Predicting the combined effects of oil and surfactant concentrations on the drop size distributions of homogenized emulsions

Population balance equation (PBE) models have been used extensively to predict drop size distributions (DSDs) of dispersed phase systems. Over the past decade, we have used the PBE framework to develop increasingly sophisticated process models for oil-in-water emulsions prepared with high pressure homogenizers. While these models can qualitatively predict the effects of formulation variables on the DSD, quantitatively accurate predictions over wide ranges of oil and surfactant concentrations remain elusive. The goal of this study was to develop a new PBE model that produced accurate DSD predictions in both the “surfactant limited regime” and the “surfactant rich regime” with a single set of adjustable model parameters. We found that the key modifications of our previous models required to generate a predictive model were: (1) reformulation of the two breakage frequency functions to behave properly with respect to drop size; (2) replacement of the constant continuous phase viscosity with a calculated emulsion viscosity that increased strongly with oil content; (3) reformulation of the drop breakage and coalescence functions to behave properly with respect to oil content; and (4) replacement of the equilibrium model of surfactant adsorption with a size independent dynamic model. Adjustable model parameters were estimated by nonlinear optimization using measured DSDs collected at 30 wt% oil and 2 wt% surfactant and at 30 wt% oil and 0.1 wt% surfactant. The parameterized PBE model generated satisfactory DSD predictions for 10–50 wt% oil and 0.1–2 wt% surfactant.