有限深度液体中气泡的破碎条件

针对球形气泡在有限深度液体内的运动过程，建立了气泡壁初始运动导致气泡破碎的数理模型．该模型综合考虑了流体黏性力、气泡壁初始速度、有限液面高度等因素，是传统R-P方程的一种改进．研究发现气泡临界破碎条件与液体高度、气泡壁初始速度等因素密切相关，随着液体深度的增大，气泡更容易破碎．当液体深度大于气泡半径的100倍以上时，液体深度对气泡破碎临界条件几乎无影响，此时可以近似认为气泡位于无穷深液体中．当气泡壁初始速度为0时，气泡不容易破碎；当气泡具有初始收缩速度时，气泡最容易破碎．通过分析得到了气泡壁初始速度为0时的临界破碎准则预测式，并与其他文献的结果进行了比较．

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.