A review of stochastic description of the turbulence effect on bubble-particle interactions in flotation

Flotation in mechanically agitated cells has been the workhorse of the mining industry, but our quantitative understanding of the effect of microturbulence generated by agitation on flotation is still very limited. This paper aims to review the literature on quantifying the microturbulence effects on bubble-particle interactions in flotation. The particular focus is on the stochastic description of bubble-particle interactions in the turbulent flow which is a random field. We briefly review the stochastic description of microturbulence and motions of particles of micrometre sizes and bubbles of millimetre sizes in the isotropic turbulence of mechanical flotation cells. The key starting point is the generic equation of motion, which can be decomposed into the mean turbulent variables and fluctuating turbulent variables. The turbulent flow of the carrying liquid is characterised using isotropic turbulence theory. The next focus is on reviewing bubble-particle turbulent collision and detachment interactions. Bubble-particle turbulent collision is poorly quantified; no quantitative models of the bubble-particle turbulent collision efficiency relevant for flotation are available. Current theories on bubble-particle turbulent detachment face some deficiencies. In assessing the microturbulence effect on bubble-particle detachment, the majority of studies only considers the particle acceleration in the centrifugal direction but ignore the transverse acceleration of particles, which is due to turbulent shear flow. Critically, contact angle required in quantifying the detachment is not constant, single-valued as considered in the theories, but can vary from receding to advancing value during the relaxation of the triple contact line on the particle surface. The latest experiments show that multiple-valued contact angle can significantly affect stability and detachment of floating particles. Finally, quantifying the microturbulence effect on flotation requires further research