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A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation.

Louisnard, Olivier A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation. (2012) Ultrasonics Sonochemistry, 19 (1). 56-65. ISSN 1350-4177

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Official URL: http://dx.doi.org/doi:10.1016/j.ultsonch.2011.06.007


The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient ient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Ultrasonics Sonochemistry website : http://www.sciencedirect.com/science/article/pii/S1350417711001295
HAL Id:hal-01662838
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Ecole nationale supérieure des Mines d'Albi-Carmaux - IMT Mines Albi (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
Agence Nationale pour la Recherche
Deposited On:12 Sep 2016 11:29

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