Probability of particle attachment on gas bubbles by sliding

The hydrodynamic interaction between particles and bubbles in laminar and nonlaminar flow fields during flotation consists of colliding and sliding processes. The latter takes place if a smaller particle moves over the surface of a larger bubble. During this sliding process the thin liquid film between both particles must drain off to its critical thickness and must rupture, resulting in the formation of a three-phase contact and attachment. The probability of attachment becomes higher as the sliding time, in comparison with the film drainage time, increases. In this paper explicit approximate equations for sliding, which can be solved numerically, are presented for the first time. They are based on a quasi-stationary, almost circular, movement of the particles over the bubble's surface. The criterion for attachment is the achievement of the critical film thickness. The probability of attachment is then characterized by a critical touching angle φcrit. The sliding time of the particle was evaluated from equations of motion and compared with experimental data.