Maximum entropy model of chaotic explosion and implosion of a large gas bubble in liquid

Abstract

A mathematical model for the chaotic explosion of a large gas bubble in a liquid is presented in which there is a maximum increase in entropy. It is shown that this requires that the acoustic radiation during the chaos must be minimal and that the spherical surface at the end of the chaos must be stable. Also, a model including the acoustic radiation is developed for the spherical phases of the explosion and implosion of the bubble during which there is no change in entropy. The (final) chaotic phase of the implosion is also modeled so that there is a maximum increase in entropy. There might be additional periods of the bubble during which the bubble explodes and implodes in a similar fashion as the first period. The calculations using this model are shown to agree reasonably well with the data. In particular, these calculations determined that the ratio of the duration of the second period of the bubble to the first period imply that the energy lost in the first period during its implosion is about 2/3 of the energy of the first period. Also, these calculations determine that only about 30% of the total energy is radiated and the rest is absorbed by the water for a total of about 2/3 of the total energy. This also agrees with the data. Furthermore, the data appear to scale with initial total energy as in the calculations using this chaos model.