Yi Mao
Lawrence A. Crum
Ronald A. Roy
Appl. Phys. Lab., Univ. of Washington, Seattle, WA 98105
The resonance frequency f[sub 0] and damping constant (delta) for free volume oscillations of a spherical bubble in an infinite medium are derived from the linearized, fundamental equations of fluid dynamics. There are three possible modes (acoustic, thermal, and mass diffusion) of wave propagation that satisfy the governing equations for the gas--vapor mixture inside the bubble. Outside it, only the acoustic and thermal diffusion modes need consideration because gas diffusion across the bubble surface into the liquid appears negligible for free oscillations. The parameters f[sub 0] and (delta) are values such that the boundary conditions can be satisfied. The dependence of f[sub 0] and (delta) on bubble size, ambient pressure, and temperature is examined. When a bubble contains a high concentration of gas, the values of f[sub 0] and (delta) agree with the results of Devin [J. Acoust. Soc. Am. 31, 1654--1667 (1959)]. When the concentration of vapor is high, it is found that there exists only one resonance frequency for free oscillations [compare the results of R. D. Finch and E. A. Neppiras, J. Acoust. Soc. Am. 53, 1402--1410 (1973)]. [Work supported by ONR.]