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

Abstract

Observing and understanding the motion of an intruder through opaque dense suspensions such as quicksand remains a practical and conceptual challenge. Here we use an ultrasonic probe to monitor the sinking dynamics of a steel ball in a dense glass bead packing (3D) saturated by water. We show that the frictional model developed for dry granular media can be used to describe the ball motion induced by horizontal vibration. From this rheology, we infer the static friction coefficient and effective viscosity that decrease when increasing the vibration intensity. Our main finding is that the vibration-induced reduction of the yield stress and increase of the sinking depth are presumably due to micro-slips induced at the grain contacts but without visible plastic deformation due to macroscopic rearrangements, in contrast to dry granular packings. To explain these results, we propose a mechanism of acoustic lubrication that reduces the inter-particle friction and leads to a decrease of the yield stress. This scenario is different from the mechanism of liquefaction usually invoked in loosely packed quicksands where the vibration-induced compaction increases the pore pressure and decreases the confining pressure on the solid skeleton, thus reducing the granular resistance to external load.

Time reversal of ultrasound in granular media

“…2 within the continuum elasticity still holds on the local scale of a few grain size. This appears consistent with recent wave velocity measurements performed in stressed granular layers with thickness ~ 5d where the fluctuations in V P remain less than 10% [26].…”

Triggering granular avalanches with ultrasound

“…From the Mindlin friction model, we have shown that decreases of both the shear contact stiffness k t /k t [12] and the interparticle friction coefficient μ p /μ p [42] are approximately proportional to ∼ − f t /(μ p f n ), where f t is the oscillating tangential force and f n the static normal force at a single contact. Such a scaling of vibration-induced softening ∼ −F ac /(μ p W ) can also be generalized to the effective shear contact stiffness at a multicontact interface between solids [51] and to the shear modulus [13] and the yield stress [52] in a vibrated granular medium where polydisperse contact asperities are replaced by grain contacts and inertial effects are negligible. Here F ac is the imposed macroscopic oscillating shear force, W the normal load, and μ the (averaged) effective interparticle friction coefficient.…”

Maximal submergence in dense granular suspensions

“…We begin by writing down the balance of forces on a falling sphere (shown in figure 1) [11]. This is the sum of the weight, the buoyancy force, and the frictional force due to the suspension:…”

“…where m = (4/3)πR 3 ρ b , ρ b is the mass density of the ball, ρ sus is the density of the suspension, and Δρ 1 = ρ b − ρ sus . The frictional force splits into two parts (the threshold force and the drag force), so this equation is written completely as [11] ⎛ ⎝ ⎞ ⎠…”

“…van den Wildenberg et al used an ultrasonic probe to track the motion of a steel ball sinking into a dense glass bead packing saturated with water, finding that sinking can be induced by horizontal vibrations of the bead packing [6,7]. It also been established in various works that a ball can stop sinking at a certain depth due to jamming of the particles in the suspension, which depends on the packing density of the particles, the confining pressure, and the shear stress applied by the solid body [11][12][13][14].…”