Valentin Leroy

Design and characterization of bubble phononic crystals

We report the practical realization of phononic crystals with gas inclusions, using soft lithography techniques. Ultrasonic experiments from 0.3 to 5 MHz confirm the existence of deep and wide minima of transmission through the crystal. We show that the first gap is due to the combined effects of Bragg reflections and bubble resonances. We propose a simple layered model that gives a reasonable prediction of the ultrasonic transmission.

Sound velocity and attenuation in bubbly gels measured by transmission experiments

Measurements of the phase velocity and attenuation of sound in concentrated samples of bubbly gels are presented. Hair gel was used as a matrix material to obtain well characterized distributions of bubbles. Ultrasonic measurements were conducted over a large range of frequencies, including the resonance frequencies of the bubbles. Surprisingly good agreement with Foldys prediction was found, even for monodisperse samples at resonance frequencies, up to volume fraction of 1%. Beyond this concentration, the effects of high-order multiple scattering were observed. These results support the feasability of ultrasonic techniques to investigate the size distribution of bubbles in a weak gel or liquid.

The air bubble: experiments on an unusual harmonic oscillator

We discuss a series of easily reproducible experiments with one and two air bubbles immersed in water, and we show that these systems can be analyzed in terms of harmonic oscillators.

Subwavelength focusing in bubbly media using broadband time reversal

Thanks to a Multiple Scattering Theory algorithm, we present a way to focus energy at the deep subwavelength scale, from the far-field, inside a cubic disordered bubble cloud by using broadband Time Reversal (TR). We show that the analytical calculation of an effective wavenumber performing the Independant Scattering Approximation (ISA) matches the numerical results for the focal extension. Subwavelength focusings of λ/100 are reported for simulations with perfect bubbles (no loss). A more realistic case, with viscous and thermal losses, allows us to obtain a λ/14 focal spot, with a low volume fraction of scatterers (Φ = 10−2). Bubbly materials could open new perspective for acoustic actuation in the microfluidic context.

A technique for measuring velocity and attenuation of ultrasound in liquid foams

We describe an experimental setup specifically designed for measuring the ultrasonic transmission through liquid foams, over a broad range of frequencies (60-600kHz). 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.

Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects

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.

Investigating the existence of bulk nanobubbles with ultrasound

Nanobubbles are expected to dissolve in milliseconds. Experimental evidence of nanobubbles that were stable for days had thus been first received with circumspection. If the large number of experimental confirmations has now made clear that surface nanobubbles could exist, bulk nanobubbles are still subject to debate. When observations are reported, the main problem is to make sure the observed particles are really made of gas. We show that ultrasound is an ideal tool for investigating the existence of bulk nanobubbles: 1) it is sensitive to minute quantities of gas, 2) it allows one to determine the bubble size distribution, 3) it discriminates unambiguously between gaseous and solid/liquid inclusions. To illustrate the efficiency of ultrasonic detection, we performed size measurements of bubbles produced by a commercial nano-/microbubble generator. No nanobubble was detected with this device. It would be insightful to use ultrasonic detection in experimental situations for which stable nanobubbles were reported.

Acoustic characterisation of liquid foams with an impedance tube

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.Graphical abstract

Sound propagation in a monodisperse bubble cloud: From the crystal to the glass

Abstract.We present a theoretical study of the propagation of a monochromatic pressure wave in an unbounded monodisperse bubbly liquid. We begin with the case of a regular bubble array --a bubble crystal-- for which we derive a dispersion relation. In order to interpret the different branches of this relation, we introduce a formalism, the radiative picture, which is the adaptation to acoustics of the standard splitting of the electric field in an electrostatic and a radiative part in Coulomb gauge. In the case of an irregular or completely random array --a bubble glass-- and at wavelengths large compared to the size of the bubble array spatial inhomogeneities, the difference between order and disorder is not felt by the pressure wave: a dispersion relation still holds, coinciding with that of a bubble crystal with the same bubble size and air volume fraction at the centre of its first Brillouin zone. This relation is discussed and compared to that obtained by Foldy in the framework of his multiscattering approach.

Nonlinear multiple scattering of acoustic waves by a layer of bubbles

–We present a theoretical and experimental study of the acoustic second-harmonic generation by a single layer of bubbles. This simple system allows us to investigate the subtle interplay between nonlinear effects and multiple scattering. A perturbative model is shown to give an excellent agreement with the experimental measurements, and we demonstrate the existence of an optimal concentration of bubbles, for which the harmonic generation is maximum. The potential of bubble screens as efficient subwavelength acoustic nonlinear sources is discussed. Introduction. – Wave transport in a multiple scattering environment has been a subject of intense research, demonstrating a large variety of behaviors, from the dis-persive propagation of a coherent wave [1, 2] to the existence of a diffusive regime, sometimes leading to local-ization [3, 4]. On the other hand, the nonlinear propagation of waves also comes with many intriguing phenomena , such as self-induced transparency [5] or second-harmonic generation [6], for instance. The question arises of how waves propagate when both strong multiple scattering and nonlinearities are present. For mechanical waves, this question has been addressed in granular media [7, 8], with the complication that both scattering and nonlin-earities are strongly dependent on the contact between the grains. Gas bubbles appear as perfect candidates for looking at nonlinear acoustic propagation in a multiple scattering regime: they are efficient acoustic scatter-ers, as well as strong nonlinear sources. Bubbly liquids have already been shown to exhibit substantial acoustic nonlinearities [9–12]. But an important limitation of the previous studies was the lack of quantitative comparison between the theoretical predictions and the experimental measurements, often due to a weak knowledge of the structure of the bubbly liquids used for the experiments.