Predictions of terminal rising velocity, shape and drag coefficient for particle-laden bubbles

The motion of particle-laden bubbles is common in the gas–liquid-solid three-phase process like flotation. In this study, the motion of particle-laden bubbles in the stagnant deionized water was obtained by high-speed dynamic imaging. The experimental ranges of the mean bubble diameter and particle diameter were 2.76–3.95 mm and 58.2–196.35 μm, respectively. Results show that the terminal rising velocity decreases with the increase in the diameter of covering particles and the decrease in bubble diameter. For the coverage below 50%, the terminal rising velocity decreases sharply as coverage increases; while for 50% to nearly 100%, decreases slowly. The sharp decrease is mainly because particles immobilize the bubble surface and increases the drag, which is similar to the effect of contaminants in liquid on bubble motion. When the coverage exceeding 50%, the interface mobility of particle-laden bubbles is completely retarded. The slow decrease is attributed to the decreasing net buoyancy caused by decreasing density difference between water and the particle-laden bubble. Based on the impact of particle coverage on bubble behavior, the measured data were compared with predictions by the available models of the terminal rising velocity and drag coefficient for the bare bubble in the contaminated liquid. Comparison results show that the terminal rising velocity model given by Zheng et al. (2020) and the drag coefficient model given by Wang et al. (2019) can be extended to particle-laden bubbles with a mean error of 4.8% and 0.6%, respectively. The aspect ratio of particle-laden bubbles is negatively correlated to the terminal rising velocity like that of bare bubbles. A new aspect ratio prediction model for particle-laden bubbles related to the ratio between coverage and the Eo number was introduced to facilitate direct prediction of the terminal rising velocity. The comprehensive prediction models of particle-laden bubbles behaviors given in this study are helpful for the design and optimization of equipment that contains bubble-particle aggregates.