Prediction of emulsion drop size distributions with population balance equation models of multiple drop breakage

Most population balance equation (PBE) models of emulsion drop breakage are based on the assumption of binary drop breakage. We previously developed such a PBE model for high-pressure homogenizers with a daughter drop distribution function exhibiting a maximum probability for two equal sized drops. In this paper, we present a PBE model accounting for multiple drop breakage and show that the model provides superior distribution predictions reflected by decrease in least-squares objective function for an oil-in-water emulsion processed in a pilot-scale high-pressure homogenizer. Following our previous work, two distinct rate functions for drop breakage, one due to turbulent eddies and another due to turbulent shear were used to reproduce the measured bimodal distributions. We found that multiple drop breakage was satisfactorily modeled with a uniform daughter drop distribution function if the assumed number of daughter drops formed was chosen to be sufficiently large. The PBE model with multiple drop breakage was shown to provide superior distribution predictions compared to the analogous binary breakage PBE model when adjustable model parameters were determined by nonlinear optimization. The multiple breakage PBE model was shown to be extensible to different emulsion formulations by using these base case model parameters to predict the effects of oil concentration, surfactant concentration, oil-to-surfactant ratio and emulsion premix distribution. Our experiments revealed that substantial breakage of the premix occurred during the first homogenization pass even under zero applied homogenization pressure operation, suggesting an unmodeled pressure independent breakage mechanism.