(742b) Population Balance Equation Modeling of Emulsion Drop Coalescence in High Pressure Homogenization

Previously we have developed population balance equation (PBE) models of drop breakage in oil-in-water emulsions prepared with high pressure homogenization. These models were based on the assumption of negligible drop coalescence, which is reasonable for emulsions with low dispersed phase volume fractions and large surfactant loadings. However, many industrial emulsions do not satisfy these conditions and drop coalescence must be understood for rational emulsion design and processing. Other researchers have proposed inverse PBE methods for the extraction of the coalescence kernel from transient drop distribution measurements. The major shortcoming of inverse methods and many other PBE modeling techniques is that the coalescence functions do not depend explicitly on formulation and processing variables. Such coalescence kernels have limited predictive capabilities as the PBE model must be refit to each new set of experimental data in which formulation and/or processing variables were changed.

In this contribution, we demonstrate that drop distribution data from a high-pressure homogenizer can be used to identify drop coalescence mechanisms. Collision frequency and coalescence efficiency functions that depend explicitly on the emulsion properties (disperse phase volume fraction, density, and viscosity, interfacial tension) and the homogenization pressure were considered. To minimize the impact of drop breakage and isolate the coalescence phenomenon, we performed a series of homogenization experiments in which the emulsion was processed at very high pressure until a constant drop volume distribution was obtained and the resulting emulsion was further processed at a lower pressure. Drop volume distribution measurements at the lower pressure were used to estimate adjustable parameters in the collision frequency and coalescence efficiency functions using nonlinear parameter estimation. We evaluated the ability of the PBE model to predict experimental results not used for parameter estimation. By combining the coalescence kernel with the breakage functions determined in our previous studies, we developed a single model capable of predicting the combined effects of drop breakage and coalescence.