129 research outputs found
A 2-D asymmetric exclusion model for granular flows
A 2-D version of the asymmetric exclusion model for granular sheared flows is
presented. The velocity profile exhibits two qualitatively different behaviors,
dependent on control parameters. For low friction, the velocity profile follows
an exponential decay while for large friction the profile is more accurately
represented by a Gaussian law. The phase transition occurring between these two
behavior is identified by the appearance of correlations in the cluster size
distribution. Finally, a mean--field theory gives qualitative and quantitative
good agreement with the numerical results.Comment: 13 pages, 5 figures; typos added, one definition change
Shock waves in two-dimensional granular flow: effects of rough walls and polydispersity
We have studied the two-dimensional flow of balls in a small angle funnel,
when either the side walls are rough or the balls are polydisperse. As in
earlier work on monodisperse flows in smooth funnels, we observe the formation
of kinematic shock waves/density waves. We find that for rough walls the flows
are more disordered than for smooth walls and that shock waves generally
propagate more slowly. For rough wall funnel flow, we show that the shock
velocity and frequency obey simple scaling laws. These scaling laws are
consistent with those found for smooth wall flow, but here they are cleaner
since there are fewer packing-site effects and we study a wider range of
parameters. For pipe flow (parallel side walls), rough walls support many shock
waves, while smooth walls exhibit fewer or no shock waves. For funnel flows of
balls with varying sizes, we find that flows with weak polydispersity behave
qualitatively similar to monodisperse flows. For strong polydispersity, scaling
breaks down and the shock waves consist of extended areas where the funnel is
blocked completely.Comment: 11 pages, 15 figures; accepted for PR
Footprints in Sand: The Response of a Granular Material to Local Perturbations
We experimentally determine ensemble-averaged responses of granular packings
to point forces, and we compare these results to recent models for force
propagation in a granular material. We used 2D granular arrays consisting of
photoelastic particles: either disks or pentagons, thus spanning the range from
ordered to disordered packings. A key finding is that spatial ordering of the
particles is a key factor in the force response. Ordered packings have a
propagative component that does not occur in disordered packings.Comment: 5 pages, 4 eps figures, Phys. Rev. Lett. 87, 035506 (2001
Grain Dynamics in a Two-dimensional Granular Flow
We have used particle tracking methods to study the dynamics of individual
balls comprising a granular flow in a small-angle two-dimensional funnel. We
statistically analyze many ball trajectories to examine the mechanisms of shock
propagation. In particular, we study the creation of, and interactions between,
shock waves. We also investigate the role of granular temperature and draw
parallels to traffic flow dynamics.Comment: 17 pages, 24 figures. To appear in Phys.Rev.E. High res./color
figures etc. on http://www.nbi.dk/CATS/Granular/GrainDyn.htm
Particle dynamics in sheared granular matter
The particle dynamics and shear forces of granular matter in a Couette
geometry are determined experimentally. The normalized tangential velocity
declines strongly with distance from the moving wall, independent of
the shear rate and of the shear dynamics. Local RMS velocity fluctuations
scale with the local velocity gradient to the power . These results agree with a locally Newtonian, continuum model, where the
granular medium is assumed to behave as a liquid with a local temperature
and density dependent viscosity
Signatures of granular microstructure in dense shear flows
Granular materials react to shear stresses differently than do ordinary
fluids. Rather than deforming uniformly, materials such as dry sand or
cohesionless powders develop shear bands: narrow zones containing large
relative particle motion leaving adjacent regions essentially rigid[1,2,3,4,5].
Since shear bands mark areas of flow, material failure and energy dissipation,
they play a crucial role for many industrial, civil engineering and geophysical
processes[6]. They also appear in related contexts, such as in lubricating
fluids confined to ultra-thin molecular layers[7]. Detailed information on
motion within a shear band in a three-dimensional geometry, including the
degree of particle rotation and inter-particle slip, is lacking. Similarly,
only little is known about how properties of the individual grains - their
microstructure - affect movement in densely packed material[5]. Combining
magnetic resonance imaging, x-ray tomography, and high-speed video particle
tracking, we obtain the local steady-state particle velocity, rotation and
packing density for shear flow in a three-dimensional Couette geometry. We find
that key characteristics of the granular microstructure determine the shape of
the velocity profile.Comment: 5 pages, incl. 4 figure
Thixotropy in macroscopic suspensions of spheres
An experimental study of the viscosity of a macroscopic suspension, i.e. a
suspension for which Brownian motion can be neglected, under steady shear is
presented. The suspension is prepared with a high packing fraction and is
density-matched in a Newtonian carrier fluid. The viscosity of the suspension
depends on the shear rate and the time of shearing. It is shown for the first
time that a macroscopic suspension shows thixotropic viscosity, i.e.
shear-thinning with a long relaxation time as a unique function of shear. The
relaxation times show a systematic decrease with increasing shear rate. These
relaxation times are larger when decreasing the shear rates, compared to those
observed after increasing the shear. The time scales involved are about 10000
times larger than the viscous time scale and about 1000 times smaller than the
thermodynamic time scale. The structure of the suspension at the outer cylinder
of a viscometer is monitored with a camera, showing the formation of a
hexagonal structure. The temporal decrease of the viscosity under shear
coincides with the formation of this hexagonal pattern
Granular discharge and clogging for tilted hoppers
We measure the flux of spherical glass beads through a hole as a systematic
function of both tilt angle and hole diameter, for two different size beads.
The discharge increases with hole diameter in accord with the Beverloo relation
for both horizontal and vertical holes, but in the latter case with a larger
small-hole cutoff. For large holes the flux decreases linearly in cosine of the
tilt angle, vanishing smoothly somewhat below the angle of repose. For small
holes it vanishes abruptly at a smaller angle. The conditions for zero flux are
discussed in the context of a {\it clogging phase diagram} of flow state vs
tilt angle and ratio of hole to grain size
Self-diffusion in dense granular shear flows
Diffusivity is a key quantity in describing velocity fluctuations in granular
materials. These fluctuations are the basis of many thermodynamic and
hydrodynamic models which aim to provide a statistical description of granular
systems. We present experimental results on diffusivity in dense, granular
shear in a 2D Couette geometry. We find that self-diffusivities are
proportional to the local shear rate with diffusivities along the mean flow
approximately twice as large as those in the perpendicular direction. The
magnitude of the diffusivity is D \approx \dot\gamma a^2 where a is the
particle radius. However, the gradient in shear rate, coupling to the mean
flow, and drag at the moving boundary lead to particle displacements that can
appear sub- or super-diffusive. In particular, diffusion appears superdiffusive
along the mean flow direction due to Taylor dispersion effects and subdiffusive
along the perpendicular direction due to the gradient in shear rate. The
anisotropic force network leads to an additional anisotropy in the diffusivity
that is a property of dense systems with no obvious analog in rapid flows.
Specifically, the diffusivity is supressed along the direction of the strong
force network. A simple random walk simulation reproduces the key features of
the data, such as the apparent superdiffusive and subdiffusive behavior arising
from the mean flow, confirming the underlying diffusive motion. The additional
anisotropy is not observed in the simulation since the strong force network is
not included. Examples of correlated motion, such as transient vortices, and
Levy flights are also observed. Although correlated motion creates velocity
fields qualitatively different from Brownian motion and can introduce
non-diffusive effects, on average the system appears simply diffusive.Comment: 13 pages, 20 figures (accepted to Phys. Rev. E
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