Towards classification of the bifurcation structure of a spherical cavitation bubble.

We focus on a single cavitation bubble driven by ultrasound, a system which is a specimen of forced nonlinear oscillators and is characterized by its extreme sensitivity to the initial conditions. The driven radial oscillations of the bubble are considered to be implicated by the principles of chaos physics and owing to specific ranges of control parameters, can be periodic or chaotic. Despite the growing number of investigations on its dynamics, there is not yet an inclusive yardstick to sort the dynamical behavior of the bubble into classes; also, the response oscillations are so complex that long term prediction on the behavior becomes difficult to accomplish. In this study, the nonlinear dynamics of a bubble oscillator was treated numerically and the simulations were proceeded with bifurcation diagrams. The calculated bifurcation diagrams were compared in an attempt to classify the bubble dynamic characteristics when varying the control parameters. The comparison reveals distinctive bifurcation patterns as a consequence of driving the systems with unequal ratios of R(0)lambda (where R(0) is the bubble initial radius and lambda is the wavelength of the driving ultrasonic wave). Results indicated that systems having the equal ratio of R(0)lambda, share remarkable similarities in their bifurcating behavior and can be classified under a unit category.

Suppressing chaotic oscillations of a spherical cavitation bubble through applying a periodic perturbation.

Nonlinear dynamics of a spherical cavitation bubble was studied. A method based on applying a periodic perturbation to suppress chaotic oscillations is introduced. The relation between this method and dual frequency ultrasonic irradiation is correlated to prove its applicability in applications involving cavitation phenomena. Results indicated its strong impact on reducing the chaotic oscillations to regular ones. The governing parameters are the secondary frequency value and the phase difference between the secondary frequency and the fundamental one. In the end, the possible application of this method in high intensity focused ultrasound tumor ablation as an instance, is discussed accounting for both free bubbles and microbubbles.