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

Abstract

The weakly nonlinear propagation of acoustic waves in monodisperse bubbly liquids is investigated numerically. A hydrodynamic model based on the averaged two-phase fluid equations is coupled with the Rayleigh-Plesset equation to model the dynamics of bubbles at the local scale. The present model is validated in the linear regime by comparing with the Foldy approximation. The analysis of the pressure signals in the linear regime highlights two resonance frequencies: the Minnaert frequency and a multiple scattering resonance that strongly depends on the bubble concentration. For weakly nonlinear regimes, the generation of higher harmonics is observed only for the Minnaert frequency. Linear combinations between the Minnaert harmonics and the multiple scattering resonance are also observed. However, the most significant effect observed is the appearance of softening-hardening effects that share some similarities with those observed for sandstones or cracked materials. These effects are related to the multiple scattering resonance. Downward or upward resonance frequency shifts can be observed depending on the characteristic of the incident wave when increasing the excitation amplitude. It is shown that the frequency shift can be explained assuming that the acoustic wave velocity depends on a law different from those usually encountered for sandstones or cracked materials.

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

“…The decrease of sound speed when acoustic amplitudes are raised has been previously observed in several nonlinear and dispersive media by evidencing the nonlinear shift of the resonance frequency of the system [24][25][26]. The drop of sound speed is associated to the softening of the medium when pressure amplitudes are raised.…”

“…It is well known that an increase of the pressure amplitude of an acoustic wave propagating in a bubbly liquid produces a softening of the medium, i.e., a decrease of the sound speed, which induces a shift of the resonance of the cavity (nonlinear frequency shift of the cavity resonance, nonlinear resonance) [24][25][26][27]. In this section we studied whether this effect could be detected and evaluated through the analysis of the sum frequency created by nonlinear mixing of two signals of lower frequencies (Case#2).…”

Nonlinear Resonance of Cavities Filled with Bubbly Liquids: A Numerical Study with Application to the Enhancement of the Frequency Mixing Effect

“…Although very few studies exist in the literature, the dependence of the resonance of a bubble cloud on pressure amplitude is a phenomenon, known as nonlinear frequency shift, that has been observed previously in seminal papers by Omta [22], Matsumoto and Yoshizawa [28], and Doc et al [29]. In Appendix, we show some results obtained with the model described in the above section that corroborate the conclusions of these papers: (i) the increase of pressure amplitude induces the nonlinear frequency shift of the cavity resonance; (ii) this effect relies on the softening of the bubbly liquid, that is due to the variation of the average volume of bubbles; and (iii) this nonlinear effect is more pronounced at higher void fraction in the cavity.…”

“…e objective of this section is, using the phenomenon known as nonlinear frequency shift [22,28,29], to show the enhancement of the difference-frequency component generated in a cavity that contains a bubbly liquid by nonlinearly mixing two signals of different frequencies. e following data for the bubbly liquid are set into the model: c 0l � 1500 m/s, ρ 0l � 1000 kg/m 3 , and ] l � 1.43 × 10 −6 m 2 /s for the liquid (water) and c 0g � 340 m/s, ρ 0g � 1.29 kg/m 3 , and c g � 1.4 for the gas (air).…”

“…Matsumoto and Yoshizawa, in [28], also detected the shift with pressure amplitude of the resonance of a cluster containing a bubbly liquid. is effect has also been studied in bubbly liquids for a resonance frequency associated to the multiple scattering of bubbles that changes as a function of the amplitude of an incident Gaussian pulse [29].…”