(381d) Capture of Fine Particles By Expanding Drops in Linear Flows

This theoretical work is motivated by a new agglomeration method that overcomes the inability of standard flotation methods for capturing very small particles. This method consists of vigorously mixing an aqueous suspension of particles with a binder of saltwater-filled droplets covered with semi-permeable oil layers. Here, we investigate the two-particle dynamics of a solid particle and a semi-permeable spherical drop that expands due to osmosis in an external pure extensional flow field. The computational results from the numerical integration determine a transient collision efficiency, which describes the influence of hydrodynamic interactions and osmotic flow on particle capture. The results show that drop expansion effects, which decay slowly with time, greatly increase particle capture rates. Moreover, as the engulfment parameter (a dimensionless ratio between expansion and flow effects) increases, there is a transition from a flow-dominated capture behavior to an expansion-dominated capture behavior. For the case of a non-expanding droplet, we provide a numerical solution of the transient pair distribution function, which enables us to better explain the transient particle capture rate in terms of microstructure of the suspension. Furthermore, we derive an exact expression for the initial collision efficiency at zero times, which agrees with our numerical data, and also demonstrate agreement of the numerical results for non-expanding droplets (after a short transient period) with the theoretical steady-state from traditional pairwise trajectory analyses.