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

Abstract

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 ≈5.4µm), 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.

Simulations of a full sonoreactor accounting for cavitation

“…This not only affects the local sound velocity but also the attenuation. Calculations for uncoated 2μm bubbles showed that the values of R(k 2 ) can drastically fall as acoustic pressure increases, in an increasing range of frequencies around resonance [68]. Interestingly, the authors found that the drop of R(k 2 ) could yield values of attenuation falling to near 50% of our own estimation, which is the order of magnitude of the discrepancy observed in the present work.…”

“…Sojahrood and co-workers have extended the theory in various aspects [65], including extension to coated microbubbles [66,67]. The latter group also recently performed experiments with a layer of almost monodisperse coated microbubbles to assess experimentally the attenuation and sound-velocity in the bubbly liquid and found good agreement between their extension of our model and the experimental results [68]. Both attenuation and sound velocity were found to vary with acoustic pressure, and to our best knowledge, this constitutes the first experimental results supporting the concepts raised by Louisnard in Ref.…”

“…One well-known weakness of our model is the arbitrary setting of the real part of k 2 to its classical linear expression (4), which is independent of pressure amplitude. This issue has been recently re-examined independently by Trujillo [97,64] and Sojahrood and co-workers [66,68]. They showed that both real and imaginary parts of k 2 can be expressed as period-averaged expressions involving the pressure field and the local void fraction β = N4πR 3 /3 (with possible extension to poly-disperse bubble sizes).…”

Concentration-Dependent Viscoelasticity of Poloxamer-Shelled Microbubbles

“…A previous study showed that the bubble–bubble interaction was an important factor affecting the attenuation characteristics, which was determined by the void fraction β. , The void fraction was estimated assuming that the bubble size distribution was uniform in our experimental cell, which is summarized in Table . Previous studies have suggested that low values of void fraction (β < 10 –7 ) have little effect on attenuation characteristics . At high Pluronic F-68 concentrations, the void fraction was relatively high, indicating that the attenuation characteristics may have been weakly affected by bubble–bubble interactions.…”

“…The oscillation of bubbles coated with lipid shells changes from linear to nonlinear as the sound pressure increases. In the nonlinear regime, the lipid shell buckles during contraction and ruptures during expansion, , indicating that the dilatational viscoelasticity of the shell during nonlinear oscillation dynamically changes synchronizing with its oscillation, and thus the estimated value should be misestimated to be different from that during linear oscillation. ,, Several research demonstrated that bubbles coated with a lipid shell oscillate linearly at a sound pressure of 20 kPa and exhibit moderate nonlinear oscillation at 50 kPa. , Other research groups showed that lipid-coated bubbles exhibited nonlinear oscillations as the sound pressure increased from 12.5 to 25 kPa . Although their threshold was greatly affected by the shell material and fabrication method, it is reasonable to assume that the oscillation of the Pluronic F-68 bubbles in our experiment was linear.…”