A review on determination of particle–bubble encounter using analytical, experimental and numerical methods

This paper provides a comprehensive critical review of available studies on analytical and numerical modeling including computational fluid dynamics (CFD), as well as experimental approaches to determine the particle–bubble interactions in flotation cells. The effects of some significant factors such as particle density, bubble size and velocity, and cell turbulence on the particle–bubble encounter are investigated in detail. This review indicates that interception collision models established based on stream functions are not applicable as they ignore the turbulence effect. The streamlines are not stationary in turbulent conditions and constantly change throughout time and space. Furthermore, the analytical models are restricted because of poor estimation of collision angle, Stokes numbers, effect of particle density and disregarding microhydrodynamic forces and turbulence effects. Unlike analytical modeling, numerical modeling is a very powerful technique for evaluating particle–bubble encounter interactions. The role of particle density and turbulence in particle–bubble encounter can be best identified by numerical methods. However, there is lack of experimental data to verify these models. Therefore, more specific and direct measurement techniques are required to develop accurate estimation of particle–bubble encounter probabilities. This review finally highlights the gaps in the evaluation of particle–bubble encounter efficiency and recommends further works to investigate relationships between hydrodynamic properties, particle–bubble characterizations, flotation kinetic rates and particle–bubble encounter interactions.