An integral-differential system was derived by Miksis and Ting describing the nonlinear oscillations of a gas bubble including thermal and viscous effects. Here, an efficient numerical scheme is presented to solve this system for long times relative to the forcing period. Examples are presented and compared with the Rayleigh-Plesset equation, which has no thermal damping. Numerical results show that the initial free oscillations are damped out much faster when thermal damping is included. Also shown is the fact that it is possible for a bubble to have its mean radius grow slowly with time. In this case for large time the bubble will approach a new constant mean radius, which is larger than the initial equilibrium radius. For the special case of small amplitude forcing, asymptotic periodic solutions for very large time are constructed and a method to systematically derive the higher-order terms is demonstrated.
ASJC Scopus subject areas
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics