Sonoluminescence and near self-similar spherically symmetric solutions of Navier-Stokes and Euler equations

Sonoluminescence is a phenomenon that occurs when a bubble is excited by a driving sound wave with resonant frequency. The implosion is so strong that the internal energy is spatially concentrated of about twelve orders of magnitude in a small volume of a radius in the order of 10e-6 meters. Concomitantly, emission of light is observed. A deep comprehension of this phenomenon is yet to be reached, because of the complex interaction between the bubble wall dynamics and the interior chemistry and hydrodynamics. In this work a comparison between the physical phenomenology and a recently found set of mathematical solutions to the spherically symmetric Navier-Stokes and Euler equations is conducted. The physical aspects are described through a classic Rayleigh-Plesset model for bubble dynamics, considering a polytropic behaviour inside the interface. The results show a good fit of the analytical solutions to the numerical data near the collapse, and three pairs of coefficients' values are estimated for the analytical solutions.