THE RATE OF COALESCENCE IN A SUSPENSION OF HIGH REYNOLDS-NUMBER, LOW WEBER NUMBER BUBBLES

The interactions between bubbles of nearly equal size (size ratio less than 1.1 at Re=100, and size ratio less than 1.07 at Re=200) in a sus pension of bubbles rising due to gravity were analyzed under high Reyn olds number, low Weber number conditions. The potential flow interacti on between a pair of bubbles was studied using the equations of motion derived by Kumaran and Koch [Phys. Fluids A 5, 1123 (1993)]. If the h orizontal distance between the bubbles is smaller than a critical valu e, the bubbles approach each other along the horizontal plane and coll ide. Previous studies suggest that in a collision, the bubbles could e ither coalesce or bounce off each other. If it is assumed that the bub bles bounce when they collide, they continue to collide repeatedly. Th e amplitude of the oscillations decrease due to viscous drag, and ulti mately the bubbles rise as a horizontally aligned pair. In this config uration, scaling arguments indicate the bubbles coalesce in finite tim e. The coalescence frequency in a suspension of bubbles was calculated by averaging over pair interactions. This procedure is valid for V mu ch less than 18/Re, where V is the volume fraction of the bubbles. The coalescence frequency is proportional to V Re-2/5 in this limit.