The impact of mass transfer and interfacial expansion rate on droplet size in membrane emulsification processes

In membrane emulsification, especially under conditions where droplets are forming with a narrow droplet size distribution, it is conjectured that the interfacial phenomena are determining the emulsification result. The process parameters of continuous phase flow and dispersed phase flux were analysed from the perspective of how they could be affecting the interfacial tension of the growing droplet. This work first reviews the applicability of current droplet formation models (force balance and spontaneous transformation based (STB)), describes the interfacial transport of surfactant molecules to an expanding oil-water interface, and models the flow of dispersed phase through a pore using MATLAB. The data from these calculations are then applied in a model to predict the final size of the droplets, which includes dynamic effects of mass transfer and expansion rate. The droplet detachment mechanism in membrane emulsification was modelled from the point of view of Gibbs free energy. An interactive finite element program called the surface evolver was used to test the model. A program was written and run in the surface evolver, which allows the user to track the droplet shape as it grows, to identify the point of instability due to free energy, and thus predict the maximum stable volume (MSV) attached to the pore. The final droplet size was found by applying a pressure pinch constraint (PPC), which is based on the division of the surface into two volumes, a droplet and a segment, which remains attached to the pore mouth. The relative size of these two volumes is such that the resulting radii of curvature of the droplet will maintain an equal Laplace pressure across the surface of both volumes. Predicted droplet sizes were compared to experimental data from the literature. It was found that changes in surfactant coverage caused by mass transfer coupled to the expansion rate of the oil-water interface have a significant and predictable effect on the final droplet size in