559 research outputs found
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
Effective boundary conditions for dense granular flows
We derive an effective boundary condition for granular flow taking into
account the effect of the heterogeneity of the force network on sliding
friction dynamics. This yields an intermediate boundary condition which lies in
the limit between no-slip and Coulomb friction; two simple functions relating
wall stress, velocity, and velocity variance are found from numerical
simulations. Moreover, we show that this effective boundary condition
corresponds to Navier slip condition when GDR MiDi's model is assumed to be
valid, and that the slip length depends on the length scale that characterises
the system, \emph{viz} the particle diameter.Comment: 4 pages, 5 figure
Shear bands in granular flow through a mixing length model
We discuss the advantages and results of using a mixing-length, compressible
model to account for shear banding behaviour in granular flow. We formulate a
general approach based on two function of the solid fraction to be determined.
Studying the vertical chute flow, we show that shear band thickness is always
independent from flowrate in the quasistatic limit, for Coulomb wall boundary
conditions. The effect of bin width is addressed using the functions developed
by Pouliquen and coworkers, predicting a linear dependence of shear band
thickness by channel width, while literature reports contrasting data. We also
discuss the influence of wall roughness on shear bands. Through a Coulomb wall
friction criterion we show that our model correctly predicts the effect of
increasing wall roughness on the thickness of shear bands. Then a simple
mixing-length approach to steady granular flows can be useful and
representative of a number of original features of granular flow.Comment: submitted to EP
On the dependence of the avalanche angle on the granular layer thickness
A layer of sand of thickness h flows down a rough surface if the inclination
is larger than some threshold value theta which decreases with h. A tentative
microscopic model for the dependence of theta with h is proposed for rigid
frictional grains, based on the following hypothesis: (i) a horizontal layer of
sand has some coordination z larger than a critical value z_c where mechanical
stability is lost (ii) as the tilt angle is increased, the configurations
visited present a growing proportion $_s of sliding contacts. Instability with
respect to flow occurs when z-z_s=z_c. This criterion leads to a prediction for
theta(h) in good agreement with empirical observations.Comment: 6 pages, 2 figure
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Continuous Avalanche Segregation of Granular Mixtures in Thin Rotating Drums
We study segregation of granular mixtures in the continuous avalanche regime
(for frequencies above ~ 1 rpm) in thin rotating drums using a continuum theory
for surface flows of grains. The theory predicts profiles in agreement with
experiments only when we consider a flux dependent velocity of flowing grains.
We find the segregation of species of different size and surface properties,
with the smallest and roughest grains being found preferentially at the center
of the drum. For a wide difference between the species we find a complete
segregation in agreement with experiments. In addition, we predict a transition
to a smooth segregation regime - with an power-law decay of the concentrations
as a function of radial coordinate - as the size ratio between the grains is
decreased towards one.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmaks
The reversible polydisperse Parking Lot Model
We use a new version of the reversible Parking Lot Model to study the
compaction of vibrated polydisperse media. The particle sizes are distributed
according to a truncated power law. We introduce a self-consistent desorption
mechanism with a hierarchical initialization of the system. In this way, we
approach densities close to unity. The final density depends on the
polydispersity of the system as well as on the initialization and will reach a
maximum value for a certain exponent in the power law.Comment: 7 pages, Latex, 12 figure
Granular flow down a rough inclined plane: transition between thin and thick piles
The rheology of granular particles in an inclined plane geometry is studied
using molecular dynamics simulations. The flow--no-flow boundary is determined
for piles of varying heights over a range of inclination angles . Three
angles determine the phase diagram: , the angle of repose, is the
angle at which a flowing system comes to rest; , the maximum angle
of stability, is the inclination required to induce flow in a static system;
and is the maximum angle for which stable, steady state flow is
observed. In the stable flow region , three
flow regimes can be distinguished that depend on how close is to
: i) : Bagnold rheology, characterized by a
mean particle velocity in the direction of flow that scales as
, for a pile of height , ii)
: the slow flow regime, characterized by a linear
velocity profile with depth, and iii) : avalanche flow
characterized by a slow underlying creep motion combined with occasional free
surface events and large energy fluctuations. We also probe the physics of the
initiation and cessation of flow. The results are compared to several recent
experimental studies on chute flows and suggest that differences between
measured velocity profiles in these experiments may simply be a consequence of
how far the system is from jamming.Comment: 19 pages, 14 figs, submitted to Physics of Fluid
Thick surface flows of granular materials: The effect of the velocity profile on the avalanche amplitude
A few years ago, Bouchaud al. introduced a phenomenological model to describe
surface flows of granular materials [J. Phys. Fr. I, 4, 1383 (1994)]. According
to this model, one can distinguish between a static phase and a rolling phase
that are able to exchange grains through an erosion/accretion mechanism.
Boutreux et al. [Phys. Rev. E, 58, 4692 (1998)] proposed a modification of the
exchange term in order to describe thicker flows where saturation effects are
present. However, these approaches assumed that the downhill convection
velocity of the grains is constant inside the rolling phase, a hypothesis that
is not verified experimentally. In this article, we therefore modify the above
models by introducing a velocity profile in the flow, and study the physical
consequences of this modification in the simple situation of an avalanche in an
open cell. We present a complete analytical description of the avalanche in the
case of a linear velocity profile, and generalize the results for a power-law
dependency. We show, in particular, that the amplitude of the avalanche is
strongly affected by the velocity profile.Comment: 7 figures, accepted for publication in Phys. Rev.
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