Acoustic and electromagnetic quasimodes in dispersed random media

Propagation of coherent shear waves in scattering elastic media

We measure the reflection and transmission of shear waves by slabs of random dispersions of hard, dense spheres in a viscoelastic matrix. By modeling the slab as a Fabry-Pérot interferometer, we determine the effective wave number of coherent shear waves in this scattering medium and its effective mass density. We evidence the effect of the resonant rigid-body translation and rotation of the spheres on the propagation. We validate a vectorial model of multiple scattering for volume fractions of spheres up to 10%, revealing the signature of two modes of propagation.

Onset of interfacial waves in the terahertz spectrum of a nanoparticle suspension

We used inelastic x-ray scattering to gain insight into the complex terahertz dynamics of a diluted Au-nanoparticle suspension in glycerol. We observe that, albeit sparse, Au nanoparticles leave clear signatures on the dynamic response of the system, the main one being an additional mode propagating at the nanoparticle-glycerol interface. A Bayesian inferential analysis of the line shape reveals that such a mode, at variance with conventional acoustic modes, keeps a hydrodynamiclike behavior well beyond the continuous limit and down to subnanometer distances.

Effective dynamic properties of random complex media with spherical particles

The effective dynamic bulk modulus and density are presented for random media consisting of particles in a viscous host fluid, using a core-shell, self-consistent effective medium model, under the large compressional wavelength assumption. These properties are relevant to acoustic or dynamic processes in nano- and micro-particle fluids including particle density determination, resonant acoustic mixing, and acoustic characterisation. Analytical expressions are obtained for the effective bulk modulus and mass density, incorporating the viscous nature of the fluid host into the core-shell model through wave mode conversion phenomena. The effective density is derived in terms of particle concentration, particle and host densities, particle size, and the acoustic and shear wavenumbers of the liquid host. The analytical expressions obtained agree with prior known results in the limit of both static and inviscid cases; the ratio of the effective bulk modulus to that of the fluid is found to be quasi-static. Numerical calculations demonstrate the dependence of the effective mass density on frequency, particle size (from nano- to micro-regime), and concentration. Herein it is demonstrated both theoretically and numerically that the viscosity, often neglected in the literature, indeed plays a significant role in the effective properties of nanofluids.

Dynamic sound scattering: Field fluctuation spectroscopy with singly scattered ultrasound in the near and far fields

Dynamic sound scattering (DSS) is a powerful acoustic technique for investigating the motion of particles or other inclusions inside an evolving medium. In DSS, this dynamic information is obtained by measuring the field autocorrelation function of the temporal fluctuations of singly scattered acoustic waves. The technique was initially introduced 15 years ago, but its technical aspects were not adequately discussed then. This paper addresses the need for a more complete account of the method by describing in detail two different implementations of this sound scattering technique, one of which is specifically adapted to a common experimental situation in ultrasonics. The technique is illustrated by the application of DSS to measure the mean square velocity fluctuations of particles in fluidized suspensions, as well as the dynamic velocity correlation length. By explaining the experimental and analytical methods involved in realizing the DSS technique in practice, the use of DSS will be facilitated for future studies of particulate suspension dynamics and particle properties over a wide range of particle sizes and concentrations, from millimeters down to nanometers, where the use of optical techniques is often limited by the opacity of the medium.

Symmetry issues in the hybridization of multi-mode waves with resonators: an example with Lamb waves metamaterial

Locally resonant metamaterials derive their effective properties from hybridization between their resonant unit cells and the incoming wave. This phenomenon is well understood in the case of plane waves that propagate in media where the unit cell respects the symmetry of the incident field. However, in many systems, several modes with orthogonal symmetries can coexist at a given frequency, while the resonant unit cells themselves can have asymmetric scattering cross-sections. In this paper we are interested in the influence of symmetry breaking on the hybridization of a wave field that includes multiple propagative modes. The A₀ and S₀ Lamb waves that propagate in a thin plate are good candidates for this study, as they are either anti-symmetric or symmetric. First we designed an experimental setup with an asymmetric metamaterial made of long rods glued to one side of a metallic plate. We show that the flexural resonances of the rods induce a break of the orthogonality between the A₀/S₀ modes of the free-plate. Finally, based on numerical simulations we show that the orthogonality is preserved in the case of a symmetric metamaterial leading to the presence of two independent polariton curves in the dispersion relation.

Velocity and attenuation of scalar and elastic waves in random media: a spectral function approach

This paper investigates the scattering of scalar and elastic waves in two-phase materials and single-mineral-cubic, hexagonal, orthorhombic-polycrystalline aggregates with randomly oriented grains. Based on the Dyson equation for the mean field, explicit expressions for the imaginary part of Green's function in the frequency-wavenumber domain (ω, p), also known as the spectral function, are derived. This approach allows the identification of propagating modes with their relative contribution, and the computation of both attenuation and phase velocity for each mode. The results should be valid from the Rayleigh (low-frequency) to the geometrical optics (high-frequency) regime. Comparisons with other approaches are presented for both scalar and elastic waves.

Characterizing a model food gel containing bubbles and solid inclusions using ultrasound

Ultrasonic spectroscopy is used to characterize a model aerated food system consisting of agar gel in which both bubbles and polystyrene beads are embedded. By exploiting the distinct frequency dependence of each inclusion's acoustic resonances, it is demonstrated that the sizes of the bubbles and beads can be measured by ultrasound even when the size distributions are so similar that these inclusions are difficult to distinguish in optical images. While these results demonstrate the potential for applying ultrasonic spectroscopy to evaluate any soft heterogeneous material in which both bubbles and solid inclusions are present, the technique is especially relevant for functional foods, in which solid functional ingredients must be incorporated without degrading the aerated structure of the food and causing unacceptable quality impairment.

Acoustic quasimodes in two-dimensional dispersed random media

Using the generalized coherent-potential-approximation approach, we present the dispersion relation of the two-dimensional dispersed random media. In the intermediate-frequency regime, two acoustic modes are found in colloidal suspensions including cylindrical plastic rod in water background. The scattering cross section offers a good explanation for the two modes and the observed frequency gaps in the excitation spectra.

Diffusing acoustic wave spectroscopy

We have developed a technique in ultrasonic correlation spectroscopy called diffusing acoustic wave spectroscopy (DAWS). In this technique, the motion of the scatterers (e.g., particles or inclusions) is determined from the temporal fluctuations of multiply scattered sound. In DAWS, the propagation of multiply scattered sound is described using the diffusion approximation, which allows the autocorrelation function of the temporal field fluctuations to be related to the dynamics of the multiply scattering medium. The expressions relating the temporal field autocorrelation function to the motion of the scatterers are derived, focusing on the types of correlated motions that are most likely to be encountered in acoustic measurements. The power of this technique is illustrated with ultrasonic data on fluidized suspensions of particles, where DAWS provides a sensitive measure of the local relative velocity and strain rate of the suspended particles over a wide range of time and length scales. In addition, when combined with the measurements of the rms velocity of the particles using dynamic sound scattering, we show that DAWS can be used to determine the spatial extent of the correlations in the particle velocities, thus indirectly measuring the particle velocity correlation function. Potential applications of diffusing acoustic wave spectroscopy are quite far reaching, ranging from the ultrasonic nondestructive evaluation of the dynamics of inhomogeneous materials to geophysical studies of mesoscopic phenomena in seismology.

Light scattering by optically anisotropic scatterers: T-matrix theory for radial and uniform anisotropies

We extend the T-matrix approach to light scattering by spherical particles to some simple cases in which the scatterers are optically anisotropic. Specifically, we consider cases in which the spherical particles include radially and uniformly anisotropic layers. We find that in both cases the T-matrix theory can be formulated using a modified T-matrix ansatz with suitably defined modes. In a uniformly anisotropic medium we derive these modes by relating the wave packet representation and expansions of electromagnetic field over spherical harmonics. The resulting wave functions are deformed spherical harmonics that represent solutions of the Maxwell equations. We present preliminary results of numerical calculations of the scattering by spherical droplets. We concentrate on cases in which the scattering is due only to the local optical anisotropy within the scatterer. For radial anisotropy we find that nonmonotonic dependence of the scattering cross section on the degree of anisotropy can occur in a regime to which both the Rayleigh and semiclassical theories are inapplicable. For uniform anisotropy the cross section is strongly dependent on the angle between the incident light and the optical axis, and for larger droplets this dependence is nonmonotonic.