Application of Population Balance Models in Particle-Stabilized Dispersions

In this study, a first approach to model drop size distributions in agitated nanoparticle-stabilized liquid/liquid systems with population balance equations is presented. Established coalescence efficiency models fail to predict the effect of steric hindrance of nanoparticles at the liquid/liquid interface during the film drainage process. A novel modified coalescence efficiency is developed for the population balance framework based on the film drainage model. The elaborate submodel considers the desorption energy required to detach a particle from the interface, representing an energy barrier against coalescence. With an additional implemented function in the population balance framework, the interface coverage rate by particles is calculated for each time step. The transient change of the coverage degree of the phase interface by particles is thereby considered in the submodel. Validation of the modified submodel was performed with experimental data of agitated water-in-oil (w/o) dispersions, stabilized by well-defined spherical silica nanoparticles. The nanospheres with a size of 28 nm are positively charged and were hydrophobized by silanization with dimethyloctadecyl[3-(trimethoxysilyl)propyl]ammoniumchloride. This modeling approach is a first step toward predicting time-resolved dynamic drop size distributions of nanoparticle-stabilized liquid/liquid systems.