506 research outputs found
Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow
Granular materials will segregate by particle size when subjected to shear,
as occurs, for example, in avalanches. The evolution of a bidisperse mixture of
particles can be modeled by a nonlinear first order partial differential
equation, provided the shear (or velocity) is a known function of position.
While avalanche-driven shear is approximately uniform in depth, boundary-driven
shear typically creates a shear band with a nonlinear velocity profile. In this
paper, we measure a velocity profile from experimental data and solve initial
value problems that mimic the segregation observed in the experiment, thereby
verifying the value of the continuum model. To simplify the analysis, we
consider only one-dimensional configurations, in which a layer of small
particles is placed above a layer of large particles within an annular shear
cell and is sheared for arbitrarily long times. We fit the measured velocity
profile to both an exponential function of depth and a piecewise linear
function which separates the shear band from the rest of the material. Each
solution of the initial value problem is non-standard, involving curved
characteristics in the exponential case, and a material interface with a jump
in characteristic speed in the piecewise linear case
Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime
We model the dynamics of avalanches in granular assemblies in partly filled
rotating cylinders using a mean-field approach. We show that, upon varying the
cylinder angular velocity , the system undergoes a hysteresis cycle
between an intermittent and a continuous flow regimes. In the intermittent flow
regime, and approaching the transition, the avalanche duration exhibits
critical slowing down with a temporal power-law divergence. Upon adding a white
noise term, and close to the transition, the distribution of avalanche
durations is also a power-law. The hysteresis, as well as the statistics of
avalanche durations, are in good qualitative agreement with recent experiments
in partly filled rotating cylinders.Comment: 4 pages, RevTeX 3.0, postscript figures 1, 3 and 4 appended
Lattice-Boltzmann Method for Geophysical Plastic Flows
We explore possible applications of the Lattice-Boltzmann Method for the
simulation of geophysical flows. This fluid solver, while successful in other
fields, is still rarely used for geotechnical applications. We show how the
standard method can be modified to represent free-surface realization of
mudflows, debris flows, and in general any plastic flow, through the
implementation of a Bingham constitutive model. The chapter is completed by an
example of a full-scale simulation of a plastic fluid flowing down an inclined
channel and depositing on a flat surface. An application is given, where the
fluid interacts with a vertical obstacle in the channel.Comment: in W. Wu, R.I. Borja (Edts.) Recent advances in modelling landslides
and debris flow, Springer Series in Geomechanics and Geoengineering (2014),
ISBN 978-3-319-11052-3, pp. 131-14
Diffusion as mixing mechanism in granular materials
We present several numerical results on granular mixtures. In particular, we
examine the efficiency of diffusion as a mixing mechanism in these systems. The
collisions are inelastic and to compensate the energy loss, we thermalize the
grains by adding a random force. Starting with a segregated system, we show
that uniform agitation (heating) leads to a uniform mixture of grains of
different sizes. We define a characteristic mixing time, , and
study theoretically and numerically its dependence on other parameters like the
density. We examine a model for bidisperse systems for which we can calculate
some physical quantities. We also examine the effect of a temperature gradient
and demonstrate the appearance of an expected segregation.Comment: 15 eps figures, include
Long-time asymptotics of the long-range Emch-Radin model
The long-time asymptotic behavior is studied for a long-range variant of the
Emch-Radin model of interacting spins. We derive upper and lower bounds on the
expectation values of a class of observables. We prove analytically that the
time scale at which the system relaxes to equilibrium diverges with the system
size N, displaying quasistationary nonequilibrium behavior. This finding
implies that, for large enough N, equilibration will not be observed in an
experiment of finite duration.Comment: 12 pages, 2 figures. Compared to the published version, a 1/2 has
been corrected in Eq. (9) and subsequent equations; the modifications are
insubstantial and leave the main results of the article unaltered. arXiv
admin note: substantial text overlap with arXiv:1103.083
The influence of localised size reorganisation on short-duration bidispersed granular flows
We investigate experimentally the runout resulting from the collapse of a granular column containing two particle species that differ in size only. The experimental configuration is strictly twodimensional (only one particle per width of the experimental tank) and we explore both the role of the initial arrangement and proportion of the two particle sizes in the column, using high-speed videography, and by determining the centres of mass of the big and small particles in the initial column and the final deposit. The duration of the experiment is sufficiently short that large-scale segregation does not occur, however, we find a clear dependence of runout on both initial mixture arrangement and proportion for all conditions. We investigated this observation through detailed analysis of the flow front motion, and identify a characteristic "stopping" phase when dissipation dominates, and we apply a shallow layer model at the flow front to show how the initial mixture arrangement and proportion influence the effective coefficient of friction during emplacement. We find that a bidispersed mixture can induce a larger friction on emplacement than a monodispersed mixture, and the highest coefficient of friction was found for a well-mixed initial arrangement of particles at the proportion that shows maximum horizontal spreading of the flow. These observations suggest that downwards percolation of fine particles takes place at the front of the collapsing column, and so localised size segregation processes at the flow front can control flow mobility. This effect is likely to be important in controlling the mobility of large geophysical flows that occur on finite time scales, and whose deposits typically show granular segregation at the front and edges but not throughout the entire deposit
Tracer diffusion in granular shear flows
Tracer diffusion in a granular gas in simple shear flow is analyzed. The
analysis is made from a perturbation solution of the Boltzmann kinetic equation
through first order in the gradient of the mole fraction of tracer particles.
The reference state (zeroth-order approximation) corresponds to a Sonine
solution of the Boltzmann equation, which holds for arbitrary values of the
restitution coefficients. Due to the anisotropy induced in the system by the
shear flow, the mass flux defines a diffusion tensor instead of a
scalar diffusion coefficient. The elements of this tensor are given in terms of
the restitution coefficients and mass and size ratios. The dependence of the
diffusion tensor on the parameters of the problem is illustrated in the
three-dimensional case. The results show that the influence of dissipation on
the elements is in general quite important, even for moderate values
of the restitution coefficients. In the case of self-diffusion (mechanically
equivalent particles), the trends observed in recent molecular dynamics
simulations are similar to those obtained here from the Boltzmann kinetic
theory.Comment: 5 figure
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
Partially fluidized shear granular flows: Continuum theory and MD simulations
The continuum theory of partially fluidized shear granular flows is tested
and calibrated using two dimensional soft particle molecular dynamics
simulations. The theory is based on the relaxational dynamics of the order
parameter that describes the transition between static and flowing regimes of
granular material. We define the order parameter as a fraction of static
contacts among all contacts between particles. We also propose and verify by
direct simulations the constitutive relation based on the splitting of the
shear stress tensor into a``fluid part'' proportional to the strain rate
tensor, and a remaining ``solid part''. The ratio of these two parts is a
function of the order parameter. The rheology of the fluid component agrees
well with the kinetic theory of granular fluids even in the dense regime. Based
on the hysteretic bifurcation diagram for a thin shear granular layer obtained
in simulations, we construct the ``free energy'' for the order parameter. The
theory calibrated using numerical experiments with the thin granular layer is
applied to the surface-driven stationary two dimensional granular flows in a
thick granular layer under gravity.Comment: 20 pages, 19 figures, submitted to Phys. Rev.
A nonlinear hydrodynamical approach to granular materials
We propose a nonlinear hydrodynamical model of granular materials. We show
how this model describes the formation of a sand pile from a homogeneous
distribution of material under gravity, and then discuss a simulation of a
rotating sandpile which shows, in qualitative agreement with experiment, a
static and dynamic angle of repose.Comment: 17 pages, 14 figures, RevTeX4; minor changes to wording and some
additional discussion. Accepted by Phys. Rev.
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