Development of a flotation recovery model with CFD predicted collision efficiency

In this study, a novel flotation recovery model based on a first-order kinetics is proposed. The collision efficiency in the recovery model was directly obtained from 3D computational fluid dynamics (CFD) simulations involving a single-bubble-multi-particle aggregate system with typical flotation operating conditions (bubble diameter of 1 mm and particles diameter of 30 µm). The effect of the fluctuating flow field on collision was accounted using a large eddy simulation (LES) turbulence model for two turbulence intensity cases namely 4% and 20%, respectively. It was noted that the collision efficiency decreased in the radial direction away from the symmetry axis of the bubble. The normalized equivalent critical radius K₁ for the overall collision efficiency, was found to be optimum at the lower turbulence intensity of 4%. A maximum bubble surface loading, 0.142 was determined by fitting the model-predicted bubble velocity with available experimental data. With this maximum bubble surface loading constraint, the recovery model predicted two regimes namely a loading regime in the early flotation period and a saturated regime wherein the bubble loading capability was entirely exhausted. Simulation of a batch flotation system suggested that loss in bubble surface loading capacity occurred faster in a dense pulp compared to a dilute pulp system and the predicted recovery decreased with increasing solids concentration for the same gas volume fraction. Similar to the collision efficiency, the optimum recovery was obtained at Ti = 4%. Further, the model predicted recovery was compared to a lab scale coal flotation test and reasonable agreement was obtained.