Eigenmodal resonances of polydisperse bubble systems on a rigid boundary

This paper presents theory and experimental data on the resonance frequency of systems consisting of different-sized air bubbles attached to a rigid wall. Effects of the change in resonant frequency with bubble size and distance between the bubbles were studied. It was found that the symmetric mode resonance frequency of the bubble system decreased with increasing r=R02/R01, where R01 and R02 are the equilibrium radii of bubbles in the system. Both the symmetric and antisymmetric modes of oscillation were detected in the experiments, with the resonant frequency of the symmetric mode dominant at small bubble separation and the frequency of the antisymmetric mode dominant when the bubbles were farther apart. A linear coupled-oscillator theoretical model was used to describe the oscillations of the bubble system, in which the method of images was used to approximate the effects of the wall. It was found that there was fair to good agreement between the predictions of the coupled-oscillator model with the experimental data.