On the eigenfrequency of a gas bubble in a liquid

Abstract

This investigation concerns free linear gas bubble oscillations in liquids. Of prime interest is the eigenfrequency, and in particular its real part, here named as the transient frequency. The conceptual difference between the more frequently consulted resonance frequency and the transient frequency is first addressed by means of the classical mechanical oscillator. Next, bubble pulsations in liquids are discussed and an existing model is used for the gas–liquid interaction from which an approximate expression for the eigenfrequency is derived. A rationale for the approximate evaluation of the functions modeling the thermal processes is suggested which is independent of the frequency content of any possible pressure excitation. Moreover, compressibility effects are not approximated in the derivation presented here. The quantitative difference between the adiabatic resonance frequency and the derived estimate of the transient frequency is found to be of significance for small bubbles. Finally, the similarity between a standard mechanical oscillator and a bubble in a liquid for the case of liquid-compressibility effects only is discussed.