 3–6) has been calculated by fitting one additional parameter for each of both temperature functions to the characteristic “fish-tail” point. The agreement with the experimental data is reasonably well. For systems with very small three-phase areas the results can considerably be improved by individual temperature functions that incorporate the experimental temperature maximum of the “fish” into the parameter fit. Based on the parameters of the system water + C 8E 4 + n-C 8H 18 the “fish-shaped” phase diagram of the system water + C 8E 4 + n-C 14H 30 was predicted reasonably well.