Abstract: The numerical results obtained by Rayleigh--Plesset (R-P) equation failed to agree with the experimental Mie scattering data of a bubble in water without inappropriately increasing the shear viscosity and decreasing the surface tension coefficient. In this paper, a new equation proposed by the present authors (Qian and Xiao) is solved. Numerical solutions obtained by using the symbolic computation program from both the R-P equation and the Qian-Xiao (Q-X) equation clearly demonstrate that Q-X equation yields best results matching the experimental data (in expansion phase). The numerical solutions of R-P equation also demonstrate the oscillation of a bubble in water depends strongly upon the surface tension and the shear viscosity coefficients as well as the amplitude of driving pressure, so that the uniqueness of the numerical solutions may be suspected if they are varied arbitrarily in order to fit the experimental data. If the bubble's vibration accompanies an energy loss such as the light radiation during the contract phase, the mechanism of the energy loss has to be taken into account. We suggest that by use of the bubble's vibration to investigate the state equations of aqueous solutions seem to be possible. We also believe that if one uses this equation instead of R-P equation to deal with the relevant problems such as the `phase diagrams for sonoluminescing bubbles', etc., some different results may be expected.

Key words: bubble, sonoluminescence, finite-amplitude vibration of a bubble