Nonlinear Oscillations of Gas Bubbles in Liquids: Transient Solutions and the Connection Between Subharmonic Signal and Cavitation

Abstract

The transient nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid subject to the action of a sound field are investigated by means of an asymptotic method. Approximate analytical solutions are presented for the frequency regions of the fundamental resonance, the first and second subharmonic, and the first and second harmonic. Based on the results of this investigation, a new hypothesis to explain the connection between subharmonic signal and cavitation is put forward. It is suggested that bubbles emitting the subharmonic signal act primarily as monitors of cavitation events, and are smaller than resonance size. Finally, the free oscillations of the bubble are briefly considered.