Under some circumstances, a bubble impacting at a free surface bounces repeatedly prior to coalescence. This phenomenon can be very quick (about few milliseconds), so the human eye cannot be able to observe it.
Time evolution:
Figure 1: Snapshots of rising bubbles and the interaction with the free surface. From top to bottom: bubble equivalent diameters of 1.62, 1.06 and 0.43 mm respectively.
In Figure 2, the time evolution of the vertical position of the bubble center during the bouncing process is presented.
Figure 2: Time evolution of vertical position of the bubble center during the bouncing process.
Steady rise:
The drag coefficient in the steady rise zone can be approximated as
where G is given by
and H must be obtained numerically, although a convenient approximation for aspect ratios lower than 2 is:
To characterize the effects of the Weber number on aspect ratio, Moore employed potential low solution over an oblate spheroid to obtain the following implicit relation:
which is applicable to bubbles with a slip flow along the bubble surface, driven by internal circulation.
Effect of bubble size:
Smallest bubbles coalesce just as they touch the free surface, while larger bubbles can bounce a few times before coalescing.
Figure 3: Time evolution of the normalized vertical position and normalized velocity of the bubble center during the bouncing process.
