Radial pulsations of a fluid sphere in a sound wave

Abstract

Journal of Fluid Mechanics, vol. 380 (1999), pp. 1–38

I am indebted to Professor Prosperetti and to Dr Ren for finding a significant error in my detailed analysis of the temperature and pressure fluctuations in a pulsating particle. As they point out, the error invalidates the results of that analysis for the temperature fluctuations in gas bubbles. Those results are withdrawn. The error also affects, although in a less significant manner, the results for the temperature fluctuations in pulsating liquid drops with specific heat ratio significantly different from 1. This includes the droplets chosen to illustrate the results, namely toluene droplets. However, correct results for both bubbles and droplets may be easily obtained and this is done here.

The error found by Prosperetti and Ren (see Prosperetti & Ren 2001) exists in both the internal and external solutions, but because the external fluid is in both cases a liquid having a very small value of (γ_f − 1), the error has no effect there. Thus, fortuitously, the external solution is valid, provided the correct values of the interfacial temperature and pressure fluctuations are used. In addition, the simple solution presented in Appendix B, as well as the general expressions for derived quantities, such as those for the energy dissipation rates and the attenuation coefficients, are not affected by the error, provided, again, that the values of the temperature and pressure ratios appearing in them are properly evaluated. This is done below for both drops and bubbles by complementing the analysis of Appendix B with the polytropic approximation. The required steps are straightforward.