Hydrodynamics of liquid flows around air bubbles in flotation: a review

This review aims to predict liquid velocity components around an air bubble in flotation. The prediction is based on the Navier-Stokes equations expre ssed in terms of stream function and vorticity. The relevant analytical and approximate solutions for a bubble mobile and immobile surface are reviewe d. Numerical solutions to the Navier-Stokes equations with particular refer ence on the flow fore-and-aft asymmetry, surface vorticity and surface pres sure are graphically illustrated and discussed. Based on the analytical, ap proximate and numerical solutions, the liquid velocity components in close proximity to a surface of air bubbles with intermediate Reynolds numbers an d finite gas holdups are predicted. Application of the predicted velocity c omponents is illustrated for the modelling of the bubble-particle encounter and sliding interactions. Generalised formulas for the bubble-particle enc ounter and attachment efficiencies are demonstrated. The analysis of the in ertial effect on the bubble-particle interactions with a small particle Sto kes number is undertaken and reveals that the inertial effect is relevant i f the bubble surface is mobile. The significance of the gas holdup and the bubble surface mobility in the bubble-particle interactions is analysed and discussed. (C) 1999 Elsevier Science B.V. All rights reserved.