Chaotic oscillations of a single cavitating bubble immersed in a maxwell liquid

Abstract

In the present work we develop a mathematical model for a bubble immersed in a Maxwell fluid insonified by an ultrasonic field. As in previous works we wanted to see the effect of the viscoelasiticy in the overall behavior of the bubble in time. With a modified Rayleigh-Plesset equation we obtain the evolution of radius in time, for different Deborah and Reynolds Numbers. Of interest the phase space graphs that show the chaotic oscillations for different values of the parameters, and how these parameters can be used as controllers of the oscillations. For a more complete analysis we perform a Perturbation Multiple Scale technique to get a frequency analysis, which can demonstrate how the parameters might modulate the resonance.