Incorporating Surfactant Coverage and Drop Coalescence Into Population Balance Models of High Pressure Emulsification

Population balance equation (PBE) models of emulsification processes allow the prediction of the drop size distribution, a critical determinant of emulsion properties. Many PBE models that account only for drop breakage have been developed for model emulsion systems with relatively low oil-to-surfactant ratios. However, industrial practice is to reduce manufacturing costs by minimizing surfactant use and establish process conditions under which drop coalescence is appreciable. In this study, we incorporated surfactant coverage and drop coalescence into our previously developed breakage-only PBE model of high pressure homogenization (Raikar et al., 2009, Raikar et al., 2010)  to allow the prediction of drop size distributions for high oil-to-surfactant ratios used industrially.

Drop breakage under turbulent homogenization conditions was modeled with two distinct breakage rate functions and a distribution function that accounted for the formation of multiple daughter drops from a single breakage event. Drop coalescence was incorporated through the addition of two functions for the drop collision rate and the coalescence efficiency of binary collision events. The coalescence efficiency was assumed to be dependent on the surfactant surface coverage of each drop, with no coalescence possible when both drops have maximum coverage and the efficiency increasing as both drop become less covered. We investigated both equilibrium and dynamic equations for predicting the surface coverage from the drop size distribution and the free surfactant concentration. The system of equations was closed by adding a dynamic balance on the free surfactant, which also allowed a time varying interfacial tension to be computed.

By utilizing nonlinear optimization to estimate six adjustable parameters in the breakage and coalescence functions from measured drop distributions, the combined breakage-coalescence model was shown to provide superior predictions as compared to the breakage-only model for Pluronic F-68 surfactant and emulsions with high oil-to-surfactant ratios. Because mechanistic breakage and coalescence functions that included emulsion properties and homogenization conditions were used, the model was able to satisfactorily predict drop size distributions at other surfactant concentrations and operating pressures without re-estimation of the parameters. The model was able to generate acceptable predictions for other non-ionic surfactants if the appropriate surfactant coverage model was used and model parameters were re-estimated using data for the particular surfactant.

References

Raikar N.B., Bhatia S.R., Malone M.F. and Henson M.A, “Experimental Studies and Population Balance Equation Models for Breakage Prediction of Emulsion Drop Size Distributions”, Chemical Engineering Science, 64 (2009), 2433-2447.

Raikar N.B., Bhatia S.R., Malone M.F., McClements D.J., Almeida-Rivera C., Bongers P. and Henson M.A., “Prediction of emulsion drop size distribution with population balance equation models of multiple drop breakage”,Colloids and surfaces A: Physicochemical and engineering Aspects, doi: 10.1016/j.colsurfa.2010.03.020