Permeation Network Model for the Swelling of Water-in-Oil-in-Water (W/O/W) Emulsions

Fast agglomeration by emulsion binders was recently developed as an alternative to froth flotation. It involves mixing an aqueous particle suspension with a saltwater-in-oil emulsion that swells due to osmosis and captures nearby hydrophobic particles. We previously developed a model by considering the binary interactions between single droplets and particles. In practical situations, however, particles collide with droplet agglomerates, resulting in osmotic flux being limited by the permeation of water across the oil layers between droplets. In this paper, we propose a simple network model for permeation-dominated swelling kinetics. It considers spherical saltwater droplets packed inside a spherical oil droplet. The agglomerate is generated and relaxed using a swelling Monte Carlo algorithm, which gives rise to a dynamic permeation network with water permeation between the neighboring droplets. For smaller droplets, the salt concentration is similar to the concentration-boundary-layer profiles from the effective-diffusion model. The agglomerate swelling displays a fast expansion behavior followed by the agglomerate radius increasing with the square root of time for longer times. Lower volume fractions and larger droplets result in slower growth and greater sensitivity to changes in the microstructure.