Instability of the Motion of a Pulsating Bubble in a Sound Field

TLDR: In this paper, the authors describe two related instabilities of spherical bubbles that are set into pulsation by a sound field, one instability occurs when the sound pressure amplitude exceeds a threshold value, and they measured the threshold for bubbles driven below resonance in water and in isopropyl alcohol.

Abstract: This paper describes two related instabilities of spherical bubbles that are set into pulsation by a sound field. One instability is the observed onset of erratic dancing by bubbles that are trapped in a standing wave. This instability occurs when the sound‐pressure amplitude exceeds a threshold value, and we measured the threshold for bubbles driven below resonance in water and in isopropyl alcohol. The other instability, which also requires that the sound‐pressure amplitude exceed a threshold value, is the theoretically predicted onset of oscillation of the bubble shape. This threshold was calculated for the conditions of the previous experiments by a theory of parametric excitation based on Hill's equation. All results refer to pressure amplitudes less than 0.7 bar and frequencies from 23.6 to 28.3 kHz. From the close agreement of the measured dancing thresholds and the calculated shape‐oscillation thresholds, we conclude that the erratic dancing of pulsating bubbles in a sound field is caused by shape oscillations that are parametrically excited by the bubble pulsations.