Hydrodynamic forces on high Bond bubbles rising near a vertical wall at moderate Reynolds numbers: An experimental approach

Abstract

The optimisation of industrial processes involving bubbly flows requires a deeper understanding of the forces acting on the bubbles, being particularly challenging when they rise in the presence of solid surfaces. The evolution of the drag and lift forces on a bubble rising in a stagnant liquid near a vertical wall is experimentally characterised here by high-speed imaging. The hydrodynamic forces are determined non-intrusively by applying the Kirchhoffequations to the bubble motion, using the experimental evolution of the bubble velocity and geometry. Three different rising regimes are investigated, namely, rectilinear, zigzag, and spiral, where the initial dimensionless initial horizontal wall-bubble distance, L, is varied from 1 ≤ L ≤ 4. The three cases, which fall near the transition between regimes, are defined by the Bond and Galilei numbers, (Bo,Ga) ≈ (5,60), (4,99), and (10,108), respectively, being the resulting Reynolds numbers, 60≤ Re ≤ 110. In all regimes, both the drag and lift forces increase as L decreases, even after the bubble has moved far enough away from the wall. In the rectilinear case, they remain nearly constant as the bubble rises, whereas in the unstable cases, they oscillate at twice the frequency of the bubble trajectory. The drag coefficient reaches its maximum value when the velocity is vertically aligned, while the lift coefficient peaks when the bubble is at its largest lateral distance. These results are of particular interest because, to our knowledge, there are currently no correlations in the literature that can accurately estimate the hydrodynamic forces within this range of parameters and under the influence of a nearby wall. Furthermore, the experimental measurements presented here could be used as a benchmark for more detailed numerical investigations.