Session W14: Granular Flow

Clustering in a Dense, Freely-Falling Granular Stream

We investigate the breakup of a freely-falling granular stream into discrete, compact clusters of grains. This breakup, occurring for grain diameters less than about 200 microns falling out of a hopper opening, is reminiscent of the breakup of a liquid stream, though granular materials are generally thought of as lacking a surface tension. Our experiments employ high-speed video imaging in the co-moving frame, which allows us to track the onset of clustering and the subsequent cluster evolution in detail. Varying the material, size, roughness, and wetting properties of the grains as well as the surrounding gas pressure and the hopper opening diameter, we investigate the role of capillary, electrostatic and van der Waals forces in the clustering process. We find that the clustering provides a window to observe very weak cohesive forces between the grains which are masked in other experiments.   

Vector Force Measurements of a Dense Granular Flow

We have made force measurements at the wall of a dense granular flow. The data was acquired at rate of 800 Hz in all three spatial directions. The fluctuations in the forces were examined for a wide range of flow speeds. Correlations in the forces decay by the time the flow moves one ball diameter. The force along the flow direction is highly correlated with the force normal to the wall. For a given value of normal force, the force along the flow has a gaussian distribution about the tangential force that would be predicted from a constant friction angle.   

Space-Time Structure of Granular Flows in a Rough Vertical Channel

We report measurements using PFG-NMR of the space and time structure of steady granular flows through a long vertical channel of circular cross section with roughened walls. The granular sample consisted of seeds approximately 400$~\mu$m in diameter, flowing through a 9.8~mm ID tube to which was adhered a monolayer of glass beads similar in diameter to the grains. Data was acquired from a region approximately 50 channel diameters higher than the aperture at the channel bottom used to control the flow rate. The mean velocity of the grains as well as the RMS fluctuations in the grain motion were measured as functions of the radial coordinate and for time intervals in the range 5-200~ms, for several different granular flow speeds. For some flow regimes the displacement distributions are distinctly non-Gaussian, at odds with a ``molecular fluid'' model of the granular medium. The time dependence of the fluctuation distribution provides clues to the mechanism by which the gravitational body force is transmitted to the channel walls.   

Vibrheology of Granular Matter

We show how weak agitations substantially modify the rheology of granular materials. We experimentally probe dry granular flows in a weakly vibrated split bottom shear cell -- the weak vibrations act as the agitation source. By tuning the applied stress and vibration strength, and monitoring the resulting strain, we uncover a rich phase diagram in which non-trivial transitions separate a jammed phase, a creep flow case, and a steady flow case.   

Shear zones at the walls of a 2D gravity-driven flow of grains

We study the flow of spherical grains under gravity in a vertical, straight-walled 2-dimensional hopper, where the flow velocity is controlled by a taper at the outlet. We perform these studies both for monodisperse steel spheres as well as for a bidisperse system of equal numbers of spheres with a ratio of diameters of 1.25. The monodisperse system shows crystalline order even in flow, whereas there is no obvious structural order in the bidisperse system. The velocity profile across the flow is profoundly different in the two systems: the wall shear zone in the monodisperse system extends only a few particle diameters, and there are only small velocity gradients in the bulk of the flow. In contrast to this nearly-plug-like flow, there are significantly broader shear zones in the disordered flow. We report these profiles as a function of the width of the hopper in order to study the scaling of the shear zone with the system size, and with the flow rate.   

A Void Diffusion Model of Granular Flow

In an earlier paper$^{1}$ we derived a nonlinear diffusion equation to describe the dynamics in granular flow based on a Diffusion Void Model (DVM). The equation was successfully used to describe the flow of a homogeneous granular material through the hole of a container under gravity. It also properly described similar flow in the presence of a flat horizontal barrier placed above the hole. Recently, however, we have found out that the above nonlinear equation does not lead to correct static equilibrium. For example, the stability of the free surface of a granular aggregate cannot be described by the equation. The equation also fails to describe, say, how an unstable vertical column of a granular material will change to a stable $\Lambda $-shaped pile at the angle of repose. In this paper work we derive an equation using an appropriate current density of voids that can explain all the observed dynamical characteristics of a simple granular state. $^{1}$Jayanta K. Rudra and D. C. Hong, Phys. Rev. E47, R1459(1993).   

The Role of Extensional Viscosity in Sedimentation of Dense Suspensions

When two particles in a viscous fluid approach contact the motion of the interstitial fluid is dominated by extensional flows. We are interested in how the details of these flows influence the sedimentation of sense suspensions. To highlight the effects of extensional flows on particle motion we compare systems in which the fluids have the same shear viscosities, but drastically different extensional viscosities. We enhance the extensional viscosity by adding a flexible, high molecular weight polymer. In the case of a system without polymer there is a dense, static packing which grows from the bottom of the container, a region which remains at the initial grain density and settles at a constant velocity, and a clear supernatant at the top. In the polymeric fluid particles settle more slowly, and rather than sedimenting directly from the initial density to a static packing there is a long consolidation process during which the particle density increases at a constant rate.   

Local Rearrangements in a Dense Granular Medium During Steady and Oscillatory Shear

Cooperative motion is a hallmark of dense granular media. Using the laser sheet scanning method described in [1], we are able to track the motions of all particles in a dense packing of spheres in three dimensions. We analyze the motions of all particles within a split bottom shear cell. We study both steady and oscillatory shearing processes. We compare relative motions of neighboring particles using a measure, P(cos($\alpha ))$, based on a measure originally used by Ellenbroek et al [1]. The angle, $\alpha $, is the angle between the relative displacements of neighboring particles and their bond vectors. A pair of neighboring particles where cos($\alpha )$=0 is called a rolling contact. We find that particles in contact tend to roll past one another, which is consistent with the findings made by Ellenbroek et al for systems close to jamming. We also find that the number of rolling contacts drops at the onset of a shear reversal. [1] Slotterback et al, to appear in Phys Rev Lett [2] Ellenboek et al., Phys Rev Lett, 97 258001 (2006)   

Three-dimensional Order and Self-Diffusion in a Cyclically Sheared Granular System

We investigate the structure and dynamics of a dense granular packing (consisting of one millimeter diameter spherical glass beads) undergoing cyclic shear obtained by smoothly deforming a parallelepiped shaped cell. Using a fluorescent refractive index matched particle tracking technique, we obtain the three dimensional position of particles in the central region of the shear cell as a function of shear cycle. The granular packing is observed to evolve towards crystallization over thousands of shear cycles and the packing fraction is correspondingly observed to increase smoothly from loose packing fraction. We obtain the Voronoi cell volume distributions from the measured positions, and compare them with various models which predict a Gamma-distribution and help us define a regularity factor. Further, we discuss the measured radial distribution and the bond-order parameter Q6 which are widely used to quantify local order in spherical particle systems. We find that the initial self-diffusion of the particles is anisotropic with diffusion greater in the flow direction compared with the velocity gradient direction which in turn is greater than the vorticity direction.   

Dynamic effective mass of granular media

We report an experimental and theoretical investigation of the frequency-dependent effective mass, $\tilde{M}(\omega)$, of loose granular particles which occupy a rigid cavity to a filling fraction of 48\%, the remaining volume being air of differing humidities. We demonstrate that this is a sensitive and direct way to measure those properties of the granular medium that are the cause of the changes in acoustic properties of structures containing grain-filled cavities. Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The dominant features of $\tilde{M}(\omega)$ are a sharp resonance and a broad background, which we analyze within the context of simple models. We find that: a) These systems may be understood in terms of a height-dependent and diameter-dependent effective sound speed ($\sim 130$ m/s) and an effective viscosity ($\sim 2\times 10^4$ Poise). b) There is a dynamic Janssen effect in the sense that, at any frequency, and depending on the method of sample preparation, approximately one-half of the effective mass is borne by the side walls of the cavity and one-half by the bottom. c) On a fundamental level, dissipation is dominated by adsorbed films of water at grain-grain contacts in our experiments.   

Visualization of displacement fields in sheared granular systems

The jamming transition, i.e. the transition in a granular system from rest to flow is a fundamental problem of great importance to the understanding of a wide class of disordered materials: grains, clay and glassy materials such as molecular glasses and gels. We visualize the particles in a sheared three-dimensional granular packing immersed in an index matching liquid using confocal microscopy and laser sheet imaging. These experimental methods allow for an accurate determination of the displacement field of the particles at the onset of flow.