General Formalism for New Generation Geometrical Model: Application to the Thermodynamics of Liquid Mixtures

In our previous papers, a new geometric model has been proposed for calculating the thermodynamic properties of a multi-component system in terms of the properties of its three sub-binary systems. This new model can overcome the inherent defects of the traditional symmetrical and asymmetrical geometric models. Consequently, it is more reasonable theoretically and more reliable in practical applications. However, calculations using this new model involve a series of integration processes which make it complicated and affects its applications. Since a large number of real systems can be approximately fit through a Redlich-Kister polynomial, in this paper a new formalism is presented for the model, based on the binary Redlich-Kister type parameters. The advantage of this treatment is that the whole integration process is avoided by using algebraic operations, thereby simplifying the calculation.