Experimental studies and population balance equation models for breakage prediction of emulsion drop size distributions

A population balance equation (PBE) model for pure drop breakage processes was developed from homogenization experiments and used to investigate model extensibility over a range of emulsion formulation and homogenizer operating variables. Adjustable parameters in the mechanistic breakage functions were estimated from measured drop volume distributions by constrained nonlinear least-squares optimization. Satisfactory prediction of measured bimodal distributions was achieved by the incorporation of two different breakage functions that accounted for large drop breakage due to turbulent shear and for small drop breakage due to collisions between drops and turbulent eddies. Model extensibility to different emulsion compositions and homogenizer pressures was investigated by comparing model predictions generated with the base case parameters to drop volume distributions measured under different conditions. The PBE model satisfactorily accounted for changes in the dispersed phase volume fraction and the interfacial tension with the base case parameters. By contrast, significantly improved predictions for the continuous phase viscosity or multiple formulation variables were obtained through re-estimation of the model parameters using multiple data sets in which the associated variables were systematically varied. The model was not able to satisfactorily predict drop volume distributions resulting from homogenizer pressure changes, perhaps due to the assumption of a constant pressure throughout the homogenizer. We conclude that PBE models of drop breakage can be used to reasonably predict the effects of emulsion formulation variables on drop volume distributions and have the potential for guiding experimental efforts aimed at the design of novel emulsified products.