Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices

Propagation of internal deformations in dense granular flows

This paper analyses how local deformation develops in dense granular flows. Local kinematic fields including particle velocity fluctuations, local strain, and non-affine deformation are measured in simulated homogeneous shear flows at different inertial numbers I, prescribing the shear strain rate  and the normal stress. Results evidence that these fields are unsteady and spatially correlated, as previously observed in a wide range of soft materials. They reveal a mechanism of propagation of local deformation by which seed events of particle rearrangements trigger further rearrangements in their vicinity. It appears that this mechanism is strongly dependent on the inertial number, with cluster size and propagation velocity increasing as a power law of I when I → 0. This mechanism can help understand and model some behaviours of granular flows such as non-locality and transient rheology.

Mechanisms for recirculation cells in granular flows in rotating cylindrical rough tumblers

Friction at the endwalls of partially filled horizontal rotating tumblers induces curvature and axial drift of particle trajectories in the surface flowing layer. Here we describe the results of a detailed discrete element method study of the dry granular flow of monodisperse particles in three-dimensional cylindrical tumblers with endwalls and cylindrical wall that can be either smooth or rough. Endwall roughness induces more curved particle trajectories, while a smooth cylindrical wall enhances drift near the endwall. This drift induces recirculation cells near the endwall. The use of mixed roughness (cylindrical wall and endwalls having different roughness) shows the influence of each wall on the drift and curvature of particle trajectories as well as the modification of the free surface topography. The effects act in opposite directions and have variable magnitude along the length of the tumbler such that their sum determines both direction of net drift and the recirculation cells. Near the endwalls, the dominant effect is always the endwall effect, and the axial drift for surface particles is toward the endwalls. For long enough tumblers, a counter-rotating cell occurs adjacent to each of the endwall cells having a surface drift toward the center because the cylindrical wall effect is dominant there. These cells are not dynamically coupled with the two endwall cells. The competition between the drifts induced by the endwalls and the cylindrical wall determines the width and drift amplitude for both types of cells.

Experimental assessment of the effective friction at the base of granular chute flows on a smooth incline

We report on direct measurements of the basal force components for granular material flowing down a smooth incline. We investigate granular flows for a large range of inclination angles from θ=13.4^{∘} to 83.6° and various gate openings of the chute. We find that the effective basal friction coefficient μ_{B}, obtained from the ratio of the longitudinal force to the normal one, exhibits a systematic increase with increasing slope angle and a significant weakening with increasing particle holdup H (the depth-integrated particle volume fraction). At low angles, the basal friction is slightly less than or equal to tanθ. The deviation from tanθ can be interpreted as a contribution from the sidewall to the overall friction. At larger angles, the basal friction μ_{B} saturates at an asymptotic value that is dependent on the gate opening of the chute. Importantly, our data confirm the outcomes of recent discrete numerical simulations. First, for steady and fully developed flows as well as for moderately accelerated ones, the variation of the basal friction can be captured through a unique dimensionless number, the Froude number Fr, defined as Fr=U[over ¯]/(gHcosθ)^{1/2}, where U[over ¯] is the mean flow velocity. Second, the mean velocity scales with the particle holdup H with a power exponent close to 1/4, contrasting with the Bagnold scaling (U[over ¯]∼H^{3/2}).

Sidewall friction in confined surface flows of granular materials

We report numerical simulations of surface granular flows confined between two sidewalls. These systems exhibit both very slow and very energetic flows. Zhu et al. [1] have shown that in energetic confined systems, the Froude number at sidewalls and the sidewall effective friction coefficient are linked through a unique relation. We show that this relation is also valid for creep flows. It is independent of the angle of the flow but depends on the sidewall-grain friction coefficient. Our results shed light on boundary conditions that have to be used at sidewalls in continuum theories aiming to capture the behavior of granular systems from creeping to energetic flows.

Influence of granular temperature and grain rotation on the wall friction coefficient in confined shear granular flows

A depth-weakening wall friction coefficient, µw, has been reported from three-dimensional numerical simulations of steady and transient dense granular flows. To understand the degradation mechanisms, a scaling law for µw/ f and χ has been proposed where f is the intrinsic particle-wall friction and χ is the ratio of slip velocity to square root of granular temperature (Artoni & Richard, Phys. Rev. Lett., vol. 115 (15), 2015, 158001). Independently, a friction degradation model has been derived which describes a monotonically diminishing friction depends on a ratio of grain angular and slip velocities, Ω (Yang & Huang, Granular Matter, vol. 18 (4), 2016, 77). In search of experimental evidence for how these two parameters degrade the µw, an annular shear cell experiment was performed to estimate the bulk granular temperature, angular and slip velocities at sidewall through image-processing. Meanwhile, µw was measured by a force sensor to confirm the weakening towards the creep zone. The measured µw/ f − χ and µw/ f − Ω were both well-fitted to the corresponding models showing that both granular temperature and angular velocity are significant mechanisms to degrade the µw which broadens the research perspective on modeling the boundary condition of dense granular flows.

Effect of dissipation in rapid-gravitational granular flows

We investigate numerically high speed granular flows down an incline and focus our attention on the influence of the restitution coefficient e of binary collisions on the nature of the flow regimes. We show in particular that e plays a major role in rapid flows. Decreasing e leads in general to denser flows but also quicker flows. The increase of the mean flow velocity with decreasing e is explained as the result of the clustering instability which produces a dense and cold core moving very fast as a plug.

Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows

Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient μ scales with the square root of the local Péclet number Pe provided that the particle diameter exceeds the particle mean free path. With decreasing Pe and granular temperature gradient M, this general scaling breaks down, leading to a yield condition with a variable yield stress ratio characterized by M.

Inclined granular flow in a narrow chute

In this paper we presents a detailed description of granular flow down a flat, narrow chute using discrete element method simulations, with emphasis on the influence of sidewalls on the flow. The overall phase diagram is provided and it is found that there are four flow regimes (no flow, bulk flow, surface flow, and gas flow). The H̃_stop curve is very complicated and quite different from that in the case without sidewalls. The effective friction coefficient [Formula: see text] increases with pile height H̃ and a surface flow occurs when the inclination angle [Formula: see text] exceeds a critical value. The profile of [Formula: see text] shows that the [Formula: see text] rheology is valid in boundary layers. Furthermore, [Formula: see text] increases with the velocity of particles and there is a saturation to a nonzero value in static heap. For small H̃, the static heap vanishes and there is a bulk flow. A similarity between basal particles and sidewall particles indicates a universal role of the boundaries. In this bulk flow, there is a transition of the velocity profile with wall friction [Formula: see text]. When [Formula: see text] is large, the velocity is linear and decreases with increasing height. With small [Formula: see text], the velocity is nonlinear and the flow rate is roughly proportional to H̃^3/2.

Empirical investigation of friction weakening of terrestrial and Martian landslides using discrete element models

Understanding what controls the travelling distance of large landslides has been the topic of considerable debate. By combining observation and experimental data with depth-averaged continuum modelling of landslides and generated seismic waves, it was empirically observed that lower effective friction had to be taken into account in the models to reproduce the dynamics and runout distance of larger volume landslides. Moreover, such simulation and observation results are compatible with a friction weakening with velocity as observed in earthquake mechanics. We investigate here as to whether similar empirical reduced friction should be put into discrete element models (DEM) to reproduce observed runout of large landslides on Earth and on Mars. First we show that, in the investigated parameter range and for a given volume, the runout distance simulated by 3D DEM is not much affected by the number (i.e. size) of grains once this number attains ~ 8000. We then calibrate the model on laboratory experiments and simulate other experiments of granular flows on inclined planes, making it possible for the first time to reproduce the observed effect of initial volume and aspect ratio on runout distances. In particular, the normalised runout distance starts to depend on the volume involved only above a critical slope angle > 16-19°, as observed experimentally. Finally, based on field data (volume, topography, deposit), we simulate a series of landslides on simplified inclined topography. The empirical friction coefficient, calibrated to reproduce the observed runout for each landslide, is shown to decrease with increasing landslide volume (or velocity), going down to values as low as 0.1-0.2. No distinguishable difference is observed between the behaviour of terrestrial and Martian landslides.

Spreading of a granular droplet under horizontal vibrations

By means of three-dimensional discrete element simulations, we study the spreading of a granular droplet on a horizontally vibrated plate. Apart from a short transient with a parabolic shape, the droplet adopts a triangular profile during the spreading. The dynamics of the spreading is governed by two distinct regimes: a superdiffusive regime in the early stages driven by surface flow followed by a second one which is subdiffusive and governed by bulk flow. The plate bumpiness is found to alter only the spreading rate but plays a minor role on the shape of the granular droplet and on the scaling laws of the spreading. Importantly, we show that in the subdiffusive regime, the effective friction between the plate and the granular droplet can be interpreted in the framework of the μ(I)-rheology.

Recirculation cells for granular flow in cylindrical rotating tumblers

To better understand the velocity field and flowing layer structure, we have performed a detailed discrete element method study of the flow of monodisperse particles in a partially filled three-dimensional cylindrical rotating tumblers. Similar to what occurs near the poles in spherical and conical tumblers, recirculation cells (secondary flows) develop near the flat endwalls of a cylindrical tumbler in which particles near the surface drift axially toward the endwall, while particles deeper in the flowing layer drift axially toward the midlength of the tumbler. Another recirculation cell with the opposite sense develops next to each endwall recirculation cell, extending to the midlength of the tumbler. For a long enough tumbler, each endwall cell is about one quarter of the tumbler diameter in length. Endwall cells are insensitive to tumbler length and relatively insensitive to rotation speed (so long as the flowing layer remains flat and continuously flowing) or fill level (from 25% to 50% full). However, for shorter tumblers (0.5 to 1.0 length/diameter aspect ratio) the endwall cell size does not change much, while center cells reduce their size and eventually disappear for the shortest tumblers. For longer tumblers (length/diameter aspect ratio larger than 2), a stagnation zone appears in between the central cells. These results provide insight into the mixing of monodisperse particles in rotating cylindrical tumblers as well as the frictional effects of the tumbler endwalls.

Effective Wall Friction in Wall-Bounded 3D Dense Granular Flows

We report numerical simulations on granular shear flows confined between two flat but frictional sidewalls. Novel regimes differing by their strain localization features are observed. They originate from the competition between dissipation at the sidewalls and dissipation in the bulk of the flow. The effective friction at sidewalls is characterized (effective friction coefficient and orientation of the friction force) for each regime, and its interdependence with slip and force fluctuations is pointed out. We propose a simple scaling law linking the slip velocity to the granular temperature in the main flow direction which leads naturally to another scaling law for the effective friction.

Granular flows on a dissipative base

We study inclined channel flows of sand over a sensor-enabled composite geotextile fabric base that dissipates granular fluctuation energy. We record strain of the fabric along the flow direction with imbedded fiber-optic Bragg gratings, flow velocity on the surface by correlating grain position in successive images, flow thickness with the streamwise shift of an oblique laser light sheet, velocity depth profile through a transparent side wall using a high-speed camera, and overall discharge rate. These independent measurements at inclinations between 33∘ and 37∘ above the angle of repose at 32.1±0.8∘ are consistent with a mass flow rate scaling as the 3/2 power of the flow depth, which is markedly different than flows on a rigid bumpy boundary. However, this power changes to 5/2 when flows are forced on the sand bed below its angle of repose. Strain measurements imply that the mean solid volume fraction in the flowing layer above the angle of repose is 0.268±0.033, independent of discharge rate or inclination.