Abstract: © 2020, Springer Nature B.V. The time-domain propagation of scalar waves across a periodic row of inclusions is considered in 2D. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime. Furthermore, a high contrast between one of the constitutive moduli of the inclusions and of the background medium is also assumed. So the wavelength within the inclusions is of the order of their typical size, which can further induce local resonances within the microstructure. In Pham et al. (J. Mech. Phys. Solids 106:80–94, 2017), two-scale homogenization techniques and matched-asymptotic expansions have been employed to derive, in the harmonic regime, effective jump conditions on an equivalent interface. This homogenized model is frequency-dependent due to the resonant behavior of the inclusions. In this context, the present article aims at investigating, directly in the time-domain, the scattering of waves by such a periodic row of resonant scatterers. Its effective behavior is first derived in the time-domain and some energy properties of the resulting homogenized model are analyzed. Time-domain numerical simulations are then performed to illustrate the main features of the effective interface model obtained and to assess its relevance in comparison with full-field simulations.

Abstract: © 2020, The Author(s). Dilute gas–particle suspensions in which the particles are carried by the fluid are found in various industrial and geophysical contexts. One fundamental issue that limits our understanding of such systems is the difficulty to obtain information on the particle concentration inside these often optically opaque suspensions. To overcome this difficulty, we develop ultrasonic spectroscopy to monitor the local particle concentration ϕ of glass particles (with diameters d∼ 77 μ m or 155 μ m) suspended in air. First, we determine the minimal air velocity, U∗, necessary to suspend the particles from the maximum decrease in the transmitted wave amplitude and velocity of ultrasound propagating through the suspension. Next, setting the air velocity at U∗, we increase the mass of particles and monitor acoustically the local solid volume fraction, ϕ, by measuring the ultrasound wave attenuation coefficient and phase velocity as a function of frequency on the basis of classical scattering and hydrodynamic models. For the frequency ranges and suspensions considered here, the viscous dissipation dominates over scattering and thermal conduction losses. We show that, for a characteristic air velocity U∗, the locally measured ϕ reaches a critical value, in agreement with a recent study on turbulent gas–particle mixtures. Moreover, we find that this critical ϕ increases with the size of the particles. Finally, analysis of the temporal fluctuations of the locally measured solid volume fraction, suggests that high density regions (clusters) are present even in suspensions with concentrations below the critical concentration. This differs from the current hypothesis according to which the critical concentration coincides with the onset of cluster formation.