Abstract
A model for the compressible gas inside a single oscillating bubble is developed and found to have a wave-like distribution. Both gas sphere and ambient incompressible liquid are simplified as inviscid, ideal fluids. The density and pressure in the gas sphere are described by the Euler equations with analytical solutions obtained using the perturbation method. The zero-order quantities follow a uniform distribution. By introducing co-moving coordinates, the first-order quantities, which indicate the wave-like gas distribution, are obtained. The effect of the bubble oscillation on acoustic gas perturbations is included in our theory, and it results in a new wave equation, which describes internal wave-like distribution. According to our theory, the gas vibration induces local pressure peaks in the ambient liquid. Our theoretical description of the pressure peaks agrees with experimental observations. The observability of the internal oscillation is also discussed.
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