The secret of the Wilson equation

60 years ago, Grant Wilson proposed the first successful activity coefficient model based on the local composition concept he introduced. The model has received wide acceptance and extensive applicability as it could represent accurately the vapor-liquid equilibria of complex mixtures. It could be readily extended to multicomponent systems without additional parameters and with good results. It has not dominated the chemical engineering practice compared to models proposed a few years after (NRTL and UNIQUAC) possibly due to one important shortcoming. The Wilson equation could never represent liquid-liquid equilibria no matter the values of the model's parameters. While this is well-established, the "physical" reasons behind this deficiency had not been fully explored. This work presents and explores the secret of the Wilson equation related to its ability to predict partial miscibility. It will be established that the capabilities of the Wilson model are possibly broader compared to what was originally thought. The presentation is also inspired by several discussions with professor Michael L. Michelsen over the years which are also cited in the manuscript.