Abstract
A simple model is proposed for investigating bubble pulsation in a constrained medium. In free space, compressibility of the surrounding medium introduces primarily radiation losses that can often be neglected. In a constrained medium, compressibility plays an essential role. The example we investigate here is linear pulsation of an acoustically driven spherical bubble between two parallel rigid plates. The method of images is used to obtain a bubble dynamic equation that accounts for time delays associated with reflections of pressure waves radiated by the bubble. When the bubble is midway between the plates, the series of terms for the reflections can be expressed in closed form. For narrow plate separations, less than about ten bubble diameters, the bubble resonance frequency is reduced from its value in a free field due to increased effective inertia of the liquid, and radiation damping is increased. For larger plate separations, but less than the acoustic wavelength, the quality factor associated with radiation damping is proportional to plate separation. If effects of compressibility are ignored, the effective inertia becomes infinite, and bubble pulsation is prohibited by the equations of fluid mechanics. [Work supported by NIH Grant EB004047 and ARL IR&D funds.]
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