Acoustic transparency in dense granular suspensions

Abstract

We demonstrate the existence of a frequency band exhibiting acoustic transparency in 2D and 3D dense granular suspensions, enabling the transmission of a low-frequency ballistic wave excited by a high-frequency broadband ultrasound pulse. This phenomenon is attributed to spatial correlations in the structural disorder of the medium. To support this interpretation, we use an existing model that incorporates such correlations via the structure factor. Its predictions are shown to agree well with those of the Generalized Coherent Potential Approximation (GCPA) model, which is known to apply at high volume fractions, including the close packing limit, but does not explicitly account for disorder correlation. Within the transparency band, attenuation is found to be dominated by absorption rather than scattering. Measurements of the frequency dependence of the absorption coefficient reveal significant deviations from conventional models, challenging the current understanding of acoustic absorption in dense granular media.

Figures (5)

• Figure 1: (a) Schematic representation of the experimental setup used for the Time Reversal experiment. The photograph reveals that the beads forming the sample are not perfectly spherical and exhibit slight polydispersity. (b) A typical waveform recorded inside the medium when a two-cycle sinusoidal pulse is emitted by one element of the transducer array. The signal consists of an initial low-frequency arrival - corresponding to the coherent ballistic wave - followed by a long, multiply scattered tail known as the coda. A closer look reveals that the frequencies contained in the ballistic pulse are significantly lower than those in the coda. Comparing the spectrum of the full signal (solid line) to that of a reference pulse transmitted through water (dashed line) highlights how propagation through the suspension enhances the relative contribution of the low-frequency ballistic component. Please note that both spectra are normalized to their respective maxima to facilitate comparison since the amplitude of the signal transmitted through the suspension is much lower than that of the reference.
• Figure 2: Experimental setup (2D). The samples consist of random arrangements of copper cylinders. (a) A dilute random medium with a surface coverage $\Phi_S = 4.4\%$. (b) A compact medium with surface coverage $\Phi_S= 72\%$. (c) The sample is immersed in water between two piezo-electric transducers (diameter: 12.5 mm) operating at a central frequency of 1 MHz. The emitting transducer on the left is driven by a three-cycle sine wave at its central frequency.
• Figure 3: Averaged transmitted waveforms through a 2D arrangement of copper cylinders and corresponding time-frequency maps, as a function of sample thickness. The wave field is spatially averaged over the surface of the receiving transducer surface, whose diameter is about 2.5 times the wavelength at 0.3 MHz. In panel (a) (respectively, panel (b)), an additional average is taken over 12 (respectively, 10) different relative source-receiver positions with respect to the sample. Note that the number of realizations is not sufficient to fully suppress the coda. Time-frequency analysis is performed using 15$\mu s$-long sliding windows with a step size of 0.3 $\mu s$. (a) Dilute medium: $\Phi_S = 4.4\%$. The coherent wave tends to vanish for the largest sample thickness. (b) Compact medium: $\Phi_S= 72\%$. As the sample thickness increases, high-frequency components tend to disappear, leaving only the low-frequency ballistic wave.
• Figure 4: Impact of structural correlations on ultrasound scattering in dense granular suspensions, for two packing fractions of glass beads. Top: structure factor $S(q)$ as a function of the reduced scattering wave number $qd$, where $q=\frac{4\pi}{\lambda}\sin(\theta/2)$, with $\lambda$ the wavelength in water, $\theta$ the scattering angle, and $d$ the bead diameter. The gray-shaded region highlights the low-$q$ range where $S(q)$ falls below unity (except at $q=0$ where $S(0)=1$ in any case). Middle: angular and frequency dependence of the structure factor. Bottom: Effective scattering cross section. Predictions based on the structure factor $S(q)$ (thick solid red line) and the GCPA model (thin solid blue line) show good agreement. In particular, both models predict a vanishing cross section within the frequency band marked by the gray-shaded area. For reference, the theoretical scattering cross section of a single glass bead 10.1121/1.1906780 is shown as a dotted line.
• Figure 5: (a) Experimental setup used to measure acoustic transmission through a dense granular suspension of glass beads (diameter $d=1.5\mathrm{mm}$). The emitting transducer is excited with a half-period sine wave at its central frequency (3.5 MHz). The receiving transducer is mounted on a computer-controlled translation stage, allowing signal acquisition over source-receiver distances ranging from 5 mm to 50 mm in steps of 0.5 mm. (b) Top: transmitted signal amplitude as a function of frequency and propagation distance. Middle: spectra extracted from the top panel at two propagation distances and comparison with the spectrum in water (red solid line). Bottom: measured extinction length (crosses) compared with the GCPA prediction for the scattering mean free path (solid line).