### ASA 125th Meeting Ottawa 1993 May

## 4pAO4. Resonance frequency and damping constant of a spherical gas-vapor
bubble in an infinite medium.

**Yi Mao
**

**
Lawrence A. Crum
**

**
Ronald A. Roy
**

**
**
*Appl. Phys. Lab., Univ. of Washington, Seattle, WA 98105
*

*
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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.]