434 research outputs found
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
Gravity-driven Dense Granular Flows
We report and analyze the results of numerical studies of dense granular
flows in two and three dimensions, using both linear damped springs and
Hertzian force laws between particles. Chute flow generically produces a
constant density profile that satisfies scaling relations suggestive of a
Bagnold grain inertia regime. The type of force law has little impact on the
behavior of the system. Bulk and surface flows differ in their failure criteria
and flow rheology, as evidenced by the change in principal stress directions
near the surface. Surface-only flows are not observed in this geometry.Comment: 4 pages, RevTeX 3.0, 4 PostScript figures (5 files) embedded with
eps
Granular Elasticity without the Coulomb Condition
An self-contained elastic theory is derived which accounts both for
mechanical yield and shear-induced volume dilatancy. Its two essential
ingredients are thermodynamic instability and the dependence of the elastic
moduli on compression.Comment: 4pages, 2 figure
Aeolian sans ripples: experimental study of saturated states
We report an experimental investigation of aeolian sand ripples, performed
both in a wind tunnel and on stoss slopes of dunes. Starting from a flat bed,
we can identify three regimes: appearance of an initial wavelength, coarsening
of the pattern and finally saturation of the ripples. We show that both initial
and final wavelengths, as well as the propagative speed of the ripples, are
linear functions of the wind velocity. Investigating the evolution of an
initially corrugated bed, we exhibit non-linear stable solutions for a finite
range of wavelengths, which demonstrates the existence of a saturation in
amplitude. These results contradict most of the models.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Title changed,
figures corrected and simplified, more field data included, text clarifie
Continuum approach to wide shear zones in quasi-static granular matter
Slow and dense granular flows often exhibit narrow shear bands, making them
ill-suited for a continuum description. However, smooth granular flows have
been shown to occur in specific geometries such as linear shear in the absence
of gravity, slow inclined plane flows and, recently, flows in split-bottom
Couette geometries. The wide shear regions in these systems should be amenable
to a continuum description, and the theoretical challenge lies in finding
constitutive relations between the internal stresses and the flow field. We
propose a set of testable constitutive assumptions, including
rate-independence, and investigate the additional restrictions on the
constitutive relations imposed by the flow geometries. The wide shear layers in
the highly symmetric linear shear and inclined plane flows are consistent with
the simple constitutive assumption that, in analogy with solid friction, the
effective-friction coefficient (ratio between shear and normal stresses) is a
constant. However, this standard picture of granular flows is shown to be
inconsistent with flows in the less symmetric split-bottom geometry - here the
effective friction coefficient must vary throughout the shear zone, or else the
shear zone localizes. We suggest that a subtle dependence of the
effective-friction coefficient on the orientation of the sliding layers with
respect to the bulk force is crucial for the understanding of slow granular
flows.Comment: 11 pages, 7 figure
Aeolian transport layer
We investigate the airborne transport of particles on a granular surface by
the saltation mechanism through numerical simulation of particle motion coupled
with turbulent flow. We determine the saturated flux and show that its
behavior is consistent with a classical empirical relation obtained from wind
tunnel measurements. Our results also allow to propose a new relation valid for
small fluxes, namely, , where and
are the shear and threshold velocities of the wind, respectively, and
the scaling exponent is . We obtain an expression for the
velocity profile of the wind distorted by the particle motion and present a
dynamical scaling relation. We also find a novel expression for the dependence
of the height of the saltation layer as function of the wind velocity.Comment: 4 pages, 4 figure
Low-speed impact craters in loose granular media
We report on craters formed by balls dropped into dry, non-cohesive, granular
media. By explicit variation of ball density , diameter , and
drop height , the crater diameter is confirmed to scale as the 1/4 power of
the energy of the ball at impact:
. Against expectation, a different
scaling law is discovered for the crater depth:
. The scaling with properties of
the medium is also established. The crater depth has significance for granular
mechanics in that it relates to the stopping force on the ball.Comment: experiment; 4 pages, 3 figure
Jump at the onset of saltation
We reveal a discontinuous transition in the saturated flux for aeolian
saltation by simulating explicitly particle motion in turbulent flow. The
discontinuity is followed by a coexistence interval with two metastable
solutions. The modification of the wind profile due to momentum exchange
exhibits a second maximum at high shear strength. The saturated flux depends on
the strength of the wind as
Stratification Instability in Granular Flows
When a mixture of two kinds of grains differing in size and shape is poured
in a vertical two-dimensional cell, the mixture spontaneously stratifies in
alternating layers of small and large grains, whenever the large grains are
more faceted than the small grains. Otherwise, the mixture spontaneously
segregates in different regions of the cell when the large grains are more
rounded than the small grains. We address the question of the origin of the
instability mechanism leading to stratification using a recently proposed set
of equations for surface flow of granular mixtures. We show that the stable
solution of the system is a segregation solution due to size (large grains tend
to segregate downhill near the substrate and small grains tend to segregate
uphill) and shape (rounded grains tend to segregate downhill and more faceted
grains tend to segregate uphill). As a result, the segregation solution of the
system is realized for mixtures of large-rounded grains and small-cubic grains
with the large-rounded grains segregating near the bottom of the pile.
Stability analysis reveals the instability mechanism driving the system to
stratification as a competition between size-segregation and shape-segregation
taking place for mixtures of large-cubic grains and small-rounded grains. The
large-cubic grains tend to size-segregate at the bottom of the pile, while at
the same time, they tend to shape-segregate near the pouring point. Thus, the
segregation solution becomes unstable, and the system evolves spontaneously to
stratification.Comment: 10 pages, 10 figures, http://polymer.bu.edu/~hmakse/Home.htm
The Origin of a Repose Angle: Kinetics of Rearrangements for Granular Materials
A microstructural theory of dense granular materials is presented, based on
two main ideas. Firstly, that macroscopic shear results form activated local
rearrangements at a mesoscopic scale. Secondly, that the update frequency of
microscopic processes is determined by granular temperature. In a shear cell,
the resulting constitutive equations account for Bagnold's scaling and for the
existence of a Coulomb criterion of yield. In the case of a granular flow down
an inclined plane, they account for the rheology observed in recent experiments
and for the temperature and velocity profiles measured numerically.Comment: submitted to PR
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