Modeling of hydrophobic particle capture by expanding droplets

The method of froth flotation by small air bubbles has been traditionally used in industry to capture fine minerals and other hydrophobic particles. This method, however, has shown to not be efficient for capturing smaller particles. The present work is motivated by a new agglomeration method proposed to overcome this lack of efficiency. It consists of mixing a particle suspension and saltwater-filled droplets covered with semi-permeable oil layers. The present work investigates the two-particle dynamics of a solid particle and an expanding semi-permeable spherical drop in an external pure extensional flow field. The computational results from the numerical integration determine a collision efficiency, which describes the influence of hydrodynamic interactions and osmotic flow on particle capture. An engulfment parameter measures the relative effects of droplet growth and convective flow.