(47g) 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