Drag force in a cold or hot granular medium

Force on a sphere suspended in flowing granulate

We investigate the force of flowing granular material on an obstacle. A sphere suspended in a discharging silo experiences both the weight of the overlaying layers and drag of the surrounding moving grains. In experiments with frictional hard glass beads, the force on the obstacle was practically flow-rate independent. In contrast, flow of nearly frictionless soft hydrogel spheres added drag to the gravitational force. The dependence of the total force on the obstacle diameter is qualitatively different for the two types of material: It grows quadratically with the obstacle diameter in the soft, low-friction material, while it grows much weaker, nearly linearly with the obstacle diameter, in the bed of glass spheres. In addition to the drag, the obstacle embedded in flowing low-friction soft particles experiences a total force from the top as if immersed in a hydrostatic pressure profile, but a much lower counterforce acting from below. In contrast, when embedded in frictional, hard particles, a strong pressure gradient forms near the upper obstacle surface.

Rheology of a 2D granular film

We study experimentally the rheology of a macroscopic particle-laden soap film, designated as a "Granular Film", in the simple shear configuration. Macroscopic particles are dispersed in a soap film, while being large enough that they bridge both fluid interfaces. We simultaneously perform macroscopic rheological measurements with a classical rheometer and investigate interactions at the particle scale with a camera underneath the film. The determination of the velocity field of the grains reveals the presence of an inhomogeneous shear within the granular film. Trying to correlate both measurements unveils the non-locality of the rheology of the granular film: similar to what has been observed in a dry granular material, we find an highly-sheared zone close to the moving wall contrasting with a large quasistatic area. This behavior can be accounted for through extended kinetic theory and correlated with a transition in the dominant component of the stress.

Rheology of granular rafts

Rheology of macroscopic particle-laden interfaces, called "granular rafts," has been experimentally studied in the simple shear configuration. The shear-stress relation obtained from a classical rheometer exhibits the same behavior as a Bingham fluid, and the viscosity diverges with the surface fraction according to evolutions similar to 2D suspensions. The velocity field of the particles that constitute the granular raft has been measured in the stationary state. These measurements reveal nonlocal rheology similar to dry granular materials. Close to the walls of the rheometer cell, one can observe regions of large local shear rate while in the middle of the cell a quasistatic zone exists. This flowing region, characteristic of granular matter, is described in the framework of an extended kinetic theory showing the evolution of the velocity profile with the imposed shear stress. Measuring the probability density functions of the instantaneous local shear rate, we provide evidence of a balance between positive and negative instantaneous local shear rate. This behavior is the signature of a quasistatic region inside the granular raft.

Added-mass force in dry granular matter

From two-dimensional (2D) numerical simulations of the motion of a circular intruder into a dry granular packing, we provide evidence for a specific force term in the case of unsteady motion in addition to the force corresponding to a steady motion. We show that this additional term is proportional to the acceleration of the intruder relative to the grains as the added-mass force known for simple fluids. This force term corresponds to a variation in the kinetic energy of the surrounding flow and is characterized by a coefficient C_{AM} which is intrinsically linked to the nature of the granular media. An analytical calculation of the added-mass coefficient C_{AM} is developed based on the specific velocity field known for 2D granular flow around a cylinder. The theoretical value is shown to depend on the grain-cylinder size ratio, in good agreement with the measurements from our unsteady simulations.

Static and dynamic features of granular material failure due to upward pulling of a buried sphere by a slowly increasing force

A spherical intruder embedded in a confined granular column is extracted by pulling it upward by an attached string. As the tension of the string gradually increases, a failure event occurs at a certain pulling force, leading to rapid upward acceleration of the intruder. The threshold force and the dynamics of the failure event are experimentally investigated for different filling heights and column diameters, using Ottawa sand and glass beads. For the Ottawa sand, we find that the failure force can be fit by a model describing the weight of the granular material in a cone with the vertex at the bottom of the intruder and a vertex angle of 72°. The agreement between the model and experiments is good for heights less than the column (tube) diameter, but measured values deviate from the model for larger heights. We also report on experiments with glass beads that reveal unexpected effects for relatively small ratios of tube diameters to grain size. The dynamics of the intruder during the failure event is studied using high-speed video analysis. The granular drag force monotonically decays during the pullout for sufficiently large tube diameters. In narrow columns, a monotonic decay of drag force after failure is observed for low heights, whereas a secondary peak can be seen in sufficiently deep and narrow columns, indicating the existence of different mechanisms of failure. The normalized drag force declines with intruder displacement closely for all tube diameters within small displacements.

Nonlocal continuum modeling of dense granular flow in a split-bottom cell with a vane-shaped intruder

Shear flow in one spatial region of a dense granular material-induced, for example, through the motion of a boundary-fluidizes the entire granular material. One consequence is that the yield condition vanishes throughout the granular material-even in regions that are very far from the "primary," boundary-driven shear flow. This phenomenon may be characterized through the mechanics of intruders embedded in the granular medium. When there is no primary flow, a critical load must be exceeded to move the intruder; however, in the presence of a primary flow, intruder motion occurs even when an arbitrarily small external load is applied to an intruder embedded in a region far from the sheared zone. In this paper, we apply the nonlocal granular fluidity (NGF) model-a continuum model that involves higher-order flow gradients-to simulate the specific case of dense flow in a split-bottom cell with a vane-shape intruder. Our simulations quantitatively capture the key features of the experimentally observed phenomena: (1) the vanishing of the yield condition, (2) an exponential-type relationship between the applied torque and the rotation rate, (3) the effect of the distance between the intruder and the primary flow zone, and (4) the direction-dependence of the torque/rotation-rate relation, in which the observed relation changes depending on whether the intruder is forced to rotate along with or counter to the primary flow. Importantly, this represents the first fully three-dimensional validation test for a nonlocal model for dense granular flow in general and for the NGF model in particular.

A heavy intruder in a locally-shaken granular solid

We experimentally investigate the gravitational-driven motion of a heavy object inside a vertical 2D assembly of identical, plastic cylinders arranged in a regular, triangular lattice. The bottom of the assembly is in contact with a rough plate whose horizontal, sinusoidal motion induces the formation of shear bands in the granular solid, aligned with the edges of the lattice. The intruder sinks when the width of the shear band is as large as its size and halts once the regular configuration of the grains is recovered. The resulting vertical motion of the intruder is random and intermittent, as in disordered granular or colloidal systems near jamming, with alternate flows and blockades. We show, in analogy with earthquakes, that the relation between the size and the duration of the flowing events follows a power-law with an exponent larger than one, and that the statistics of their size is compatible with the Gutenberg-Richter law. We also show that the probability density function of times between flowing events is similar to the Omori law governing the distribution of aftershock sequences following large earthquakes. Finally, the analysis of the velocity fluctuations of the intruder points to a transition from a strong to a weak contact network in the ordered granular assembly, similar to the transition from jammed to fragile states in disordered systems.

The role of initial speed in projectile impacts into light granular media

Projectile impact into a light granular material composed of expanded polypropylene (EPP) particles is investigated systematically with various impact velocities. Experimentally, the trajectory of an intruder moving inside the granular material is monitored with a recently developed non-invasive microwave radar system. Numerically, discrete element simulations together with coarse-graining techniques are employed to address both dynamics of the intruder and response of the granular bed. Our experimental and numerical results of the intruder dynamics agree with each other quantitatively and are in congruent with existing phenomenological model on granular drag. Stepping further, we explore the ‘microscopic’ origin of granular drag through characterizing the response of granular bed, including density, velocity and kinetic stress fields at the mean-field level. In addition, we find that the dynamics of cavity collapse behind the intruder changes significantly when increasing the initial speed . Moreover, the kinetic pressure ahead of the intruder decays exponentially in the co-moving system of the intruder. Its scaling gives rise to a characteristic length scale, which is in the order of intruder size. This finding is in perfect agreement with the long-scale inertial dissipation type that we find in all cases.

Buckling of a rod penetrating into granular media

We investigate experimentally the possible buckling of a thin rod when penetrating downwards into a granular packing. When its bottom end reaches a specific depth, the rod may start buckling provided that the embrace is not enough to stop that phenomenon. The critical rod depth z_{c} at buckling is observed to scale with the rod length L either as 1/L or 1/L^{2}. These two scalings are shown to arise from the two resistant force terms that come into play during the rod penetration: a pressure force at the bottom of the rod that increases linearly with depth and a frictional force on the rod side that increases quadratically with depth. At the buckling point, the destabilizing force corresponds to the expected value given from conventional Euler's critical load for a rod bottom end considered as fixed in the granular clutch. Finally, we draw a buckling-nonbuckling phase diagram in a parameter space given by the rod aspect ratio and a rod-to-grain stress ratio.