Nonlinear Phenomena in Rayleigh-Plesset Equations for Single Bubble Dynamics

摘要

In this paper, we study nonlinear dynamics of a small air bubble in water under forced oscillating pressure at a constant temperature. First, we briefly describe the mathematical model of Rayleigh-Plesset equations and then we consider the bifurcation phenomena appeared in bubble dynamics. We investigate how a small bubble may grow and collapse; namely, it is shown how it may cause chaotic phenomena by repeating period-doubling bifurcations as an amplitude of input pressure increases. Furthermore, we also examine their transitions to chaotic states associated to different frequencies. Finally, we show that there exists some stable state for the small bubble under forcing the pressure with very high frequencies.