The collision efficiency of small particles with spherical air bubbles

Abstract

Trajectories are calculated for particles in the path of a spherical bubble rising in an infinite pool of liquid. From grazing trajectories, collision efficiences are calculated corresponding to values of a particle inertia parameter K down to 0·001 and a particle gravity parameter G up to 0·3 for both Stokes and potential flow fields around the bubble. Limiting values of collision efficiency corresponding to K → 0 are derived and are shown to be the same for both potential and Stokes solutions. The solutions of the equations of motion are verified experimentally and the existence of an optimum bubble size for recovering an ore particle by flotation is demonstrated. From a simplified description of a bubble assemblage, it is shown that the collision efficiency of particles with bubbles in a swarm can be several times as large as those calculated from a single sphere model even at large bubble separations.