Particle–bubble encounter probability with mobile bubble surfaces

Abstract

The mechanics of encounter between a particle and a bubble with a mobile surface and of intermediate Reynolds number has been analysed. Water velocities around the forward bubble surface are approximately predicted using the numerical solution to the Navier–Stokes equation. The order-of-magnitude analysis is employed to investigate the influence of inertia on the particle velocities around the bubble surface and the particle–bubble encounter (collision) probability. The predicted probability agrees well with the available experimental data. The particle–bubble encounter probability is strongly reduced when the inertial effect is considered. The physical reason behind this is the non-zero tangential water velocity on a mobile bubble surface, which pulls particles away from the forward bubble surface. The predicted collision angle is significantly influenced by the inertial effect. The encounter probability prediction in this article is complementary to the available encounter probability models with immobile bubble surfaces in flotation.