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.

In acute hypercapnic Chronic obstructive pulmonary disease (COPD) patients, the Ward model of NIV care achieved equivalent clinical outcomes, whilst being more cost-effective than HDU or ICU models.

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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=R(02)/R(01), where R(01) and R(02) 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.

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