On acoustic cavitation of slightly subcritical bubbles

Abstract

An analytic expression is obtained for the threshold acoustic pressure amplitude which causes gas bubbles that are slightly smaller than the critical size to undergo cavitation in a liquid. The derivation is based on the Rayleigh–Plesset equation which describes nonlinear bubble oscillations. In the limit where the steady part of the pressure field in the vicinity of the bubble is decreased to a value less than the vapor pressure inside the bubble, it is well known that there exists a critical bubble radius above which bubbles spontaneously cavitate. For bubbles which are below this critical size and would otherwise be stable, imposition of a time-harmonic acoustic pressure of the right frequency causes the bubbles to become unstable and undergo cavitation. The threshold value of this acoustic pressure is found by employing a nonlinear analysis which reduces the Rayleigh–Plesset equation to a damped and forced Mathieu equation for the case of such slightly subcritical bubbles.