Cylindrical bubble dynamics: Exact and direct numerical simulation results

Abstract

The axially symmetric collapse and growth of a cylindrical bubble are considered. A universal law of cylindrical bubble dynamics is obtained when the pressure at the boundary and that inside the bubble satisfy certain conditions. Both vapor bubbles having constant pressure and gas bubbles obeying the isothermal law are considered. Moreover, for gas bubbles, the energy equation within the bubble is considered in the uniform pressure approximation for the effect of heat conduction through the bubble wall, and an exact particular solution, leading to explicit gas pressure and gas temperature expressions, is obtained. Finally, the findings are validated by direct numerical simulations by using the front tracking/finite volume method.