Criteria for bubble collapse in finite depth liquid

A mathematical model of bubble collapse in the finite depth liquid owing to initial bubble wall motion is established. The proposed model considers some important influences, such as fluid viscosity, initial bubble wall motion, height of liquid on the bubble collapse. It is a modified model of the traditional R-P equation, and the criterion closely relates to the height of liquid and the initial bubble wall motion. With the increase of the liquid depth, the bubble is apt to collapse in advance. In addition, the height of liquid affects hardly the criteria of bubble collapse if it is 100 times more than the initial radius of bubble, which can be regarded as the bubble situating in an infinite depth liquid. The bubble is hard to collapse if the initial bubble wall velocity is zero. On the contrary, the bubble collapses easily if the bubble wall has the initial shrinkage velocity. A correlation to predict the critical bubble collapse is proposed under the condition of the zero initial bubble wall moving velocity and compared with the results in the existing references.