圆锥泡声致发光气泡动力学过程的理论分析

在绝热压缩模型的基础上, 详细讨论了圆锥泡声致发光中气泡运动的动力学过程，得到了气泡塌陷速度方程、气泡内压强方程以及温度方程. 结果显示在气泡进入圆锥腔的初始阶段，气泡的塌陷速度随着压缩半径的不断减小近似线性地增加；然后随着压缩半径的进一步减小，气泡塌陷的加速度逐渐减小；当气泡塌陷速度达到最大值后，随着气泡压缩半径的进一步减小, 塌陷速度迅速下降至零. 在假设初始气压为1000,Pa的基础上，理论分析得到气泡的最高塌陷速度可以达到5.8,m/s; 气泡的最小压缩半径可以达到1.37,cm, 相应的气泡内极限压强超过$4.5times10^5$,Pa, 极限温度超过3,150,K, 而液流能够提供给气泡的能量达到0.02,J. 理论推导得到的结果可以比较好地用来解释实验中的现象. 最后分析得到气泡内的初始气压对气泡所能达到的极端条件有着重要的影响.

THEORETICAL STUDY ON DYNAMIC PROCESS OF CONICAL BUBBLE SONOLUMINESCENCE

The dynamics process of the conical bubble sonoluminescence hasbeen discussed based on the adiabatic process. The equations of velocity ofbubble collapse, the pressure and temperature within the bubble have beenachieved. Result show the velocity of collapsing bubble approximatelylinearly increases with the decrease of the radius of collapsing bubblefirstly, then the maximal velocity of collapsing bubble can be achieved,subsequently the velocity of collapsing bubble quickly decreases. Based onthe supposition of initial pressure equal to 1,000,Pa, the maximal value ofthe velocity of bubble collapse reaches 5.8,m/s, the minimum radius of thebubble is 1.37,cm, then the huge pressure of $4.5times 10^5$,Pa, thecollapsing temperature above 37,000,K, and the maximal energy about 0.02,Jproviding to the bubble can be achieved. The equations obtained in thispaper could explain the phenomena of experiment. Finally, results show thatthe initial pressure within the bubble has important effects on the finalextreme conditions.