Classification Of The Nonlinear Dynamics Of Ultrasonically Excited Bubbles And Their Effect On The Acoustical Properties Of The Medium: Theory, Experiment And Numerical Simulations

Abstract

<div>Acoustically excited microbubbles (MBs) are the building blocks of several applications as diverse as underwater acoustics to sonochemistry and medicine. MBs are used in numerous diagnostic and therapeutic procedures. MBs dynamics are complex and nonlinear. Moreover, the presence of the MBs in a medium changes the medium’s attenuation and sound speed. The changes are nonlinear and depend on the complex MB dynamics. Within this complexity lies great potential for applications. For instance, the nonlinear response of MBs is used to increase the contrast to tissue ratio in imaging. Achieving the full potential of MBs in applications requires not only understanding the MB behavior, but also a detailed knowledge on the effect of the MBs pulsations on the medium acoustical properties. For instance, increased attenuation due to MBs in the ultrasound beam path limits the focal ultrasound energy which can reach a target. In this work, nonlinear MB dynamics are studied with unprecedented detail over wide ranges of ultrasound exposure parameters. Methods of nonlinear dynamics and chaos including bifurcation diagrams and resonance curves are used to visualize the results. In tandem, the scattered pressure from single bubble oscillations was experimentally investigated. Nonlinear dynamics of the MBs is classified both experimentally and numerically. We show, for the first time, that higher order subharmonic oscillations can be generated at very low acoustic pressures (e.g. 1kPa) in the oscillations of the lipid coated MBs. We address one of the open problems in acoustics by developing a comprehensive model to calculate the nonlinear attenuation and sound speed of bubbly media. Unlike current models, our new model is not limited by any linear or semi-linear approximations. The predictions of the model are verified by comparing it to other simplified models and experimental observations in bubbly media. We show, for the first time, the numerical and experimental evidence of the pressure dependent sound speed in bubbly media. The nonlinear attenuation and sound speed of the bubbly media are classified over a large range of acoustic exposure parameters. The classified regimes are then used to engineer the attenuation of a bubbly medium, during which ultrasound can pass through a highly dissipative bubbly medium with minimum loss.</div>