On modelling of bubble–particle attachment probability in flotation

Abstract

We have developed the theoretical basis for experimental determination of bubble–particle attachment probability in single-bubble flotation experiments. We use these experimentally determined data to simulate the dependence of induction time on particle size. Using these simulated results, we verify the bubble–particle attachment probability prediction developed on the basis of sliding time and induction time (the Sutherland approach). We have calculated the induction times of fine quartz particles of different diameters less than 80 μm and different hydrophobicity, collected by single bubbles with diameters of 0.75 mm, 1.2 mm and 2.0 mm. The simulation reported in this present paper shows that the calculated induction times increase with decreasing particle size, except for particles of strong hydrophobicity (advancing water contact angle of 65° and 88°) collected by the small bubbles with a diameter of 0.75 mm. These results for induction time indicate that extant attachment probability models, based on sliding time and induction time, cannot adequately describe the elementary steps in the bubble–particle attachment microprocess in flotation. A detailed analysis of induction time, as originally defined and measured by Sven-Nilsson and others was performed. The necessity of the elementary step `rupture of liquid film and formation of three-phase contact of a critical radius (TPC nuclei)' in bubble–particle attachment has been demonstrated. It is suggested that attachment probability can be adequately described by the product of the probabilities of three elementary steps: (1) thinning of intervening liquid film to a critical film thickness; (2) rupture of intervening liquid film and formation of TPC nuclei; (3) expansion of three-phase contact line from the critical radius to form a stable wetting perimeter. The attachment probability model developed according to the Sutherland approach describes only the first elementary step. The poor response of fine particle flotation may be attributed to the decreasing probability of the second elementary step. A more detailed investigation of these elementary steps is required for understanding the attachment microprocess in flotation.