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For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.

Sonoluminescence, the transduction of sound into light, is a phenomenon that pushes fluid mechanics beyond its limit. An initial state with long wavelength and low Mach number, such as is realized for a gas bubble driven by an audible sound field, spontaneously focuses the energy density so as to generate supersonic motion and a different phase of matter, from which are then emitted picosecond flashes of broad-band UV light. Although the most rational picture of sonoluminescence involves the creation of a “cold” dense plasma by an imploding shock wave, neither the imploding shock nor the plasma has been directly observed. Attempts to attack sonoluminescence from the perspective of continuum mechanics have led to interesting issues related to bubble shape oscillations, shock shape instabilities, and shock propagation through nonideal media, and chemical hydrodynamics. The limits of energy focusing that can be achieved from collapsing bubbles in the far-off equilibrium motion of fluids have yet to be determined either experimentally or theoretically.