An Interfacial Curvature Distribution Model and Phase Inversion

The state of the two-phase system is described by the interfacial curvature distribution. A phenomenological closure model is proposed for the exact (unclosed) equations. Parameters of the model are related to the existing correlations for drop size in stirred flows. If water is dispersed in oil, the curvature has a uni-modal distribution with a positive mode. When a control parameter, e.g., water volume fraction is increasing, the distribution becomes bi-modal with both negative and positive values. After a while, the phase inversion occurs, and the distribution becomes uni-modal with a negative mode. Going in the other direction the phase inversion happens at lower volume fraction of water, i.e., there is an ambivalent region, where both phases might be in the dispersed state. The model implies, that even if the conditions for phase inversion are met, there might be a significant delay before the new morphology is established.