Translation and nonspherical oscillation of single bubble in ultrasound field

Abstract

Based on the perturbation theory and generalized Bernoulli equation, the equations describing the radius, translation and deformation of a single gas bubble in ultrasonic field are derived. The evolutions of the radius, displacement and deformation of the bubble with time can be obtained by numerically calculating these equations. The calculation results show that when the initial radius of the bubble and the driving pressure both keep constant, the displacement and shape variable of the bubble increase with the augment of the initial translational velocity of the bubble’s center, and the non-spherical vibration of the bubble becomes more intense. However, the radial vibration of the bubble almost remains unchanged. When the initial translation velocity of the bubble is relatively small, the unstable region is concentrated only in the region of high driving sound pressure in the <inline-formula><tex-math id="M3">\begin{document}$R_{0}\text-p_{\rm a}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M3.png"/></alternatives></inline-formula> phase diagram of the bubble. As the initial translational velocity increases, the region with small radius and driving sound pressure begins to show instability, and the overall unstable region gradually increases. In addition, a bubble presents different vibration characteristics at different positions in the acoustic standing wave field. The closer to the antinode of sound wave the bubble is, the greater the radial amplitude of the bubble’s vibration is. However, the variable of the translation and shape of the bubble are very small. The error between the plane fractions of the unstable region in the phase diagram of <inline-formula><tex-math id="M4">\begin{document}$R_{0}\text{-} p_ {\rm a}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M4.png"/></alternatives></inline-formula> is less than 4%.