Numerical simulation of single bubble dynamics under acoustic standing waves

The objective of this paper is to apply numerical method to simulate the single bubble dynamics under the acoustic standing waves, which is an extensive research of our previous work (Ma et al. Ultrason. Sonochem., vol. 42, 2018, pp. 619-630). The Navier-Stokes equation, which considers the acoustic radiation force caused by acoustic standing wave, is used to capture the transient shape variation, pressure fluctuation, and the direction of the bubble motion, especially for the case of the bubble near the rigid boundary. Several normalized parameters, such as acoustic pressure amplitude, acoustic wave number, and bubble size, are investigated in temporal and spatial scales to actively influence the direction of the liquid jet caused by bubble collapse. The numerical results show that due to the strong interaction with the acoustic standing wave, the bubble loses the spherical shape and generates a high-speed liquid jet. It worth noting that a significantly high pressure and velocity peak is respectively founded at the boundary wall, which is caused by the toroidal bubble collapse. Furthermore, in the standing wave field, single bubble would have distinctly different behaviors with the change of its resonance radius size. The high-speed liquid jet is always directed towards the node of an acoustic standing wave when the radius of bubble is larger than the resonance size, while the liquid jet is directed to the antinode when the radius of bubble is much smaller than the resonance size, closely with the primary Bjerknes force. Finally, the investigation shows that the single bubble will collapse much earlier during the deformation process with the increase of the normalized pressure amplitude.