2016
DOI: 10.1121/1.4945452
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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 scatter… Show more

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Cited by 15 publications
(10 citation statements)
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“…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.…”
Section: Introductionmentioning
confidence: 55%
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“…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.…”
Section: Introductionmentioning
confidence: 55%
“…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).…”
Section: Nonlinear Resonance Of the Cavitymentioning
confidence: 99%
“…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.…”
Section: Resultsmentioning
confidence: 95%
“…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).…”
Section: Resultsmentioning
confidence: 99%
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