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 suspension of bubbles rising due to gravity were analyzed under high Reynolds number, low Weber number conditions. The potential flow interaction 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 horizontal distance between the bubbles is smaller than a critical value, the bubbles approach each other along the horizontal plane and collide. Previous studies suggest that in a collision, the bubbles could either coalesce or bounce off each other. If it is assumed that the bubbles bounce when they collide, they continue to collide repeatedly. The amplitude of the oscillations decrease due to viscous drag, and ultimately the bubbles rise as a horizontally aligned pair. In this configuration, scaling arguments indicate the bubbles coalesce in finite time. The coalescence frequency in a suspension of bubbles was calculated by averaging over pair interactions. This procedure is valid for V much 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.