Quadratic Modeling and Optimization of Quaternary Equilibria of Liquid-Liquid Systems of General Types, Reactive Extraction Mixtures and Aqueous Biphasic Systems

Abstract

This paper studies quadratic modeling and optimization of quaternary equilibria of liquid-liquid systems of general types, reactive extraction mixtures and aqueous biphasic systems in order to develop an understandable basis of functionally dependent variables that govern optimal solute partitioning within the relevant system. The proposed three quadratic models (QMG, QMR and QMAB), being compatible with multilinear methodology, mimic the equilibrium properties of six test systems relatively accurately, and subsequently, are applied to globally optimizing quaternary equilibria. To remedy an appropriate optimization algorithm, the hybrid gradient method and the derivative variation method are treated and their use for tackling different problems is discussed. The problem of fair imitation of a global optimality is then addressed. The algorithmic solution is completed by the numerical results of six testing problems, being indicative of the fact that the distribution, geometric and solvatochromic properties of components are primary concern to be accounted for a reliable prediction of optimal phase equilibria.