Predicting the effects of surfactant coverage on drop size distributions of homogenized emulsions

Abstract

Population balance equation (PBE) models have been extensively used to predict drop size distributions of processed oil-in-water emulsions. Our previous work on high pressure homogenization demonstrated that both drop coalescence and breakage must be included to obtain satisfactory distribution predictions at high oil-to-surfactant ratios. While it was capable of predicting drop size distributions over a range of surfactant concentrations, this PBE model was not extensible to other surfactant types without re-estimation of adjustable model parameters. The objective of the present study was to develop a new PBE model that allows satisfactory prediction for emulsion systems with different surfactant types and concentrations given model parameters estimated from drop size distribution data collected for a single surfactant at a single concentration. This extended PBE model was developed from our previous model by adding a surfactant mass balance, including the effects of the free surfactant concentration on the interfacial tension and the surface coverage of drops and by modeling the coalescence frequency to be a function of the surfactant coverage. To demonstrate the approach, model parameters were obtained by nonlinear optimization using measured drop size distributions collected at 50wt% oil and 1wt% Pluronic F68 surfactant. These parameters were used to predict drop size distributions at 50wt% oil and 0.5–2.0wt% surfactant for Pluronic F68 and three other surfactants from the Pluronic family. We found that the extended PBE model generated substantially improved distribution predictions compared to our previous model, with the degree of improvement dependent of the surfactant used. These results represent an important step towards the use of PBE models for emulsified product design.