Power-law dependence describing subharmonic generation from a non-spherically oscillating bubble

Abstract

In this paper, we propose a technique to detect the surface oscillation of an attached bubble with radius ranging from 20 to 200 mm in an acoustic standing wave using a laser Doppler vibrometer (LDV) and a high-speed camera. The threshold condition, where the surface oscillation mode of the bubble was excited, was investigated for three different driving frequencies of 28, 39, and 81 kHz. Frequency spectrum analyses of bubble oscillation measured by the LDV and the images of the bubble simultaneously obtained by the high-speed camera experimentally demonstrated that the surface oscillation was excited when the power-law dependence ΔRfth = ARB0 was satisfied. Here, R0 is the initial bubble radius and Rfth is the oscillation displacement of the bubble for the fundamental frequency of the incident ultrasound under the threshold condition where the displacement for the subharmonic component abruptly increased. Interestingly, the coefficient B was independent of the driving frequency. This result suggests that the proposed system can be used to check the validity of current models of surface instability on an oscillating bubble.