A model of sonoluminescence

Abstract

A bubble of air, trapped at the centre of a spherical container of water on the surface of which spherical sound waves are maintained by transducers, may emit light, a phenomenon known as sonoluminescence. The surface of the bubble expands and contracts in obedience to the Rayleigh–Lamb equation, which requires knowledge of the gas pressure on the surface of the bubble. In many investigations of bubble pulsations, it is assumed that the air in the bubble moves adiabatically. To understand sonoluminescence, however, it is necessary to allow for the possibility that shocks are generated within the bubble. We couple the Rayleigh–Lamb equation governing the bubble radius to Euler’s equations governing the motion of air in the bubble, and solve the two equations simultaneously. The air is modelled by a van der Waals gas. Results are presented for a number of slightly different conditions of excitation, but in which the response of the system is widely different. If the frequency of the sound is high, the gas in the bubble moves adiabatically and no light is emitted. As the frequency is reduced (for the same ambient bubble radius and driving pressure), the incoming bubble surface acts as a piston that generates an ingoing shock wave that passes through the centre of the bubble, and then, when it strikes the bubble surface, halts and reverses its inward motion; a sequence of such inwardly and outwardly moving shocks occur. The shock waves generate such high temperatures that the air near the centre of the bubble is almost completely ionized, and emits light, which we attribute to bremmstrahlung. The light created by the second inwardly moving shock exceeds that created by the first but, as the frequency of the sound is further reduced, the energy from the first shock rises, and the overall luminosity of the bubble increases. When the sound frequency is further reduced, two shocks are launched successively by the inward moving bubble surface, the second colliding with the first after it has passed through the centre of symmetry but before it can collide with the bubble surface. Even higher temperatures are reached and the luminosity of the bubble continues to increase with decreasing frequency. Details of these solutions are presented, and estimates are made of the luminosity of the bubble in different conditions of excitation. Two other families of solutions are presented. In one, the frequency and ambient bubble radius are fixed and the driving amplitude is varied. In the other, the frequency and driving amplitude are fixed and the radius is varied. The effects of changing only the molecular weight of the trapped gas is also examined.