Probing the pressure dependence of sound speed and attenuation in bubbly media: Experimental observations, a theoretical model and numerical calculations

The problem of attenuation and sound speed of bubbly media has remained partially unsolved. Comprehensive data regarding pressure-dependent changes of the attenuation and sound speed of a bubbly medium are not available. Our theoretical understanding of the problem is limited to linear or semi-linear theoretical models, which are not accurate in the regime of large amplitude bubble oscillations. Here, by controlling the size of the lipid coated bubbles (mean diameter of ~5.4um), we report the first time observation and characterization of the simultaneous pressure dependence of sound speed and attenuation in bubbly water below, at and above MBs resonance (frequency range between 1-3MHz). With increasing acoustic pressure (between 12.5-100kPa), the frequency of the attenuation and sound speed peaks decreases while maximum and minimum amplitudes of the sound speed increase. We propose a nonlinear model for the estimation of the pressure dependent sound speed and attenuation with good agreement with the experiments. The model calculations are validated by comparing with the linear and semi-linear models predictions. One of the major challenges of the previously developed models is the significant overestimation of the attenuation at the bubble resonance at higher void fractions (e.g. 0.005). We addressed this problem by incorporating bubble-bubble interactions and comparing the results to experiments. Influence of the bubble-bubble interactions increases with increasing pressure. Within the examined exposure parameters, we numerically show that, even for low void fractions (e.g. 5.1*10-6) with increasing pressure the sound speed may become 4 times higher than the sound speed in the non-bubbly medium.Comment: arXiv admin note: text overlap with arXiv:1811.0778

A simple method to analyze the super-harmonic and ultra-harmonic behavior of the acoustically excited bubble oscillator

The bubble oscillator is a highly nonlinear system, which makes it difficult to generate a comprehensive understanding of its oscillatory behavior. One method used to investigate such complex dynamical systems is the bifurcation analysis. Numerous investigations have employed the method of bifurcation diagrams to study the effect of different control parameters on the bubble behavior. These studies, however, focused mainly on investigating the subharmonic (SH) and chaotic oscillations of the bubbles. Super-harmonic (SuH) and ultra-harmonic (UH) bubble oscillations remain under-investigated. One reason is that the conventional method used for generating bifurcation diagrams cannot reliably identify features that are responsible for the identification of SuH and UH oscillations. Additionally, the conventional method cannot distinguish between the UHs and SHs. We introduce a simple procedure to address this shortcoming. In this method, the maxima of the bubble oscillatory response were selected and plotted alongside the traditional bifurcation points for the corresponding control parameter. Results show that depending on the control parameters the conventional method or the method of maxima may miss intricate details of the oscillations. In order to have a comprehensive knowledge on the rich dynamics of the system, the two methods should be employed side by side. Through plotting the two bifurcation structures in tandem, the oscillatory behavior of the bubble was analyzed with more detail, and stable SuH and UH bubble oscillations were investigated. Based on this new analysis, the conditions for the generation and amplification of UH and SuH regimes are discussed.</p