Predicting Catastrophic Phase Inversion on the Basis of Droplet Coalescence Kinetics

Abstract

A predictive model for catastrophic phase inversion, based on the kinetics of droplet breakup and coalescence, is presented here. Two inversion mechanisms can be distinguished, depending on the direction of the phase inversion process. With the surfactant predominantly present in the dispersed phase, the coalescence rate is high and phase inversion takes place at relatively low volume fractions. Going in the other direction, surfactant is predominantly present in the continuous phase. The coalescence rate is dramatically lowered because of the Gibbs-Marangoni effect, and difficult inversion will not take place up to relatively high volume fractions. Experiments were carried out in a stirred vessel, where phase inversion was detected by a jump in emulsion conductivity. Easy inversion points were found on the order of 20-50% volume fraction of the dispersed phase. Difficult inversion was not detected up to 97% dispersed phase. The easy inversion point increases with dispersed phase addition rate and is independent of the stirrer speed below a stirrer speed of 1500 rpm. A simple model based on the breakup and coalescence rate of emulsion droplets in the easy inversion regime allows us to calculate the stationary droplet size as a function of the volume fraction of the dispersed phase, as well as the evolution of the droplet size in time under addition of dispersed phase. The stationary droplet size diverges above a critical volume fraction of 26.4%, indicating phase inversion. This model can qualitatively describe hysteresis and the phase inversion point dependence on stirrer speed and dispersed phase addition rate, as found in our experiments.