Particle capture by expanding droplets: effects of inner diffusion

Abstract

Fast agglomeration by emulsion binders to capture fine, hydrophobic particles has been developed in the past few years as an alternative to froth flotation by small air bubbles. This new method consists of mixing a particle suspension and saltwater-filled droplets covered with semi-permeable oil layers. These droplets expand due to an osmotic flux of water caused by the presence of salt inside the droplets. To better understand the physics underlying this novel particle capture method, we investigate binary interactions between droplets and particles. The current work examines the dynamics of a rigid spherical particle and a semi-permeable spherical drop that expands due to osmosis in an external, pure-extensional flow field. The droplet is governed by an expansion-diffusion problem, which is coupled to the set of dynamical equations governing the relative particle trajectory. By performing multiple trajectory simulations, we calculate transient collision efficiencies, which can be used to determine the collision kernel for population dynamics. We also use these simulations to better understand the evolution of the microstructure by determining the transient behaviour of the pair distribution function. Our results indicate that the presence of drop expansion increases the collision efficiency of the system, especially for very small particles, which are the most difficult to capture by froth flotation. Moreover, although the presence of slow salt diffusion inside the drops can mitigate this improvement, the contribution of expansion to the collision efficiency may still be considerable, even in the absence of hydrophobic or other attractive forces.