Symmetric mode resonance of bubbles attached to a rigid boundary

Abstract

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.

Eigenmodal resonances of polydisperse bubble systems on a rigid boundary

“…Thus, the net effect of the mirror-image bubble ͑and hence the wall͒ was to reduce the resonance frequency of the bubble. Payne et al 20 showed that the mirror-image bubble approach can also be successfully extended to model the behavior of a group of bubbles close to a wall; predictions showed good agreement with the experimental data.…”

“…As a reference, and in order to determine the frequency response of the tank itself, data from the hydrophone were initially obtained for cases when no bubbles were present in the tank. 20 Typical frequency response is shown in Fig. 6͑a͒.…”

“…5. The rig and postprocessing methodology is very similar to that used by Payne et al 20 The excitation signal is generated by a computer and is passed into a stereo amplifier. The amplified signal is then passed into the mechanical oscillatory unit which converts the electrical signal into oscillations in the liquid where the bubbles exist.…”

“…For small pressure fluctuations, the main effect of the solid boundary is to change the natural frequencies of the collective bubble system. Recent experimental studies by Payne et al 20 have measured the resonant frequency of identical bubbles attached to a rigid boundary. In the same study, Payne et al 20 proposed to use an image-bubble concept, formulated as a coupledoscillator problem, to model the behavior of a group of bubbles close to a wall.…”

“…Recent experimental studies by Payne et al 20 have measured the resonant frequency of identical bubbles attached to a rigid boundary. In the same study, Payne et al 20 proposed to use an image-bubble concept, formulated as a coupledoscillator problem, to model the behavior of a group of bubbles close to a wall. This approach was originally introduced by Strasberg 21 where he showed that a bubble oscillating close to a rigid boundary can be modeled by introducing a mirror-image bubble oscillating in phase with the original bubble.…”