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In flotation, among the key parameters that dictate the hydrodynamic characteristics are bubble rising velocity and trajectory. This study aims to investigate the trajectory and rise velocity of lo...

In this study, a theoretical evaluation of the effect of inertial forces in particle-bubble interactions during the flotation process is presented and supported by the experimental data. The effects of positive and negative inertial forces were analyzed by comparing the differences between the models, which either consider or neglect the inertial forces. The Sutherland collision model and the Nguyen attachment model that completely ignore the effect of particle’s inertial forces (inertialess models) were implemented into the general flotation kinetic model. The modified model was then compared with one of the most accurate inertial models, which considers the Generalized Sutherland Equation (GSE) for collision efficiency along with the Dobby-Finch model for attachment efficiency. The flotation kinetics of chalcopyrite and galena particles were estimated using the general flotation kinetic model in order to demonstrate the effect of particle density on the model, which emphasizes the effect of inertial forces. The influence of positive and negative inertial forces on flotation kinetics was evaluated for various explicit parameters such as particle density, turbulence (energy dissipation), and bubble size and velocity. Obtained theoretical results clearly showed the potential of the particle density to counterbalance the negative effects of the inertial forces. The capability of the positive inertial forces for galena particles (high density) to overcome its negative effect was shown when the general flotation kinetic model was used. Theoretical calculations were further confirmed by experimental bubble loading measurements. It was shown that the inertial forces should not be omitted in any flotation model amidst concerns over the complexity.

This study aimed to introduce a new approach to determine the mass transfer rate constant in a laboratory column flotation through an analogy to a mass transfer process. The RTD of the column at two separate bubble sizes were modeled using both conventional N-mixer and N-mixer with back-mixing flow models. The number of perfect mixers (N) and the corresponding backflow coefficients (λ) were optimized using MINLP solver in MATLAB environment where N = 5 with λ = 0.567 at the bubble size of 1.8 mm and N = 8 with λ = 0.643 at the bubble size of 0.8 mm were obtained. The bubble active surface coefficient was introduced as a new parameter to study the flotation kinetics. Thus, the mass transfer rate constant was determined for various operational conditions based on the bubble active surface coefficient and bubble loading measurements. Results showed that the mass transfer rate depends on the physical and surface properties such as particle size, particle surface hydrophobicity, and the carrying capacity. At the fine particle size, the mass transfer continues such that a long bubble retention time is required. However, for the coarse particles, bubbles reach their maximum loading capacity prior to the pulp-froth interface so that any additional retention time does not contribute to the flotation. Besides, at the coarse particle size, due to the poor stability of the aggregates, especially for particles with low surface hydrophobicity, the mass transfer rate and thereupon the bubble loading decreases remarkably. Moreover, the fine particles show lower flotation kinetics in the presence of the large bubbles.

Loading of particles on a bubble is the result of a successful collision, attachment, and balancing of the forces between particles and the bubble. In this study, a mathematical model to estimate the bubble loading was developed based on the force balance on the lowest particle attached to the bubble. Gravity, buoyancy, hydrostatic pressure, viscous drag, capillary, and capillary pressure induced forces were taken into account in the model. The resultant force of the tangential components of the normal force applied by particles on top of the lowest particle and the viscous drag exerted on the attached particles by the surrounding fluid is balanced with other forces to predict whether detachment of the lowest particle occurs or not. The model estimation results were further compared with the experimental measurements using monodisperse silica beads and two minerals with different densities in a steady state column flotation to validate the model. Comparison results indicate a close agreement with a very minor discrepancy that could be attributed to the shape and morphological features of solid particles used for the flotation experiments.