# Laboratoire Matière et Systèmes Complexes

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## Acoustic waves propagation in bubbly media

(05/11/2010)

Bubbly media have fascinating acoustic properties. For example, a minute quantity of air bubbles in water is enough to modify the effective velocity of sound in the medium: with a volume fraction of air as low as 0.4%, the velocity becomes 200 m/s, i.e. lower than the velocity of sound in water (1500 m/s) but also smaller than the velocity in air (340 m/s). We are thus dealing with a medium whose properties are much different from the ones of its components! Anyone can daily appreciate the magnitude of the phenomenon thanks to the hot chocolate effect

Bubbles have another remarkable acoustic feature: their low frequency resonance (the Minnaert resonance). In general, when a wave is scattered by an object, nothing particular occurs as long as the wavelength is large compared with the size of the scatterer. But for bubbles and acoustic waves, it is a different story: a 1mm-radius air bubble in water interacts resonantly with an acoustic wave at 3 kHz, which corresponds to a 50 cm wavelength, i.e. 500 times the size of the bubble. In these circumstances, one can understand that the presence of bubbles in a liquid deeply affects the propagation of acoustic waves: at resonance, not only is each bubble generating a large acoustic field, but as a large number of them are potentially excited in phase, their contributions are constructive and thus constitute a major part of the total acoustic field. In a few words: bubbles are making a lot of noise (resonance), and they do it collectively (large wavelength).

Our activity on the acoustics of bubbly media covers three issues:

### 1- A model system for wave propagation in complex media

Propagation of waves in complex media is a subject of importance in all the domains of physics: seismic waves in the Earth’s crust or electromagnetic waves in a cloud of cold atoms are treated with the same formalism and often show similar issues. When interested in coherent waves, one usually uses a simple model: the independent scattering approximation (ISA). When scatterers are resonating, one expects this approximation to breakdown, mainly because of the scattering loops (i.e., multiple visits of the same scatterer) and the positional correlations. Bubbly media allow us to study these questions with a simple formalism (one single polarisation, isotropic scattering) and offer the possibility for experimental checks on well-characterized systems.

### 2- New acoustic materials

The extraordinary acoustic properties of bubbly media can be used to design new acoustic materials. An asset in this perspective is the persistence of the low frequency resonance of the bubbles when they are no longer in a liquid, but in a soft elastic medium (i.e., with a small shear modulus, lower than 10 MPa). We can thus obtain stable bubbly materials with new acoustic properties. For instance, we have made bubble phononic crystals.

### 3- Bubble Acoustic Spectroscopy

Bubbles are present in many practical applications. Whether one wants to get rid of them (float glass) or to foster them (bakery), being able to detect and characterize them (size, concentration) is a key point. As bubbles have a strong acoustic signature, ultrasonic techniques are an excellent tool for determining, for example, the bubble size distribution in a visco-elastic opaque medium. We are developing a spectroscopy technique based on the measurement of the velocity and the attenuation of ultrasounds over a large range of frequencies in the bubbly medium to characterize.

COLLABORATIONS:
Ultrasonics Research Laboratory, Winnipeg, Canada (A. Strybulevych, J. H. Page)
Food Science Department, Winnipeg, Canada (M. G. Scanlon)
Institut Langevin, Paris, France (A. Bretagne, M. Fink, A. Tourin)
Laboratoire MMN, Paris, France (P. Tabeling, H. Willaime)