Acoustic probing of the jamming transition in an unconsolidated granular medium

Finite amplitude waves in jammed matter

Here we use simulations and theory to show that, close to the jamming point, an arbitrary initial distortion of a granular media induces the formation of forward and backward non-linear finite amplitude waves. There are two regimes in the evolution of these waves (near field and far field). Initially, non-linear interactions between forward and backward waves dominate the propagation, leading to complex early evolution (near field). At longer times, forward and backwards waves cease interacting in the far field, and the propagation enters a new regime. Here the waves acquire a triangular-like profile, and evolve in a self-similar fashion characterized by a power law attenuation, whose exponent is weakly dependent on the initial pressure of the system. The finite amplitude waves gradually become linear waves when the amplitude of the initial distortion decreases, or the confining pressure on the system increases.

Drastic slowdown of the Rayleigh-like wave in unjammed granular suspensions

We present an experimental investigation of Rayleigh-like wave propagation along the surface of a dense granular suspension. Using an ultrafast ultrasound scanner, we monitor the softening of the shear modulus via the Rayleigh-like wave velocity slowdown in the optically opaque medium as the driving amplitude increases. For such nonlinear behavior two regimes are found when increasingthe driving amplitude progressively: First, we observe a significant shear modulus weakening due to the microslip on the contact level without macroscopic rearrangements of grains. Second, there is a clear macroscopic plastic rearrangement accompanied by a modulus decrease up to 88%. A friction model is proposed to describe the interplay between nonlinear elasticity and plasticity, which highlights the crucial effect of contact slipping before contact breaking or loss. Investigation of this nonlinear Rayleigh-like wave may bridge the gap between two disjoint approaches for describing the dynamics near unjamming: linear elastic soft modes and nonlinear collisional shock.

Effect of the microstructure on the propagation velocity of ultrasound in magnetic powders

We analyze experimentally and theoretically the sound propagation velocity of P-waves in granular media made of micrometer-size magnetite particles under an external magnetic field. The sound velocity is measured in a coherent (long-wavelength) regime of propagation after a controlled sample preparation consisting of a fluidization and the application of a magnetic field. Several different procedures are applied and result in different but reproducible particle arrangements and preferential contact orientations affecting the measured sound velocity. Interestingly, we find that the sound velocity increases when the magnetic field is applied parallel to the sound propagation direction and decreases when the magnetic field is applied perpendicular to the sound propagation direction. The observed qualitative relationship between the changes in the particle arrangement and the sound velocity is analyzed theoretically based on an effective medium theory adapted to account for the effect of the magnetic field in the preparation procedure and its influence on the medium contact fabric.

Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity

We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.

Sonic sands

Many desert sand dunes emit a loud sound with a characteristic tremolo around a well-defined frequency whenever sand is avalanching on their slip face. This phenomenon, called the 'song of dunes', has been successfully reproduced in the lab, on a smaller scale. In all cases, the spontaneous acoustic emission in air is due to a vibration of the sand, itself excited by a granular shear flow. This review presents a complete characterization of the phenomenon-frequency, amplitude, source shape, vibration modes, instability threshold-based on recent studies. The most prominent characteristics of acoustic propagation in weakly compressed granular media are then presented. Finally, this review describes the different mechanisms proposed to explain booming avalanches. Measurements performed to test these theories against data allow one to contrast explanations that must be rejected-sound resonating in a surface layer of the dune, for instance-with those that still need to be confirmed to reach a scientific consensus-amplification of guided elastic waves by friction, in particular.

Repulsive contact interactions make jammed particulate systems inherently nonharmonic

Many jammed particulate systems, such as granular and colloidal materials, interact via repulsive contact forces. We find that these systems possess no harmonic regime in the large system limit (N→∞) for all compressions Δϕ studied, and at jamming onset Δϕ→0 for all N. We perform fixed energy simulations following perturbations with amplitude δ along eigendirections of the dynamical matrix. The fluctuations abruptly spread to all modes for δ≈δ(c) (where a single contact breaks) in contrast to linear and weakly nonlinear behavior. For δ > δ(c), all discrete modes disappear into a continuous frequency band. <δ(c)> scales with 1/N and Δϕ, which limits harmonic behavior to only overcompressed systems. The density of vibrational modes deviates strongly from that predicted from the dynamical matrix when the system enters the nonharmonic regime, which significantly affects its mechanical and transport properties.

Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads

Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.

Experimental study of the jamming transition at zero temperature

We experimentally investigate jamming in a quasi-two-dimensional granular system of automatically swelling particles and show that a maximum in the height of the first peak of the pair correlation function is a structural signature of the jamming transition at zero temperature. The same signature is also found in the second peak of the pair correlation function, but not in the third peak, reflecting the underlying singularity of jamming transition. We also study the development of clusters in this system. A static length scale extracted from the cluster structure reaches the size of the system when the system approaches the jamming point. Finally, we show that in a highly inhomogeneous system, friction causes the system to jam in series of steps. In this case, jamming may be obtained through successive buckling of force chains.

Laboratory singing sand avalanches

Some desert sand dunes have the peculiar ability to emit a loud sound up to 110 dB, with a well-defined frequency: this phenomenon, known since early travelers (Darwin, Marco Polo, etc.), has been called the song of dunes. But only in late 19th century scientific observations were made, showing three important characteristics of singing dunes: first, not all dunes sing, but all the singing dunes are composed of dry and well-sorted sand; second, this sound occurs spontaneously during avalanches on a slip face; third this is not the only way to produce sound with this sand. More recent field observations have shown that during avalanches, the sound frequency does not depend on the dune size or shape, but on the grain diameter only, and scales as the square root of g/d--with g the gravity and d the diameter of the grains--explaining why all the singing dunes in the same vicinity sing at the same frequency. We have been able to reproduce these singing avalanches in laboratory on a hard plate, which made possible to study them more accurately than on the field. Signals of accelerometers at the flowing surface of the avalanche are compared to signals of microphones placed above, and it evidences a very strong vibration of the flowing layer at the same frequency as on the field, responsible for the emission of sound. Moreover, other characteristics of the booming dunes are reproduced and analyzed, such as a threshold under which no sound is produced, or beats in the sound that appears when the flow is too large. Finally, the size of the coherence zones emitting sound has been measured and discussed.

Jamming of soft particles: geometry, mechanics, scaling and isostaticity

Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a rigid, disordered state where they withstand finite shear stresses before yielding. Here we review the current understanding of the transition to jamming and the nature of the jammed state for disordered packings of particles that act through repulsive contact interactions and are at zero temperature and zero shear stress. We first discuss the breakdown of affine assumptions that underlies the rich mechanics near jamming. We then extensively discuss jamming of frictionless soft spheres. At the jamming point, these systems are marginally stable (isostatic) in the sense of constraint counting, and many geometric and mechanical properties scale with distance to this jamming point. Finally, we discuss current explorations of jamming of frictional and non-spherical (ellipsoidal) particles. Both friction and asphericity tune the contact number at jamming away from the isostatic limit, but in opposite directions. This allows one to disentangle the distance to jamming and the distance to isostaticity. The picture that emerges is that most quantities are governed by the contact number and scale with the distance to isostaticity, while the contact number itself scales with the distance to jamming.

Rheology of a sonofluidized granular packing

We report experimental measurements on the rheology of a dry granular material under a weak level of vibration generated by sound injection. First, we measure the drag force exerted on a wire moving in the bulk. We show that when the driving vibration energy is increased, the effective rheology changes drastically: going from a non-linear dynamical friction behavior --weakly increasing with the velocity-- up to a linear force-velocity regime. We present a simple heuristic model to account for the vanishing of the stress dynamical threshold at a finite vibration intensity and the onset of a linear force-velocity behavior. Second, we measure the drag force on spherical intruders when the dragging velocity, the vibration energy, and the diameters are varied. We evidence a so-called "geometrical hardening" effect for smaller-size intruders and a logarithmic hardening effect for the velocity dependence. We show that this last effect is only weakly dependent on the vibration intensity.

Modeling of acoustic penetration into sandy sediments: physical and geometrical aspects

Two different approaches to the problem of acoustic penetration into sandy marine sediments are considered: application of the Buckingham constitutive model for sediment with a plane surface and boundary element analysis of a rough surface of sediment represented as a homogeneous fluid. By a careful modeling of the constitutive behavior for plane seafloors, it is possible to partly reproduce some features of known experimental dependencies for acoustical pressure. However, accounting for roughness appears to be more important. Accordingly, the authors present a detailed numerical analysis of penetration into rough sediments using the boundary element method. The simulation results support conclusions reached by other investigators and demonstrate how local surface irregularities violate the evanescence condition that holds for a plane interface at subcritical incidence, thus considerably increasing penetration. The results apply to the frequency range 0.5-50 kHz and grazing angles larger than approximately 6 degrees -8 degrees at 10-50 kHz. For lower frequencies, when diffraction becomes important, the lowest possible grazing angle strongly depends on the range covered by the incident beam and is, in general, considerably larger. The authors provide several characteristic examples with frequencies 5 and 15 kHz and grazing angles 15 degrees -30 degrees illustrating the impact of roughness on penetration.

Evidence of rayleigh-hertz surface waves and shear stiffness anomaly in granular media

Using the nonlinear dependence of sound propagation speed with pressure, we evidence the anomalous elastic softness of a granular packing in the vicinity of the jamming transition. Under gravity and close to a free surface, the acoustic propagation is only possible through surface modes guided by the stiffness gradient. These Rayleigh-Hertz modes are evidenced in a controlled laboratory experiment. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of nonlinear elasticity including finite size effects. These results allow one to access the elastic properties of the packing under vanishing confining pressure.