Modeling the bubble loading based on force balance on the particles attached to the bubble

Abstract 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.