An Integrated Formulation for Particle-Bubble Detachment

"In flotation research, relatively little attention has been paid to understanding particle-bubble detachment phenomena compared with attachment processes. With CFD models now incorporating attachment/detachment kinetics, it is important to obtain more accurate formulations for detachment probability. The formula most often used is due to Bloom and Heindel (2002) who proposed that the rate of detachment would equal the product of detachment frequency, as previously estimated by other authors, and probability of destabilization, as estimated previously by Schulze. These two factors both account for the balance between stabilization and destabilization forces, so the product accounts for this effect twice. An integrated procedure has been followed to estimate the overall detachment rate by re-analysing the process. In this analysis, detachment rate is calculated as the frequency of eddy-aggregate interactions (or “collisions”) sufficiently energetic to cause detachment. The Bond number analysis of Schulze has been incorporated into the turbulence frequency analysis of previous authors in an integrated way. The new formulation has essentially the same type of dependencies as the previous model, but gives a lower detachment frequency. Detachment frequency has been calculated using the new formula for conditions relevant to an industrial flotation cell. INTRODUCTIONIt is well known that the effectiveness of froth flotation for separating different minerals is limited to the particle size range of approximately 10–100 mm (Trahar & Warren, 1976; Trahar, 1981). Fine particles tend to follow fluid streamlines around bubbles limiting the likelihood of bubble–particle collision, while coarse particles can be more easily detached from bubbles before collection can be achieved.Phenomenological models have been developed to quantify the physico-chemical aspects of flotation in order to better understand factors affecting these limitations, and to suggest ways of broadening the window of feasible flotation. Koh and Schwarz (2008) have incorporated these models into computational fluid dynamics (CFD) models of flotation cells, which have then been used for design and scale-up purposes (Schwarz et al., 2015). The models are based on dividing the process of bubble–particle interaction into three subprocesses: collision, adhesion and detachment. Of these, the hydrodynamics of bubble–particle collision and the probability of adhesion have been studied most extensively, while the dynamics of detachment have received relatively little attention from investigators."