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

Abstract

We present an experimental investigation of shear elastic wave propagation along the surface of a dense granular suspension. Using an ultrafast ultrasound scanner, we monitor the softening of the shear wave velocity inside the optically opaque medium as the driving amplitude increases. For such nonlinear behavior two regimes are found: in the first regime, we observe a significant shear modulus weakening, but without visible grain rearrangements.In the second regime, there is a clear grain 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. Investigation of these nonlinear shear waves may bridge the gap between two disjoint approaches for describing the dynamics near unjamming: linear elastic soft modes and nonlinear collisional shock.

Ultrasonic tracking of a sinking ball in a vibrated dense granular suspension

“…Then, the weakening of the granular material is presumably ascribed to the modification of the contact network by the acoustic vibration. Indeed, it has been shown that the coefficient of friction between two smooth solid spheres can be reduced via a mechanism of acoustic lubrication 34 , leading to the softening of the tangential contact stiffness and accordingly to a decrease of the sound velocities observed in granular packings 24,30,31 . To rationalize this hypothesis in disordered granular packing, we rely on a friction model developed for a multi-contact solid interface in which the shear interfacial stiffness is reduced through the slipping of asperities under oscillatory shear 33 .…”

“…To rationalize this hypothesis in disordered granular packing, we rely on a friction model developed for a multi-contact solid interface in which the shear interfacial stiffness is reduced through the slipping of asperities under oscillatory shear 33 . If we generalize this concept by replacing the asperities by the grain contacts, we can explain the softening of the shear modulus G and thus of wave velocity observed in a 3D dense granular suspension 31 via the slipping of the contacts without any rearrangement of grains. As the yield stress τ 0 (as well as µ 0 = τ 0 /P g ) is roughly proportional to the shear modulus (µ 0 ~ G) in a yield stress fluid 3,27 , we may adopt the formula developed for the shear modulus softening as 31,33 , µ 0 / µ 0 * ~ G/ G 0 ≈ 1/[1+Γ/ (2µ p ))+(5/4)(Γ/ (2µ p )) 2 ] induced by the external vibration Γ (<1).…”

“…If we generalize this concept by replacing the asperities by the grain contacts, we can explain the softening of the shear modulus G and thus of wave velocity observed in a 3D dense granular suspension 31 via the slipping of the contacts without any rearrangement of grains. As the yield stress τ 0 (as well as µ 0 = τ 0 /P g ) is roughly proportional to the shear modulus (µ 0 ~ G) in a yield stress fluid 3,27 , we may adopt the formula developed for the shear modulus softening as 31,33 , µ 0 / µ 0 * ~ G/ G 0 ≈ 1/[1+Γ/ (2µ p ))+(5/4)(Γ/ (2µ p )) 2 ] induced by the external vibration Γ (<1). Here µ 0 * is the static friction coefficient in dry granular media without external vibration and µ p is the interparticle friction coefficient.…”

“…Finally we believe that this mechanism of acoustic lubrication may also partly explain the sinking of the intruder in the vibrated dry granular packing. But the effect of the packing density change needs to be accounted for due to the plastic rearrangements of grains 31 . Note that the vibration-induced random motions of grains in dry granular media observed here at the top surface were previously analysed 19,22 using the concept of effective temperature determined by Γ. Interestingly, for a same external vibration Γ, our experiments showed that the ball takes a longer time in dry packings than in water-saturated packings to reach the final depth (see Supplementary Fig.…”

The dispersive velocity of compressional waves in magmatic suspensions

“…In dense suspensions where solids are in cohesionless contact, the bulk and rigidity moduli also depend on the confining pressure and amplitude of the perturbation, which affects the non-affine motions of the grains, contact slidings, and shear dilatancy (e.g. Makse et al 2004, Brum et al 2019. Such phenomena may induce either strengthening or weakening of the rigidity of the suspension because of the change in the contact network (Van den Wildenberg et al 2013).…”