Using phase space diagrams to interpret multiple frequency drive sonoluminescence

The recent experimental results of J. Holzfuss, M. Ruggeberg, and R. Mettin [Phys. Rev. Lett. 81, 1961 (1998)] in which a second harmonic drive system was used to generate sonoluminescence (SL) have been analyzed in the context of the dissociation hypothesis (DH) of D. Lohse and S. Hilgenfeldt [J. Chem. Phys. 107, 6986 (1997)]. The second harmonic introduces two more variables that are under experimental control: a phase and an additional pressure term to the acoustic drive pressure. Diffusive equilibrium curves for a fixed gas concentration were calculated as was the Mach criterion. A phase space diagram was constructed to permit the prediction of regions of stable SL, unstable SL, stable non-SL, and unstable non-SL. These were compared to Holzfuss' experimental observations, and excellent quantitative agreement was seen. The results provide further evidence that the underlying assumptions of DH are sound. They also indicate the utility of DH for determining appropriate experimental conditions to achieve SL and for optimizing an experimental system.