Incorporating emulsion drop coalescence into population balance equation models of high pressure homogenization

Population balance equation (PBE) models of emulsification processes allow the prediction of the drop size distribution, a critical determinant of emulsion properties. While many PBE models that account only for drop breakage have been developed for model emulsion systems with relatively low oil-to-surfactant ratios, industrial practice is to minimize surfactant use to reduce manufacturing costs and establish process conditions under which drop coalescence is appreciable. In this study, we incorporated coalescence into our previously developed breakage-only PBE model of high pressure homogenization to allow the prediction of drop size distributions under high oil-to-surfactant ratios used industrially. Drop breakage under turbulent homogenization conditions was modeled with two distinct breakage rate functions and a distribution function that accounted for the formation of multiple daughter drops. Drop coalescence was incorporated through the addition of two functions for the drop collision rate and the coalescence efficiency of collisions. By utilizing nonlinear optimization to estimate six adjustable parameters in the breakage and coalescence functions from measured drop distributions, the combined breakage–coalescence model was shown to provide superior predictions as compared to the breakage-only model for emulsions with high oil-to-surfactant ratios. Because mechanistic breakage and coalescence functions that included emulsion properties and homogenization conditions were used, the model was able to satisfactorily predict drop size distributions at other surfactant concentrations and operating pressures without re-estimation of the parameters. The model was able to generate acceptable predictions for two other surfactants if the model parameters were re-estimated using data for each surfactant.