Force Balance Model and Bubble Rebound Law for Bubble-Wall Collision

The vertical collision of rising bubbles in liquids against rigid wall in the range of Morton numbers Mo=10^-8~10^-12 and Reynolds numbers Re=5~750 were analyzed theoretically and the bubble rebound law was studied. The equations of motion for bubble rising and colliding with wall take into account buoyancy force, liquid resistance, added mass force and film-induced force. The variation of liquid film thickness between bubble interface and wall was calculated by Stokes-Reynolds equation. The fluid pressure caused by bubble deformation in membrane was solved by Young-Laplace equation. The results show that the film-induced force model based on SRYL equation can well predict the rebound trajectory of the bubble. The bubble can rebound from 0 to many times with increasing Reynolds number, and the calculated results are in good agreement with the experimental results. During bubble collision and rebound from the wall, bubble interface formed abundant film shapes, such as dimple, pimple and wimple. Deformation of the bubble interface caused the change of pressure in the film. The distribution of pressure is closely related to the shape of bubble interface. The film-induced force plays a dominant role on the bubble motion when bubble interacts with rigid wall. The maximum induced force increases with the increase of Reynolds number. The number of rebound times of air bubble is directly related to the Reynolds number. The critical Reynolds number for the transition of bubble rebound times is almost the same at different Morton numbers.