The Natural Frequency of a Bubble Oscillating in a Viscous Compressible Liquid

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Abstract
The natural frequency of a spherical gas-filled bubble oscillating in a viscous compressible liquid is derived. Surface tension is also included in this solution, but gravity, gas diffusion and thermal conduction are neglected. The solutions of Minneart Richardson, Neppiras and Noltingk, Hirose and Okuyama, and Houghton are shown to be special cases of this solution. The effects of liquid compressibility, surface tension, and viscosity on the natural frequency of a bubble in water is determined as a function of the static radius. The effect of ratio of specific heats of gas in a bubble is also examined.

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