Can liquid-liquid equilibria be predicted by the combination of a cubic equation of state and a gE model not suitable for liquid-liquid equilibria?

In modern versions of cubic equations of state (EoS), the mixing rules for EoS parameters are derived from an activity coefficient model using either the Huron-Vidal or the Zero Reference Pressure (ZRP) approach. As it is a fact that Wilson's activity coefficient model cannot predict liquid-liquid equilibria (LLE), this article attempts to answer the question: if Wilson's model is coupled with a cubic EoS, is the resulting model capable of predicting LLE?

This question is actually becoming increasingly important as recent EoS rely on such a coupling (e.g., the tc-PR EoS). We show that although Wilson's model is mathematically unable to predict instable liquid phases, this is not true for Wilson-EoS models (i.e., EoS incorporating Wilson's model). However, it is also shown that the capacity of Wilson-EoS to predict LLE depends not only on the approach chosen (Huron-Vidal or ZRP) but also on mixture characteristics (such as the ratio of covolumes, the ratio of critical attractive parameters, the binary interaction parameters etc.).