Finite-amplitude vibration of a bubble in water

The numerical results obtained by Rayleigh--Plesset (R-P) equationfailed to agree with the experimental Mie scattering data of abubble in water without inappropriately increasing the shearviscosity and decreasing the surface tension coefficient. In thispaper, a new equation proposed by the present authors (Qian andXiao) is solved. Numerical solutions obtained by using the symboliccomputation program from both the R-P equation and the Qian-Xiao(Q-X) equation clearly demonstrate that Q-X equation yields bestresults matching the experimental data (in expansion phase). Thenumerical solutions of R-P equation also demonstrate the oscillationof a bubble in water depends strongly upon the surface tension andthe shear viscosity coefficients as well as the amplitude of drivingpressure, so that the uniqueness of the numerical solutions may besuspected if they are varied arbitrarily in order to fit theexperimental data. If the bubble's vibration accompanies an energyloss such as the light radiation during the contract phase, themechanism of the energy loss has to be taken into account. Wesuggest that by use of the bubble's vibration to investigate thestate equations of aqueous solutions seem to be possible. We alsobelieve that if one uses this equation instead of R-P equation todeal with the relevant problems such as the `phase diagrams forsonoluminescing bubbles', etc., some different results may beexpected.