A multiscale analysis of nonlinear oscillations of gas bubbles in compressible liquids

The nonlinear oscillations of a spherical gas bubble in a compressible viscous liquid subject to the action of a sound field are investigated by means of the multiscale perturbation method. Approximate analytical solutions for the transient and steady-state oscillations in the region of the main resonance are presented to second order in expansion. The time dependence is shown of the pressure in the liquid near the surface of the oscillating spherical bubble either in a compressible or an incompressible liquid.