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}).

Three-dimensional analysis of the collision process of a bead on a granular packing.

We present results of the collision process of a bead onto a static granular packing. We provide, in particular, a three-dimensional (3D) extensive characterization of this process from a model experiment that allows us to propel a spherical bead onto a granular packing with a well-controlled velocity and impact angle. A collision typically produces a high-energy particle (rebound particle) and several low-energy grains (ejected particles). The collision process is recorded by means of two fast video cameras. The sequence of images from both cameras are then analyzed via image processing and the trajectories of all particles are reconstructed in 3D space. We show that the incident particle does not remain in the vertical incident plane after the rebound and that the deviation angle increases with increasing impact angle. Concerning the ejected particles, we demonstrated that the ejection angle (measured with respect to the horizontal plane) is surprisingly independent of both the impact angle and velocity of the incident particle, and is very close to 60 degrees . The horizontal component of the ejection speed of the splashed particles is found to be weakly dependent on the incident speed and impact angle, and is relatively isotropic (no particular horizontal direction is favored). This last feature suggests that the bead packing acts as a perfect diffusive medium with respect to energy propagation.

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.

Collision process between an incident bead and a three-dimensional granular packing.

We report on experimental studies of the collision process between an incident bead and a three-dimensional granular packing (made of particles identical to the impacting one). The understanding of such a process and the resulting ejection of particles is, in particular, crucial to describe eolian sand transport. We present here an extensive experimental analysis of the collision and ejection process. The analysis is two dimensional in the sense that we determined only the vertical component V{z} of the ejection velocity of the splashed particles and the horizontal component V{x} lying in the incident plane. We extracted in particular the distribution of the ejection velocities for a wide range of impact angles theta{i} and incident velocity V{i} . We show that the mean quadratic horizontal velocity of the splashed particles is almost insensitive to changes in the impact angle and velocity, while the mean quadratic vertical velocity slightly increases with increasing impact velocity (as V{i}{1/2}). Moreover, the mean number of splashed particles per collision is found to be dependent on both the impact angle and velocity, and to scale with the impact speed as V{i}{3/2}. A consequence of these outcomes is that the sum of the kinetic energy of the splashed particles is directly proportional to the kinetic energy of the incident particle. Finally, we provide the bivariate probability distribution function P(V{x},V{z}) of the ejection velocities and show that it can be approximated by the product of a log-normal distribution and a circular normal one.

Grain-scale modeling and splash parametrization for aeolian sand transport.

The collision of a spherical grain with a granular bed is commonly parametrized by the splash function, which provides the velocity of the rebounding grain and the velocity distribution and number of ejected grains. Starting from elementary geometric considerations and physical principles, like momentum conservation and energy dissipation in inelastic pair collisions, we derive a rebound parametrization for the collision of a spherical grain with a granular bed. Combined with a recently proposed energy-splitting model [Ho et al., Phys. Rev. E 85, 052301 (2012)PLEEE81539-375510.1103/PhysRevE.85.052301] that predicts how the impact energy is distributed among the bed grains, this yields a coarse-grained but complete characterization of the splash as a function of the impact velocity and the impactor-bed grain-size ratio. The predicted mean values of the rebound angle, total and vertical restitution, ejection speed, and number of ejected grains are in excellent agreement with experimental literature data and with our own discrete-element computer simulations. We extract a set of analytical asymptotic relations for shallow impact geometries, which can readily be used in coarse-grained analytical modeling or computer simulations of geophysical particle-laden flows.

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.

Two-dimensional inclined chute flows: transverse motion and segregation.

We present an experimental study of two-dimensional dense inclined chute flows consisting of both monodisperse and bidisperse disks. We analyzed the trajectories of the particles within the flow in a steady regime. (i) In monodisperse flows, particles are arranged in layers that are in motion relative to one another, and it is found that the particles have a nonzero probability of being transferred to adjacent layers. We measured the mean time spent by a particle in a given layer. This residence time is found to decrease with increasing layer height. The particle transfer between layers can be interpreted as transverse motion of a diffusive nature. The diffusion coefficient associated with each layer increases linearly with the layer height. (ii) In polydisperse flows consisting of a small percentage (less than 1%) of small disks among large ones, the small particles have a net downward motion on which a fluctuating behavior is superimposed. At short times, the small particle motion can be described as a biased Brownian motion. The ratio of the characteristic time of diffusion to that of convection is found to increase with the layer height, indicating that the segregation process is more efficient in the upper layers of the flow. At longer times, the transverse motion of the small particles seems to differ greatly from a classical biased Brownian motion.

Nonlinear sand bedform dynamics in a viscous flow.

We investigate theoretically the nonlinear evolution of a sand bedform sheared by a laminar viscous flow. On the basis of the hydrodynamic equations coupled with a sediment transport law, we derive a closed nonlinear and nonlocal equation for the spatiotemporal evolution of the bedform profile in the case of an unbounded flow. The numerical resolution of this equation shows that the bedform coarsens indefinitely in the course of time. During the coarsening process, the wavelength scales as the cube of the vertical extension w as a result of the nonlinear interactions. Interestingly, in the case of a bounded flow, we argue that coarsening is interrupted when the flow perturbation induced by the bedform extends over the whole flow depth h, and we predict that the final wavelength λ{f} and vertical extension w{f} should scale respectively as (γ/ν)h³ and h (where ν is the fluid viscosity and γ the flow shear rate).

Impact of a projectile on a granular medium described by a collision model.

We propose a model for the propagation of energy due to the impact of a granular projectile on a dense granular medium. Energy is transferred from grain to grain during binary collision events. The transport of energy may then be viewed as a random walk with a split of energy during successive collisions. There is a qualitative and quantitative agreement between this simple description and experimental results.

Superstable granular heap in a thin channel.

We observed experimentally a new regime for granular flows in an inclined channel with a flow-rate-controlled system. For high flow rates, the flow occurs atop a static granular heap whose angle is considerably higher than those usually exhibited by granular heaps. The properties of such superstable heaps (SSH) are drastically affected by a change in the channel width W. This indicates that the unusual stability of these heaps can be accounted for by the flowing layer and its friction on the sidewalls. A simple depth-averaged model, assuming Coulomb friction, shows that the SSH angle scales as h/W (W being the channel width), and that grain size plays no part.