Experimental results are compared with a theoretical analysis concerning wall effects on the symmetric mode resonance frequency of millimeter-sized air bubbles in water. An analytical model based on a linear coupled-oscillator approximation is used to describe the oscillations of the bubbles, while the method of images is used to model the effect of the wall. Three situations are considered: a single bubble, a group of two bubbles, and a group of three bubbles. The results show that bubbles attached to a rigid boundary have lower resonance frequencies compared to when they are in an infinite uniform liquid domain ͑referred to as free space͒. Both the experimental data and theoretical analysis show that the symmetric mode resonance frequency decreases with the number of bubbles but increases as the bubbles are moved apart. Discrepancies between theory and experiment can be explained by the fact that distortion effects due to buoyancy forces and surface tension were ignored. The data presented here are intended to guide future investigations into the resonances of larger arrays of bubbles on rigid surfaces, which may assist in surface sonochemistry, sonic cleaning, and micro-mixing applications.

Background: Ultrasound-targeted drug delivery relies on the unique nature of ultrasound contrast agents – they are microbubbles that respond strongly to ultrasound. Intravenously injected microbubbles are smaller than a blood cell. By increasing the ultrasound power, the bubbles can be ruptured at the targeted endothelial wall, locally releasing any molecules in the bubble shell. Furthermore, ultrasound-activated microbubbles are known to cause sonoporation – the process by which ultrasound drives molecules through cellular membranes. However, techniques are required to selectively detect and rupture only those microbubbles on target walls. Method: Experiments are presented on the behaviour of microbubbles on walls. For accuracy, imaging measurements are made on model microbubbles larger than contrast agents. Bubble size was varied and the resonant frequency peak determined. Results: Microbubbles on walls have a shifted frequency in good agreement with theory: a 20–25% downshift from the frequency when far from walls. Effects other than the presence of the wall account for less than 5% of the shift. Discussion: Theory predicts the frequency downshift should be sustained for actual contrast-agent sized bubbles. The effect of real, compliant cell walls requires investigation. An appropriate downshift in the applied ultrasound frequency could selectively tune gene or drug delivery. To make this feasible, it may be necessary to manufacture monodispersed microbubbles.

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Numerical calculations and illustrative experiments are presented on the volumetric oscillations of microbubbles on and near surfaces. There is a considerable theoretical and experimental literature on the acoustic interactions of bubbles. In the present study, the surface was represented by a mirror-image bubble and the nonlinear frequency response calculated by integrating acoustically coupled sets of Rayleigh-Plesset-like equations. A significant shift was found in the peak nonlinear response frequency of a bubble targeted onto a surface. This effect is increased when other bubbles are nearby on the surface. Owing to the asymmetric influence of the surface, experimental images were dominated by shape-mode instabilities, making optical determination of the peak nonlinear response frequency difficult. Moreover, it was found that even if bubbles are separated by only a small fraction of the sound wavelength, time delays owing to the finite speed of sound have a surprisingly significant influence. Calculations on the symmetric mode of mutual oscillation showed that the introduction of time delays significantly modified harmonics of the spectrum.