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

Abstract

This review aims to predict liquid velocity components around an air bubble in flotation. The prediction is based on the Navier–Stokes equations expressed in terms of stream function and vorticity. The relevant analytical and approximate solutions for a bubble mobile and immobile surface are reviewed. Numerical solutions to the Navier–Stokes equations with particular reference on the flow fore-and-aft asymmetry, surface vorticity and surface pressure are graphically illustrated and discussed. Based on the analytical, approximate and numerical solutions, the liquid velocity components in close proximity to a surface of air bubbles with intermediate Reynolds numbers and finite gas holdups are predicted. Application of the predicted velocity components is illustrated for the modelling of the bubble–particle encounter and sliding interactions. Generalised formulas for the bubble–particle encounter and attachment efficiencies are demonstrated. The analysis of the inertial effect on the bubble–particle interactions with a small particle Stokes number is undertaken and reveals that the inertial effect is relevant if 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.