On Rectified Diffusion and Sonoluminescence

If acoustically driven, a gas-filled bubble may exist indefinitely even in an unsaturated liquid through a process known as “rectified diffusion.” When the oscillation period is small compared with the gaseous diffusion time, the radius of the steadily oscillating bubble can be determined by asymptotic methods, in the way pioneered by Eller and Flynn (1965). The next term in their expansion is evaluated here and is shown to be significant if the radius of the bubble is small or if the amplitude of its oscillations is large. For the identical level of saturation and the same conditions of excitation, multiple solutions are possible. As a result of resonance between overtones of the frequency of free bubble oscillation with the frequency of the acoustic drive, there generally exist, in addition to a stable large-radius, stable small-radius states. The relevance of the present results to sonoluminescence is briefly discussed.