Nonlinear acoustic propagation in bubbly liquids: Multiple scattering, softening and hardening phenomena

Fractional derivative-based approximation of acoustic waveform dispersion measured in bubbly water beyond resonance frequency

Acoustic pulses transmitted across air bubbles in water are usually analyzed in terms of attenuation coefficient and phase velocity in the frequency domain. The present work expresses an analytical approximation of the acoustic waveform in the time domain. It is introduced by experiments performed with a Gaussian derivative source wavelet, S0(t), with a derivative order, β0 = 4, and a peak frequency, νp0, much larger than the bubble resonance frequency. The measurements highlight a significant shape variability of the waveform Bx(t), measured at x≤ 0.74 m and characterized by a peak frequency νpx≃νp0. The results are in good agreement with the approximation Bx(t)∝(dγx/dtγx)S0(δxt - T), where γx is an additional fractional-derivative order determined by an optimization procedure and T is related to the travel time. The time-scale parameter, δx=β0/(β0+γx), becomes a free parameter for more general source signals. The correlation coefficient between Bx(t) and the approximated waveform is used to identify the applicability of the method for a wide range of bubbly waters. The results may be of potential interest in characterizing gas bubbles in the ocean water column and, more generally, in modeling wave propagation in dispersive media with fractional-derivative orders in the time domain.

Extensive investigation of geometric effects in sonoreactors: Analysis by luminol mapping and comparison with numerical predictions

This investigation focuses on the influence of geometric factors on cavitational activity within a 20kHz sonoreactor containing water. Three vessels with different shapes were used, and the transducer immersion depth and liquid height were varied, resulting in a total of 126 experiments conducted under constant driving current. For each one, the dissipated power was quantified using calorimetry, while luminol mapping was employed to identify the shape and location of cavitation zones. The raw images of blueish light emission were transformed into false colors and corrected to compensate for refraction by the water-glass and glass-air interfaces. Additionally, all configurations were simulated using a sonoreactor model that incorporates a nonlinear propagation of acoustic waves in cavitating liquids. A systematic visual comparison between luminol maps and color-plots displaying the computed bubble collapse temperature in bubbly regions was conducted. The calorimetric power exhibited a nearly constant yield of approximately 70% across all experiments, thus validating the transducer command strategy. However, the numerical predictions consistently overestimated the electrical and calorimetric powers by a factor of roughly 2, indicating an overestimation of dissipation in the cavitating liquid model. Geometric variations revealed non-monotonic relationships between transducer immersion depth and dissipated power, emphasizing the importance of geometric effects in sonoreactor. Complex features were revealed by luminol maps, exhibiting appearance, disappearance, and merging of different luminol zones. In certain parametric regions, the luminol bright regions are reminiscent of linear eigenmodes of the water/vessel system. In the complementary parametric space, these structures either combine with, or are obliterated by typical elongated axial structures. The latter were found to coincide with an increased calorimetric power, and are conjectured to result from a strong cavitation field beneath the transducer producing acoustic streaming. Similar methods were applied to an additional set of 57 experiments conducted under constant geometry but with varying current, and suggested that the transition to elongated structures occurs above some amplitude threshold. While the model partially reproduced some experimental observations, further refinement is required to accurately account for the intricate acoustic phenomena involved.

Nonlinear Maximization of the Sum-Frequency Component from Two Ultrasonic Signals in a Bubbly Liquid

Techniques based on ultrasound in nondestructive testing and medical imaging analyze the response of the source frequencies (linear theory) or the second-order frequencies such as higher harmonics, difference and sum frequencies (nonlinear theory). The low attenuation and high directivity of the difference-frequency component generated nonlinearly by parametric arrays are useful. Higher harmonics created directly from a single-frequency source and the sum-frequency component generated nonlinearly by parametric arrays are attractive because of their high spatial resolution and accuracy. The nonlinear response of bubbly liquids can be strong even at relatively low acoustic pressure amplitudes. Thus, these nonlinear frequencies can be generated easily in these media. Since the experimental study of such nonlinear waves in stable bubbly liquids is a very difficult task, in this work we use a numerical model developed previously to describe the nonlinear propagation of ultrasound interacting with nonlinearly oscillating bubbles in a liquid. This numerical model solves a differential system coupling a Rayleigh–Plesset equation and the wave equation. This paper performs an analysis of the generation of the sum-frequency component by nonlinear mixing of two signals of lower frequencies. It shows that the amplitude of this component can be maximized by taking into account the nonlinear resonance of the system. This effect is due to the softening of the medium when pressure amplitudes rise.