A conveyor belt experimental setup to study the internal dynamics of granular avalanches

ABSTRACT

This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granular flows. To visualise the flow within the granular bulk and, in particular, determine its composition and the velocity field, we used the refractive index matching (RIM) technique combined with particle tracking velocimetry and coarse-graining algorithms. Implementing RIM posed varied technical, design and construction difficulties. To test the experimental setup and go beyond a mere proof of concept, we carried out granular flow experiments involving monodisperse and bidisperse borosilicate glass beads. These flows resulted in stationary avalanches with distinct regions whose structures were classified as: (i) a convective-bulged front, (ii) a compact-layered tail and, between them, (iii) a breaking size-segregation wave structure. We found that the bulk strain rate, represented by its tensor invariants, varied significantly between the identified flow structures, and their values supported the observed avalanche characteristics. The flow velocity fields' interpolated profiles adjusted well to a Bagnold-like profile, although a considerable basal velocity slip was measured. We calculated a segregation flux using recent developments in particle-size segregation theory. Along with vertical velocity changes and high expansion rates, segregation fluxes were markedly higher at the avalanche's leading edge, suggesting a connection between flow rheology and grain segregation. The experimental conveyor belt's results showed the potential for further theoretical developments in rheology and segregation-coupled models.

Experimental Analysis of Velocity Distribution in a Coarse-Grained Debris Flow: A Modified Bagnold’s Equation

Today, Bagnold’s theory is still applied to gravity-driven flows under the assumption of uniform sediment concentration. This study presents findings of flume experiments conducted to investigate the velocity and concentration distributions within the debris body by using high-resolution images. The analysis has shown that the concentration and mobility of grains vary along the depth. A linear law to interpret the grains concentration distribution, starting from the knowledge of the packing concentration and of the surface concentration, Cs, has been identified. By considering such a law, modified expressions of the Bagnold’s number and the velocity in stony-type debris flows are also presented. By using these expressions, three regimes of motion have been identified along the depth, and the velocity profile within the debris body is determined as a function of the parameter Cs. It has been verified that the velocity profiles estimated by using the modified equation compare well (mean square error less than 0.1) with the literature’s measured profiles when Cs is correctly measured or estimated. Results of cutting tests, conducted for a sample of the used material, have also allowed us to verify that Cs could be determined as a function of the static friction angle of the material.

Interfacial Instability during Granular Erosion

The complex interplay between the topography and the erosion and deposition phenomena is a key feature to model granular flows such as landslides. Here, we investigated the instability that develops during the erosion of a wet granular pile by a dry dense granular flow. The morphology and the propagation of the generated steps are analyzed in relation to the specific erosion mechanism. The selected flowing angle of the confined flow on a dry heap appears to play an important role both in the final state of the experiment, and for the shape of the structures. We show that the development of the instability is governed by the inertia of the flow through the Froude number. We model this instability and predict growth rates that are in agreement with the experiment results.

Nonlocal effects in sand flows on an inclined plane

The flow of sand on a rough inclined plane is investigated experimentally. We directly show that a jammed layer of grains spontaneously forms below the avalanche. Its properties and its relation with the rheology of the flowing layer of grains are presented and discussed. In a second part, we study the dynamics of erosion and deposition solitary waves in the domain where they are transversally stable. We characterize their shapes and velocity profiles. We relate their translational velocity to the stopping height and to the mass trapped in the avalanche. Finally, we use the velocity profile to get insight into the rheology very close to the jamming limit.

Erosion dynamics of a wet granular medium

Liquid may give strong cohesion properties to a granular medium, and confer a solidlike behavior. We study the erosion of a fixed circular aggregate of wet granular matter subjected to a flow of dry grains inside a half-filled rotating drum. During the rotation, the dry grains flow around the fixed obstacle. We show that its diameter decreases linearly with time for low liquid content, as wet grains are pulled out of the aggregate. This erosion phenomenon is governed by the properties of the liquids. The erosion rate decreases exponentially with the surface tension while it depends on the viscosity to the power -1. We propose a model based on the force fluctuations arising inside the flow, explaining both dependencies: The capillary force acts as a threshold and the viscosity controls the erosion time scale. We also provide experiments using different flowing grains, confirming our model.

Nonadditivity of fluctuation-induced forces in fluidized granular media

We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media.

Rheology of dense granular mixtures: boundary pressures

Models for dense sheared granular materials indicate that their rheological properties depend on particle size, but the representative size for mixtures is not obvious. Here, we computationally study pressure on a boundary due to sheared granular mixtures to determine its dependence on particle size distribution. We find that the pressure does not depend monotonically on average particle size. Instead it has an additional dependence on a measure of the effective free volume per particle we adapt from an expression for packing of monosized particles near the jammed state.

Isolating segregation mechanisms in a split-bottom cell

We study the segregation of mixtures of particles in a split-bottom cell to isolate three possible driving mechanisms for segregation of densely sheared granular mixtures: gravity, porosity, and velocity gradients. We find that gravity alone does not drive segregation associated with particle size without a sufficiently large porosity or porosity gradient. A velocity gradient, however, appears to be capable of driving segregation associated with both particle size and material density. In all cases, the final segregation state is approached exponentially.

Kinematics of densely flowing granular mixtures

We measure the kinematics of segregating granular mixtures in dense free-surface boundary-layer flow in a rotated drum. We find that in a segregating mixture, the different components move with roughly the same velocities, except for a relatively small segregation velocity perpendicular to the direction of flow. On the other hand, the mean variance of the velocities--often associated with a granular temperature--may differ for the two components. In the majority of the high-density boundary layer, the difference is driven by relative particle size and may be understood considering a geometrically motivated model. In the low-density region at the top of the boundary layer, the difference is driven by relative particle mass, similar to observations in more energetic systems.