99 research outputs found
Velocity correlations in dense granular flows
Velocity fluctuations of grains flowing down a rough inclined plane are
experimentally studied. The grains at the free surface exhibit fluctuating
motions, which are correlated over few grains diameters. The characteristic
correlation length is shown to depend on the inclination of the plane and not
on the thickness of the flowing layer. This result strongly supports the idea
that dense granular flows are controlled by a characteristic length larger than
the particle diameter
Rapid granular flows on a rough incline: phase diagram, gas transition, and effects of air drag
We report experiments on the overall phase diagram of granular flows on an
incline with emphasis on high inclination angles where the mean layer velocity
approaches the terminal velocity of a single particle free falling in air. The
granular flow was characterized by measurements of the surface velocity, the
average layer height, and the mean density of the layer as functions of the
hopper opening, the plane inclination angle and the downstream distance x of
the flow. At high inclination angles the flow does not reach an x-invariant
steady state over the length of the inclined plane. For low volume flow rates,
a transition was detected between dense and very dilute (gas) flow regimes. We
show using a vacuum flow channel that air did not qualitatively change the
phase diagram and did not quantitatively modify mean flow velocities of the
granular layer except for small changes in the very dilute gas-like phase.Comment: 10 pages, 16 figures, accepted to Phys. Rev.
Flow of wet granular materials
The transition from frictional to lubricated flow of a dense suspension of
non-Brownian particles is studied. The pertinent parameter characterizing this
transition is the Leighton number ,
which represents the ratio of lubrication to frictional forces. The Leighton
number defines a critical shear rate below which no steady flow without
localization exists. In the frictional regime the shear flow is localized. The
lubricated regime is not simply viscous: the ratio of shear to normal stresses
remains constant, as in the frictional regime; moreover the velocity profile
has a single universal form in both frictional and lubricated regimes. Finally,
a discrepancy between local and global measurements of viscosity is identified,
which suggests inhomogeneity of the material under flow.Comment: Accepted for publication by Physical Review Letters (december 2004
The S shape of a granular pile in a rotating drum
The shape of a granular pile in a rotating drum is investigated. Using
Discrete Elements Method (DEM) simulations we show that the "S shape" obtained
for high rotation speed can be accounted for by the friction on the end plates.
A theoretical model which accounts for the effect of the end plates is
presented and the equation of the shape of the free surface is derived. The
model reveals a dimensionless number which quantifies the influence of the end
plates on the shape of the pile. Finally, the scaling laws of the system are
discussed and numerical results support our conclusions
Scaling of the critical slip distance in granular layers
We investigate the nature of friction in granular layers by means of
numerical simulation focusing on the critical slip distance, over which the
system relaxes to a new stationary state. Analyzing a transient process in
which the sliding velocity is instantaneously changed, we find that the
critical slip distance is proportional to the sliding velocity. We thus define
the relaxation time, which is independent of the sliding velocity. It is found
that the relaxation time is proportional to the layer thickness and inversely
proportional to the square root of the pressure. An evolution law for the
relaxation process is proposed, which does not contain any length constants
describing the surface geometry but the relaxation time of the bulk granular
matter. As a result, the critical slip distance is scaled with a typical length
scale of a system. It is proportional to the layer thickness in an
instantaneous velocity change experiment, whereas it is scaled with the total
slip distance in a spring-block system on granular layers.Comment: 4 papge
A two-dimensional depth-averaged μ(I)-rheology for dense granular avalanches
Steady uniform granular chute flows are common in industry and provide an important test case for new theoretical models. This paper introduces depth-integrated viscous terms into the momentum-balance equations by extending the recent depth-averaged μ(I) -rheology for dense granular flows to two spatial dimensions, using the principle of material frame indifference or objectivity. Scaling the cross-slope coordinate on the width of the channel and the velocity on the one-dimensional steady uniform solution, we show that the steady two-dimensional downslope velocity profile is independent of scale. The only controlling parameters are the channel aspect ratio, the slope inclination angle and the frictional properties of the chute and the sidewalls. Solutions are constructed for both no-slip conditions and for a constant Coulomb friction at the walls. For narrow chutes, a pronounced parabolic-like depth-averaged downstream velocity profile develops. However, for very wide channels, the flow is almost uniform with narrow boundary layers close to the sidewalls. Both of these cases are in direct contrast to conventional inviscid avalanche models, which do not develop a cross-slope profile. Steady-state numerical solutions to the full three-dimensional μ(I) -rheology are computed using the finite element method. It is shown that these solutions are also independent of scale. For sufficiently shallow channels, the depth-averaged velocity profile computed from the full solution is in excellent agreement with the results of the depth-averaged theory. The full downstream velocity can be reconstructed from the depth-averaged theory by assuming a Bagnold-like velocity profile with depth. For wide chutes, this is very close to the results of the full three-dimensional calculation. For experimental validation, a laser profilometer and balance are used to determine the relationship between the total mass flux in the chute and the flow thickness for a range of slope angles and channel widths, and particle image velocimetry (PIV) is used to record the corresponding surface velocity profiles. The measured values are in good quantitative agreement with reconstructed solutions to the new depth-averaged theory
Force transmission in a packing of pentagonal particles
We perform a detailed analysis of the contact force network in a dense
confined packing of pentagonal particles simulated by means of the contact
dynamics method. The effect of particle shape is evidenced by comparing the
data from pentagon packing and from a packing with identical characteristics
except for the circular shape of the particles. A counterintuitive finding of
this work is that, under steady shearing, the pentagon packing develops a lower
structural anisotropy than the disk packing. We show that this weakness is
compensated by a higher force anisotropy, leading to enhanced shear strength of
the pentagon packing. We revisit "strong" and "weak" force networks in the
pentagon packing, but our simulation data provide also evidence for a large
class of "very weak" forces carried mainly by vertex-to-edge contacts. The
strong force chains are mostly composed of edge-to-edge contacts with a marked
zig-zag aspect and a decreasing exponential probability distribution as in a
disk packing
A constitutive law for dense granular flows
A continuum description of granular flows would be of considerable help in
predicting natural geophysical hazards or in designing industrial processes.
However, the constitutive equations for dry granular flows, which govern how
the material moves under shear, are still a matter of debate. One difficulty is
that grains can behave like a solid (in a sand pile), a liquid (when poured
from a silo) or a gas (when strongly agitated). For the two extreme regimes,
constitutive equations have been proposed based on kinetic theory for
collisional rapid flows, and soil mechanics for slow plastic flows. However,
the intermediate dense regime, where the granular material flows like a liquid,
still lacks a unified view and has motivated many studies over the past decade.
The main characteristics of granular liquids are: a yield criterion (a critical
shear stress below which flow is not possible) and a complex dependence on
shear rate when flowing. In this sense, granular matter shares similarities
with classical visco-plastic fluids such as Bingham fluids. Here we propose a
new constitutive relation for dense granular flows, inspired by this analogy
and recent numerical and experimental work. We then test our three-dimensional
(3D) model through experiments on granular flows on a pile between rough
sidewalls, in which a complex 3D flow pattern develops. We show that, without
any fitting parameter, the model gives quantitative predictions for the flow
shape and velocity profiles. Our results support the idea that a simple
visco-plastic approach can quantitatively capture granular flow properties, and
could serve as a basic tool for modelling more complex flows in geophysical or
industrial applications.Comment: http://www.nature.com/nature/journal/v441/n7094/abs/nature04801.htm
Wide shear zones and the spot model: Implications from the split-bottom geometry
The spot model has been developed by Bazant and co-workers to describe
quasistatic granular flows. It assumes that granular flow is caused by the
opposing flow of so-called spots of excess free volume, with spots moving along
the slip lines of Mohr-Coulomb plasticity. The model is two-dimensional and has
been successfully applied to a number of different geometries. In this paper we
investigate whether the spot model in its simplest form can describe the wide
shear zones observed in experiments and simulations of a Couette cell with
split bottom. We give a general argument that is independent of the particular
description of the stresses, but which shows that the present formulation of
the spot model in which diffusion and drift terms are postulated to balance on
length scales of order of the spot diameter, i.e. of order 3-5 grain diameters,
is difficult to reconcile with the observed wide shear zones. We also discuss
the implications for the spot model of co-axiality of the stress and strain
rate tensors found in these wide shear flows, and point to possible extensions
of the model that might allow one to account for the existence of wide shear
zones.Comment: 6 pages, 6 figures, to be published in EPJ
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