Acoustics and Liquid-Gas Systems

Influence of surfactant molecules in bubble bursting events

Bubbles bursting at the surface of the sea water produce drops and is the main source of sea spray aerosol. The mechanisms underlying the drops production from a single bubble bursting event have been intensively studied and the influence of the bubble size and liquid parameters (density, viscosity, and surface tension) has been unified. However, despite the diversity of the surfactant molecules present in the oceans, their influence has been overlooked. We recently showed that SDS surfactant molecules have an astonishing effect. In particular, we quantitatively show that they modify the bubble collapse, they induce less, smaller, and faster drops, and they can even completely prevent the drop production for a particular concentration.

[1] J. Pierre, M. Poujol, T. Séon, Influence of surfactant concentration on drop production by bubble bursting, PRF 7, 073602 (2022)

Sound of effervescence

Capillary bubbles burst at a free surface following a rapid sequence of events occurring at different length- and timescales: hole nucleation, fast retraction of the micron-thick liquid film in a few microseconds preluding the much slower overall collapse of the millimeter-sized bubble in a matter of milliseconds. Each of these steps is associated with unsteady fluid forces and accelerations, and therefore with sound radiation.In this experimental study we focus on the airborne sound generated during bubble bursting. Investigating the physical mechanism at the root of sound emission with the help of synchronized fast imaging and sound recordings, we quantitatively link the film retraction dynamics with the frequency content of the acoustic signal. We demonstrate that, contrary to a Minnaert resonance scenario, the frequency here drifts and increases, consistently with a Helmholtz-type resonance of the cavity being more and more opened as the thin film retracts. We propose as an extension a simple model based on a collection of drifting Helmholtz resonators capturing the main features of the fizzing sound of an effervescing beverage.
[1] M.Poujol, R. Wunenburger, F. Ollivier, A. Antkowiak, and J. Pierre, Sound of effervescence, PRF 6, 013604 (2021)

A toy model for the effective density of acoustic metamaterials

We propose a simple mechanical system that can be used as a toy model for calculating the effective density of acoustic metamaterials. Through analytical calculations, it gives a better understanding of how the effective density can become negative, when the system responds elastically instead of inertially. We show that this toy model can reproduce, qualitatively, the acoustical behaviour of some real acoustic metamaterials.



[1] J. Pierre, V. Leroy, B. Dollet, A toy model for the effective density of acoustic metamaterials, Proc. R. Soc. A 478: 20210861 (2022)

Schematic views of the system which we propose as a toy model. (a) An annulus of mass M1 and surface S1 is around a disc of mass M2 and surface S2 , in an infinite tube of surface S = S1 + S2 = π R2 . (b) The two masses are connected via a spring K, and the annulus is linked to the tube with a spring K'. The effective mass of this system can be established by calculating how it moves when excited by an overpressure ∆Pexp(−iωt)

Acoustic absorption of solid foams with thin membranes

We investigated the audible acoustic properties of polyurethane foams with millimeter pores. Two types of foams were investigated: classical open-cell ones versus membrane foams, in which thin polyurethane membranes were preserved during solidification. Interestingly, the latter presented better absorption abilities, indicating that membranes could be an asset for sound absorption.
[1] C. Gaulon, J. Pierre, C. Derec, L. Jaouen, F.-X. Bécot, F. Chevillotte, F. Elias, W. Drenckhan and V. Leroy, Acoustic absorption of solid foams with thin membranes, APL 112, 261904 (2018) (DOI)[2] C. Gaulon, J. Pierre, C. Derec, F. Chevillotte, F.-X. Bécot, L. Jaouen, F. Elias, W. Drenckhan, V. Leroy, How to model the acoustic properties of a solid foam with thin membranes?, INTER-NOISE and NOISE-CON Congress and Conference Proceedings 258, 994 (2018)


Liquid foams act as natural metamaterials to trap acoustic waves

Liquid foams are known to be highly efficient to reduce the amplitude of acoustic or even blast waves. More surprising, this last years we have shown that liquid foams, which are natural isotropic materials, act as « acoustic metamaterials » exhibiting a negative effective density for wavelength larger than the bubble size. In this range of frequency, acoustic propagation becomes evanescent and the sound is fully blocked.This observation breaks with a widespread opinion : to efficiently dissipate acoustic energy one needs an open-cell material in order to permit large-scale motions of air in the whole structure. Indeed, a liquid foam is intrinsically a closed-cell structure, its bubbles of gas are shaped by thin films attached to a liquid skeleton, and far from being a limitation for soundproofing, these thin deformable liquid films allow a strong coupling between air and liquid motions and lead to the extraordinary acoustic properties. Very recently, we have pushed forward our investigations on the origin of acoustic attenuation in liquid foams and we have revealed that losses are due to both thermal and viscous losses in audible.
[1] Pierre J., Gaulon C., Derec C., Elias F., Leroy V. EPJE 40, 73 (2017)[2] Gaulon C., Pierre J., Leroy V., Elias F., Derec C. Acta Acustica 104 (2018)

Propagation of acoustic waves in liquid foams : How does a liquid foam move when insonified?

How does a liquid foam dance when insonified? Even if the acoustic wavelength is larger than the typical bubble size, the acoustic propagation is indeed far from trivial, and with much stronger dependencies on the foam physical parameters than on the chemical ones [1]. Experimentally the sound velocity and attenuation strongly depend on the bubble radius, R, and the acoustic frequency [1-3]. We propose a new model, based on the particular microstructure of liquid foams, to explain these experimental findings [3]. Two non-dispersive acoustic regimes and a resonance in between are observed. To distinguish the different regimes, the relevant length scale in not the acoustic wavelength in the foam, but the wavelength of the vibration wave on the liquid interfaces, at the forcing frequency [3,5-7].At low frequency the sound velocity is very low, between 25 and 50 m/s, and it can be explained by a mixture law, so called Wood’s law [4]. At the highest frequencies, the acoustic wave cannot drag the Plateau borders but only the air and the small inertial mass of the soap film; the sound velocity is close to the sound velocity in the air. In between these two regimes the acoustic properties change drastically: a resonance of the foam structure occurs. At the resonance frequency, the Plateau borders and the acoustic wave move in phase, whereas the soap films move out of phase. This complex relative motion of the liquid channels and films gives rise to an interesting regime with a maximum of attenuation and a range of negative density [3].
[1] Pierre J., Giraudet B., Chasle P., Dollet B. and Saint-Jalmes A. PRE 91, 042311 (2015).[2] Pierre J., Elias F. and Leroy V. Ultrasonics 53, 622 ( 2013).[3] Pierre J., Dollet B. and Leroy V. PRL 112, 148307 (2014).[4] Pierre J., Guillermic R.-M., Elias F., Drenckhan W. and Leroy V. EPJ E 36,1 (2013).[5] Kosgodagan Acharige S., Elias F., Derec C., Soft Matter 10, 8341 (2014)[6] Derec C., Leroy V., Kaurin D., Arbogast L., Gay C., Elias F., EPL 112, 34004 (2015)[7] Seiwert J., Pierre J., Dollet B., JFM 788, 183-208 (2016)

Ultrafast Ultrasound Localization Microscopy

Non-invasive imaging deep into organs at microscopic scales remains an open quest in biomedical imaging. Although optical microscopy is still limited to surface imaging owing to optical wave diffusion and fast decorrelation in tissue, revolutionary approaches such as fluorescence photo-activated localization microscopy led to a striking increase in resolution by more than an order of magnitude in the last decade [2]. In contrast with optics, ultrasonic waves propagate deep into organs without losing their coherence and are much less affected by in vivo decorrelation processes. However, their resolution is impeded by the fundamental limits of diffraction, which impose a long-standing trade-off between resolution and penetration. This limits clinical and preclinical ultrasound imaging to a sub-millimetre scale. Here we demonstrate in vivo that ultrasound imaging at ultrafast frame rates (more than 500 frames per second) provides an analogue to optical localization microscopy by capturing the transient signal decorrelation of contrast agents—inert gas microbubbles. Ultrafast ultrasound localization microscopy allowed both non-invasive sub-wavelength structural imaging and haemodynamic quantification of rodent cerebral microvessels (less than ten micrometres in diameter) more than ten millimetres below the tissue surface, leading to transcranial whole-brain imaging within short acquisition times (tens of seconds). After intravenous injection, single echoes from individual microbubbles were detected through ultrafast imaging. Their localization, not limited by diffraction, was accumulated over 75,000 images, yielding 1,000,000 events per coronal plane and statistically independent pixels of ten micrometres in size. Precise temporal tracking of microbubble positions allowed us to extract accurately in-plane velocities of the blood flow with a large dynamic range (from one millimetre per second to several centimetres per second). These results pave the way for deep non-invasive microscopy in animals and humans using ultrasound. We anticipate that ultrafast ultrasound localization microscopy may become an invaluable tool for the fundamental understanding and diagnostics of various disease processes that modify the microvascular blood flow, such as cancer, stroke and arteriosclerosis.
[1] Y. Desailly, J. Pierre, O. Couture, M. Tanter, Resolution limits of ultrafast Ultrasound Localization Microscopy, Phys. Med. Bio. 60, 8723 (2015)[2] C. Errico, J. Pierre, S. Pezet, Y. Desailly, Z. Lenkei, O. Couture, M. Tanter, Ultrafast ultrasound localization microscopy for deep in vivo super-resolution vascular imaging, Nature 527, 499 (2015) (DOI)
Extract from Errico, Nature (2015)

Elastic waves in periodic medium and negative refraction

The propagation of elastic waves infinite periodic structures is described by the Floquet-Bloch theory. Due to experimental constraints the phononic crystals are necessarily of finite size ; some discrepancies between the theory and the experimental data are thus possible. Moreover, the behaviour of elastic waves within these periodic structures is badly described thus far, because it is deduced from the transmitted signal. Therefore, a large number of phenomena, existing only within crystals, cannot be brought to light.The first part of this experimental work aims at better understanding the dispersion of elastic waves propagating within bi-dimensional phononic crystals. These phononic crystals consist of air inclusions engraved in a thin silicon plate by photolithography and chemical attack. A laser-ultrasonic setup is used both to generate and to detect surface elastic waves on all the surface of the sample. The analysis of the displacements field at the surface of the samples allows reveals the decomposition of wave vectors, as predicted by the Floquet-Bloch theory. At the band gap edge, an observation of elastic modes with zero group velocity has also been achieved. Finally, the influence of the dissymmetry of the inclusions on the opening of intra-band gap has been studied.The second part of this work is devoted to the negative refraction of Lamb and Rayleigh waves by two dimensional phononic crystals with a solid matrix (silicon and silica). The link between the propagation of elastic waves within the phononic crystal and the refraction at the interface with the homogeneous medium is established.
[1] B. Bonello, L. Belliard, J. Pierre, J.O. Vasseur, B. Perrin, O. Boyko, Negative refraction of surface acoustic waves in the subgigahertz range, Phys. Rev. B 82, 104109 (2010).[2] J. Pierre, O. Boyko, L. Belliard, J. O. Vasseur, B. Bonello, Negative refraction of zero order flexural Lamb waves through a two-dimensional phononic crystal, Applied Physics Letters 97, 121919 (2010). [3]J. Pierre, M. Rénier, B. Bonello, A-C. Hladky-Hennion, Intra-band gap in Lamb modes propagating in a periodic solid structure, Journal of Physics D: Applied Physics 45, 185305 (2012).
Floquet-Bloch decomposition in a 2D phononic crystal. Experimental (bottom) dispersion curves of A0 Lamb wave propagated within a silicon plate 200µm-tick structured with square holes organized in a square lattice (void fraction : 0.56, lattice parameter : a=1mm ). Experimental dispersion curves are obtained using a laser ultrasound experiment (schema).

Collaborations

Institut Jean Le Rond d'Alembert (Paris) (website)
Thomas Séon (personal page)Arnaud Antkowiak (personal page)Régis Wunenburger (personal page)François Ollivier (personal page)


Laboratoire Matière et Systèmes Complexes (Paris) (website)Valentin Leroy (personal page)Caroline Derec (personal page)Adrien Bussonière (personal page)Axel Huerre (personal page)

  

Acoustics and foams :
Institut de Physique de Rennes (website)Arnaud Saint-Jalmes (personal page)Benjamin Dollet (personal page)Jacopo Seiwert Jerôme Crassous (personal page)
Laboratoire Charles Sadron (Strasbourg) (website) Wiebke Drenkhan (personal page)
TECLIS à Tassin (Lyon) (website) A. Cagna
MATELYS Research Lab. (Lyon) (website) L. JaouenF.X. BécotF. Chevillotte

Ultrasound imaging:
Physics for medecine (website)Mickael Tanter (personal page)Olivier Couture (personal page)