Session KH: Granular Flows IV

Mixing and segregation in sheared granular materials

Granular materials typically segregate by size under shear, with the smaller particles moving in the direction of gravity and the larger particles accumulating at the top. We perform experiments in an annular cell continuously sheared from below, in which two sizes of glass spheres are initially placed in two unstably-stratified horizontal layers (smaller over larger). We observe the rate of mixing and re-segregation as a function of particle size ratio, shear speed, and confining pressure. The segregation rate is found to be exponential in time, and quite sensitive to the choice of boundary condition (free surface or constant pressure).   

A Continuum Framework for Mixing and Segregation in Granular Flows

Mixing of granular material in three-dimensional tumblers is complicated by segregation due to differences in particle density or size. However, there is one point of simplification. All of the dynamics take place in a thin flowing surface layer. Two key experimental results lead to a continuum framework for modeling of mixing and segregation. Particle tracking velocimetry measurements indicate that the streamwise velocity decreases linearly with depth in the surface layer. Measurements across the transverse direction of the free surface show that the streamwise velocity at the midpoint of the flowing layer is a linear function of the local flowing layer length. These observations enter as assumptions into a continuum model of the flow. Segregation is modeled using constitutive relations for the buoyancy of the different particle types (varying in density) by considering them as interpenetrating continua. The model captures experimental results of segregation due to particle density or size in chaotic flow in both quasi-two-dimensional and three-dimensional tumblers.   

Temperature Change in Melting of an Oscillated Granular Layer

Molecular dynamics simulations are used to study the melting of a vertically vibrated, fully three dimensional granular layer. Grains that are oscillated with non-dimensional shaking acceleration, $\Gamma <1.3$, are solid-like, while above $\Gamma=2.6$ the layers are fluid-like as indicated by the granular temperature and the mean square displacement of the particles. Our results show that a sharp increase in the granular temperature occurs at the transition from the solid to fluid state. A discontinuity in the plot of temperature versus $\Gamma$ appears as the coefficient of normal restitution is increased, the non-dimensional frequency is decreased, or the layer depth is decreased.   

Particle Rearrangements in a Granular material subject to Thermal Cycling

Repeated heating and cooling, or thermal cycling, is known to cause compaction in granular assemblies. However, the microscopic mechanism for this process is not known. Our goal is to investigate how individual grains rearrange during the compaction process. Observation of the interior of a granular pile is made possible by the use of transparent grains immersed in index-matching fluid. A new laser sheet scanning approach allows us to extract 3D positions of individual grains. We cycle the temperature of a pile of glass beads in a plastic container with a $\Delta $T of 40\r{ }C. We track the motion of individual particles through a sequence of thermal cycles using 3D particle tracking software. Overall, we observe notable compaction that is qualitatively consistent with results found by Chen et al. [1] for the same beads and container, but with index-matching fluid. When studying individual particle tracks, we find that some particles undergo sudden hopping, similar to the hopping observed under vertical tapping [2]. We will also present further analysis of particle rearrangements. \newline [1] Chen, et al. , Nature 442, 257(2006). \newline [2] P. Ribiere et al. Phys. Rev Lett, 95, 268001 (2005)   

Agitation dominated rheology of dense granular media

We have studied \textit{stationary granular fluids}, novel states of granular matter which combine a solid-like appearance with a fluid-like response to external stresses, by locally shearing a layer of sand and probing its mechanical response in far away regions where the material remains stationary. Despite this solid-like appearance, intruders of low density exponentially relax to a floating equilibrium depth given by Archimedes' principle -- which implies that the yield stress is zero. Denser probes completely submerge into the sand. The drag force on the intruder is found to be proportional to the product of a dynamical viscosity, probe speed and probe dimension, where the dynamical viscosity depends nonlinearly on the applied stress. The vanishing of the yield stress is, we believe, caused by strong fluctuations of the network of contact forces: typical grains are so hard that subtle submicronic agitation of the grains, driven by a flow far away, correspond to large fluctuations in the contact forces which effectively ``melt'' the material.   

Evolution of Stress and effective Friction in 2D granular Couette Flow

Within geologic fault zones the internal friction in a material is expected to produce a large amount of heat. However, far less heat than expected is generated, giving rise to what is known as the heat flow paradox in geophysics. One possible explanation is that a fraction of the stress is not released by sliding friction but rolling of particles, thus lowering the effective friction inside the fault zone. We study the effective friction in a 2D granular material by comparing the overall torque on the inner wheel of a Couette cell with the stress inside the material for various loads. The load is varied by changing the number density of the particles in the cell, and the stress is measured by using stress-birefringent particles. The relation between torque and mean shear stress can be interpreted as an effective friction coefficient. After cessation of shear both the internal stresses and the overall torque decay logarithmically over time confirming a slow decay of the stress network in a sheared granular material.   

Clustering instability in a freely falling granular jet

This talk is on a clustering instability of a freely falling granular jet composed of 100 micron glass spheres. The granular flow out of a circular nozzle starts out spatially uniform and then, further downstream, breaks up into well defined clusters. An optical method is used that measures inhomogeneities in the flow in order to quantify the growth of the clusters. The role of air is investigated in this phenomenon by changing the ambient air pressure down to $1/5000^{th}$ atm. Clustering is observed down to the lowest pressure and the presence of air leads to larger drops but does not initiate the drop formation. The analysis shows that the drop size is set by fluctuations on the order of the size of the particles at the nozzle.   

The role of air in granular jet formation

A steel ball impacting on a bed of very loose, fine sand results in a surprisingly vigorous jet which shoots out from the surface of the sand. When the ambient pressure is reduced, the jet is found to be less vigorous, which suggests that air should play an important role in the mechanism of jet formation. In our impact experiments it was found that the penetration depth of the ball strongly decreases with decreasing pressure, whereas all other results are consistent with the gravitational collapse of the cavity that is created upon impact. This limits the influence of air to the stage of void formation, in which the cavity is created by a balance of the initial potential energy of the sphere and the dissipation due to the drag the ball experiences when penetrating into the sand.