Theory of supercompression of vapor bubbles and nanoscale thermonuclear fusion

Abstract

This paper provides the theoretical basis for energetic vapor bubble implosions induced by a standing acoustic wave. Its primary goal is to describe, explain, and demonstrate the plausibility of the experimental observations by Taleyarkhan et al. [Science 295, 1868 (2002); Phys. Rev. E 69, 036109 (2004)] of thermonuclear fusion for imploding cavitation bubbles in chilled deuterated acetone. A detailed description and analysis of these data, including a resolution of the criticisms that have been raised, together with some preliminary HYDRO code simulations, has been given by Nigmatulin et al. [Vestnik ANRB (Ufa, Russia) 4, 3 (2002); J. Power Energy 218-A, 345 (2004)] and Lahey et al. [Adv. Heat Transfer (to be published)]. In this paper a hydrodynamic shock (i.e., HYDRO) code model of the spherically symmetric motion for a vapor bubble in an acoustically forced liquid is presented. This model describes cavitation bubble cluster growth during the expansion period, followed by a violent implosion during the compression period of the acoustic cycle. There are two stages of the bubble dynamics process. The first, low Mach number stage, comprises almost all the time of the acoustic cycle. During this stage, the radial velocities are much less than the sound speeds in the vapor and liquid, the vapor pressure is very close to uniform, and the liquid is practically incompressible. This process is characterized by the inertia of the liquid, heat conduction, and the evaporation or condensation of the vapor. The second, very short, high Mach number stage is when the radial velocities are the same order, or higher, than the sound speeds in the vapor and liquid. In this stage high temperatures, pressures, and densities of the vapor and liquid take place. The model presented herein has realistic equations of state for the compressible liquid and vapor phases, and accounts for nonequilibrium evaporation/condensation kinetics at the liquid/vapor interface. There are interacting shock waves in both phases, which converge toward and reflect from the center of the bubble, causing dissociation, ionization, and other related plasma physics phenomena during the final stage of bubble collapse. For a vapor bubble in a deuterated organic liquid (e.g., acetone), during the final stage of collapse there is a nanoscale region (diameter ∼100nm) near the center of the bubble in which, for a fraction of a picosecond, the temperatures and densities are extremely high (∼108K and ∼10g∕cm3, respectively) such that thermonuclear fusion may take place. To quantify this, the kinetics of the local deuterium/deuterium (D∕D) nuclear fusion reactions was used in the HYDRO code to determine the intensity of the fusion reactions. Numerical HYDRO code simulations of the bubble implosion process have been carried out for the experimental conditions used by Taleyarkhan et al. [Science 295, 1868 (2002); Phys. Rev. E 69, 036109 (2004)] at Oak Ridge National Laboratory. The results show good agreement with the experimental data on bubble fusion that was measured in chilled deuterated acetone.