a Theoretical Investigation of Acoustic Cavitation

Interest in cavitation dates back to the mid 1800's; however, there was no significant theoretical work in this area until the paper by Lord Rayleigh in 1917 described the collapse of a spherical cavity. Since this time there have been contributions to the theory by many scientists. In the late 1940's and early 1950's, contributions by Blake, Plesset, Neppiras, Noltingk, and Poritsky significantly advanced the theory resulting in an equation for the bubble dynamics known as the Rayleigh-Plesset equation. This equation was shown to work quite well under some conditions. Recent experiments have shown that when the acoustic driving frequency is near one of the bubble's harmonic resonances, the theoretical values predicted by the Rayleigh -Plesset equation are inconsistent with observed values. This inconsistency lead Prosperetti to consider the internal pressure term in the Rayleigh-Plesset equation in a more general manner. In the past the internal pressure of a bubble was assumed to be accurately predicted by a polytropic approximation. Prosperetti considered the internal pressure from the conservation equations, resulting in a much more accurate formulation. This study is an analysis of the two methods, showing where they agree and where they disagree. The new formulation also provides additional information about the internal thermodynamics of a bubble, which is explored in some detail. Results are shown for the internal temperature of a cavitating bubble as a function of radial coordinate and time. Internal pressures for a variety of conditions are shown and are in good agreement with earlier predicted values. Finally, the different models of acoustic cavitation are examined using some of the recent techniques in dynamical systems. "Feigenbaum trees" were made for the two models of interest. This method for analyzing an equation was shown to be very sensitive to the internal pressure term, and thus it is an appropriate method for comparing different acoustic cavitation theories.