TOWARD A HYDRODYNAMIC THEORY OF SONOLUMINESCENCE

For small Mach numbers the Rayleigh-Plesset equations (modified to inc lude acoustic radiation damping) provide the hydrodynamic description of a bubble's breathing motion. Measurements are presented for the bub ble radius as a function of time. They indicate that in the presence o f sonoluminescence the ratio of maximum to minimum bubble radius is ab out 100. Scaling laws for the maximum bubble radius and the temperatur e and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audib le sound fields these equations yield picosecond hot spots, such as ar e observed experimentally. However, the analysis indicates that a deta iled description of sonoluminescence requires the use of parameters fo r which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extensi on of bubble dynamics to include nonlinear effects such as shock waves .