Laboratoire Matière et Systèmes Complexes

SAMOUSSE is the name of a project, funded by the French ANR (2011-2015), whose aim was the development of an Acoustic Probe ("Sonde" in French) for FOAMS ("MOUSSEs" in French)

SUMMARY

Contrary to solid foams, liquid foams have not been extensively studied for their acoustical properties. We know, however, that the acoustic response of a foam strongly depends on its structure. For instance, sound does not propagate at the same speed in a dry foam or in a wet foam. It has given us the idea to develop an acoustic probe for liquid foams. In principle, many parameters can have an influence on the acoustics of foams: structure parameters (size of the bubbles, thickness of the films, ...) as well as physico-chemical ones (nature of the gas, surface rheology, ...). It opens perspectives of a very powerful probe, which can measure many parameters. But it also means one needs a good model, that can correctly relate the acoustic response to the many parameters involved. This is the simple question SAMOUSSE aims at answering: "How does sound propagate in a liquid foam?"

MEMBERS

SAMOUSSE was supervised by Florence Elias. The partners were: -* MSC in Paris (Matter and Complex Systems): C. Derec, F. Elias, C. Gay, S. Koskodagan (phd student), V. Leroy, J. Pierre (postdoc) -* IPR in Rennes (Physics Institute of Rennes): I. Cantat, J. Crassous, B. Dollet, J. Pierre (postdoc), A. Saint-Jalmes -* LPS in Orsay (Solid Physics Laboratory): W. Drenckhan, C. Honorez, S. Mariot, E. Rio -* TECLIS in Tassin (Lyon): S. Besson, A. Cagna, A. Hutin

PUBLICATIONS

"Sound and vision: visualization of music with a soap film ", C. Gaulon, C. Derec, T. Combriat, P. Marmottant, F. Elias, Eur. J. Phys. 38 (2017)

A vertical soap film, freely suspended at the end of a tube, is vibrated by a sound wave that propagates in the tube. If the sound wave is a piece of music, the soap film ‘comes alive’: colours, due to iridescences in the soap film, swirl, split and merge in time with the music. In this article, we analyse the rich physics behind these fascinating dynamical patterns: it combines the acoustic propagation in a tube, the light interferences, and the static and dynamic properties of soap films. The interaction between the acoustic wave and the liquid membrane results in capillary waves on the soap film, as well as non-linear effects leading to a non-oscillatory flow of liquid in the plane of the film, which induces several spectacular effects: generation of vortices, diphasic dynamical patterns inside the film, and swelling of the soap film under certain conditions. Each of these effects is associated with a characteristic time scale, which interacts with the char- acteristic time of the music play. This article shows the richness of those characteristic times that lead to dynamical patterns. Through its artistic interest, the experiments presented in this article provide a tool for popularizing and demonstrating science in the classroom or to a broader audience.

"Investigating the origin of acoustic attenuation in liquid foams", J. Pierre, C. Gaulon, C. Derec, F. Elias, and V. Leroy, European Physical Journal E 40 (2017)

Liquid foams are known to be highly efficient to absorb acoustic waves but the origin of the sound dissipation remains unknown. In this paper, we present low frequency (0.5–4kHz) experimental results measured with an impedance tube and we confront the recorded attenuations with a simple model that considers the foam as a concentrate bubbly liquid. In order to identify the influence of the different parameters constituting the foams we probe samples with different gases, and various liquid fractions and bubble size distributions. We demonstrate that the intrinsic acoustic attenuation in the liquid foam is due to both thermal and viscous losses. The physical mechanism of the viscous term is not elucidated but the microscopic effective viscosity evidenced here can be described by a phenomenological law scaling with the bubble size and the gas density. In our experimental configuration a third dissipation term occurs. It comes from the viscous friction on the wall of the impedance tube and it is well described by the Kirchhoff law considering the macroscopic effective viscosity classically measured in rheology experiments.

"Vibration of soap films and Plateau borders, as elementary blocks of a vibrating liquid foam", F. Elias, S. Kosgodagan Acharige, L. Rose, C. Gay, V. Leroy, C. Derec, Colloids Surf. A 534 (2017)

The propagation of an acoustic wave in a liquid foam results from the coupling of a pressure wave in the gas phase and the vibration of the liquid backbone of the foam. At the bubble scale, the foam liquid skeleton is made of soap films connected by liquid channels. We study here the transverse vibration of those constitutive elements. The measurement of the velocity and attenuation of the transverse wave on each element isolated on a rigid frame, compared with an analytical modeling, reveals the main sources of inertia, elastic restoring forces and dissipation, for frequencies ranging from a few tens of Hz to a few kHz. In the case of a transverse wave propagating on a single soap film, we show that (i) the wave velocity is set by the surface tension and the inertial mass of the film loaded by the surrounding air, and (ii) that the damping of the wave is mainly due to the viscous dissipation in the air. In the case of a transverse wave propagating along the junction line between three soap films (Plateau border), the dispersion relation reveals two different scalings at low frequency and at high frequency, which are interpreted by considering the role of the vibration of the adjacent soap films, and the role of the inertia ofthe liquid inside the channel. The attenuation of the transverse wave along the liquid channel is measured in the low frequency regime. In both investigated cases (transverse wave propagating on a soap film as well as on a liquid channel), we show that the surrounding gas plays a dominant role, whereas the role played by the interfacial rheology is negligible.

"Coupled vibrations of a meniscus and liquid films", J. Seiwert, J. Pierre and B. Dollet, Journal of Fluid Mechanics 788 (2016)

We investigate the vibration properties of a circular horizontal film that is bounded by a meniscus (or Plateau border) and suspended between two catenary films. The suspending films act as capillary springs, and the system is thus free to oscillate around its equilibrium position. We study its free and forced oscillations. In our experiments, we track simultaneously the positions of the Plateau border and the film. The model that we present predicts the eigenfrequency of the system and its resonance characteristics (in forced oscillations). In particular, we show that the dynamics of both the Plateau border and the film have to be taken into account in order to provide an accurate prediction of the oscillation frequency.

"Propagation of a transverse wave on a foam microchannel", C. Derec, V. Leroy, D. Kaurin, L. Arbogast, C. Gay and F. Elias, EPL 112 (2015)

In a dry foam, soap films meet by three in the liquid microchannels, called Plateau borders, which contain most of the liquid of the foam. We investigated here the transverse vibration of a single Plateau border isolated on a rigid frame. We measured and we computed numerically and analytically the propagation of a transverse pulse along the channel in the 20–2000 Hz frequency range. The dispersion relation shows different scaling regimes, which provide information on the role of inertial and elastic forces acting on the Plateau border. At low frequency, the dispersion relation is dominated by the vibration of the air set into motion by the transverse vibration of the adjacent soap films. The inertia of the liquid in the Plateau border plays a role at high frequency, the critical frequency separating the low-frequency and the high-frequency regimes being a decreasing function of the radius R of the Plateau border.

"Sound propagation in liquid foams: Unraveling the balance between physical and chemical parameters", J. Pierre, B. Giraudet, P. Chasle, B. Dollet, A. Saint-Jalmes, Phys. Rev. E 91 (2015)

We present experimental results on the propagation of an ultrasonic wave (40 kHz) in liquid foams, as a function of the foam physical and chemical parameters. We have first implemented an original setup, using transducers in a transmission configuration. The foam coarsening was used to vary the bubble size (remaining in the submillimeter range), and we have made foams with various chemical formulations, to investigate the role of the chemicals at the bubble interfaces or in bulk. The results are compared with recently published theoretical works, and good agreements are found. In particular, for all the foams, we have evidenced two asymptotic limits, at small and large bubble size, connected by a nontrivial resonant behavior, associated to an effective negative density. These qualitative features are robust whatever the chemical formulation; we discuss the observed differences between the samples, in relation to the interfacial and bulk viscoelasticity. These results demonstrate the rich and complex acoustic behavior of foams. While the bubble size remain here always smaller than the sound wavelength, it turns out that one must go well beyond mean-field modeling to describe the foam acoustic properties.

"An FFT approach to the analysis of dynamic properties of gas/liquid interfaces", S. Mariot, V. Leroy, J. Pierre, F. Elias, E. Bouthemya, D. Langevin, W. Drenckhan, Colloids and Surfaces A: Physicochem. Eng. Aspects 473 (2015)

The characterisation of the dynamic properties of viscoelastic monolayers of surfactants at the gas/liquid interface is very important in the analysis and prediction of foam stability. With most of the relevant dynamic processes being rapid (thermal fluctuation, film coalescence etc.) it is important to probe interfacial dynamics at high deformation rates. Today, only few techniques allow this, one of them being the characterisation of the propagation of electro-capillary waves on the liquid surface. Traditionally, this technique has been applied in a continuous mode (i.e. at constant frequency) in order to ensure reliable accuracy. Here we explore the possibility to analyse the propagation of an excited pulse in order to access the interfacial properties in one single Fourier treatment over a wide range of frequencies. The main advantage of this approach is that the measurement times and the required liquid volumes can be reduced significantly. This occurs at the cost of precision in the measurement, due partly to the presence of a pronounced resonance of the liquid surface. The pulsed approach may therefore be used to pre-scan the surface response before a more in-depth scan at constant frequency; or to follow the changes of the interfacial properties during surfactant adsorption.

"A simple technique for the automation of bubble size measurements", T. Gaillard, C. Honorez, M. Jumeau, F. Elias, W. Drenckhan, Colloids and Surfaces A: Physicochem. Eng. Aspects 473 (2015)

An increasing number of research topics and applications ask for a precise measurement of the size distribution of small bubbles in a liquid—and hence for reliable and automated image analysis. However, due to the strong mismatch between the refractive index of a liquid and a gas, bubbles deform strongly the path of light rays, rendering automated bubble size analysis a challenging task. We show here how this challenge can be met using the fact that bubbles act like inverted, spherical lenses with a curvature which is the inverse of the bubble radius. The imaging properties of each bubble can then be used to accurately determine the radius of the bubble upon imaging an object which can be filtered easily by a computer. When bubbles are large enough to be deformed under the influence of gravity, it is more appropriate to measure their size after squeezing them between two narrowly spaced glass plates. We therefore show here, how the analysis can be extended to this case; and how both approaches can be combined to measure the size distributions of strongly polydisperse foams containing simultaneously small (several 10s of micrometres) and large bubbles (several 100s of micrometres).

"Vibrating soap film: origin of the dissipation", S. Kosgodagan Acharige, F. Elias, C. Derec, Soft Matter 10 (2014) (pdf)

We investigate the complex dispersion relationship of a transverse antisymmetric wave on a horizontal soap film. Experimentally, the complex wave number k at a fixed forcing frequency is determined by measuring the vibrating amplitude of the soap film: the wavelength (linked to the real part of k) is determined by the spatial variation of the amplitude; the decay length (linked to the imaginary part of k) is determined by analyzing the resonance curves of the vibrating wave as a function of frequency. Theoretically, we compute the complex dispersion relationship taking into account the physical properties of the bulk liquid and gas phase, and of the gas–liquid interfaces. The comparison between the computation (developed to the leading order under our experimental conditions) and the experimental results confirms that the phase velocity is fixed by the interplay between surface tension, and liquid and air inertia, as reported in previous studies. Moreover, we show that the attenuation of the transverse antisymmetric wave originates from the viscous dissipation in the gas phase surrounding the liquid film. This result is an important step in understanding the propagation of an acoustic wave in liquid foam, using a bottom-up approach.

"Resonant Acoustic Propagation and Negative Density in Liquid Foams", J. Pierre, B. Dollet, V. Leroy, Phys. Rev. Lett. 112, 148307 (2014) (pdf)
	We measured the dispersion relation for acoustic longitudinal waves in liquid foams, over a broad frequency range (60–600 kHz). Strong dispersion was found, with two nondispersive behaviors, separated by a negative density regime. A new model, based on the coupled displacements of films, liquid channels, and gas in the foam, rationalizes all the experimental findings.

"Acoustic characterisation of liquid foams with an impedance tube", J. Pierre, R.-M. Guillermic, F. Elias, W. Drenckhan, V. Leroy, European Physical Journal E 36, 113 (2013) (pdf)

Acoustic measurements provide convenient non-invasive means for the characterisation of materials. We show here for the first time how a commercial impedance tube can be used to provide accurate measurements of the velocity and attenuation of acoustic waves in liquid foams, as well as their effective “acoustic” density, over the 0.5-6kHz frequency range. We demonstrate this using two types of liquid foams: a commercial shaving foam and “home-made” foams with well-controlled physico-chemical and structural properties. The sound velocity in the latter foams is found to be independent of the bubble size distribution and is very well described by Wood’s law. This implies that the impedance technique may be a convenient way to measure in situ the density of liquid foams. Important questions remain concerning the acoustic attenuation, which is found to be influenced in a currently unpredictible manner by the physico-chemical composition and the bubble size distribution of the characterised foams. We confirm differences in sound velocities in the two types of foams (having the same structural properties) which suggests that the physico-chemical composition of liquid foams has a non-negligible effect on their acoustic properties.

"Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects", I. B. Salem, R.-M. Guillermic, C. Sample, V. Leroy, A. Saint-Jalmes and B. Dollet, Soft Matter 9, 1194–1202 (2013)

We report experimental results on the propagation of ultrasonic waves (at frequencies in the range of 40 kHz) in aqueous foams. Monitoring the acoustics of the foams as they age, i.e. as the mean bubble radius increases by coarsening, we recover at short times some trends that are already known: decrease of the speed of sound and increase of attenuation. At long times, we have identified, for the first time, robust non-monotonic behaviors of the speed of sound and attenuation, associated with a critical bubble size, which decreases at increasing frequency. The experimental features appear to be surprisingly reminiscent of the Minnaert resonance known for a single isolated bubble in a fluid. Transposing the Minnaert theoretical framework to the limit of a dense packing of bubbles gives some qualitative agreement with the data, but still cannot explain quantitatively the measured properties.

"A technique for measuring velocity and attenuation of ultrasound in liquid foams", J. Pierre, F. Elias, V. Leroy, Ultrasonics 53, 622–629 (2013) (pdf)

We describe an experimental setup specifically designed for measuring the ultrasonic transmission through liquid foams, over a broad range of frequencies (60–600 kHz). The question of determining the ultrasonic properties of the foam (density, phase velocity and attenuation) from the transmission measurements is addressed. An inversion method is proposed, tested on synthetic data, and applied to a liquid foam at different times during the coarsening. The ultrasonic velocity and attenuation are found to be very sensitive to the foam bubble sizes, suggesting that a spectroscopy technique could be developed for liquid foams.