694 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
Shear-transformation-zone theory of plastic deformation near the glass transition
The shear-transformation-zone (STZ) theory of plastic deformation in
glass-forming materials is reformulated in light of recent progress in
understanding the roles played the effective disorder temperature and entropy
flow in nonequilibrium situations. A distinction between fast and slow internal
state variables reduces the theory to just two coupled equations of motion, one
describing the plastic response to applied stresses, and the other the dynamics
of the effective temperature. The analysis leading to these equations contains,
as a byproduct, a fundamental reinterpretation of the dynamic yield stress in
amorphous materials. In order to put all these concepts together in a realistic
context, the paper concludes with a reexamination of the experimentally
observed rheological behavior of a bulk metallic glass. That reexamination
serves as a test of the STZ dynamics, confirming that system parameters
obtained from steady-state properties such as the viscosity can be used to
predict transient behaviors.Comment: 15 pages, four figure
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
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
Transverse instability of dunes
The simplest type of dune is the transverse one, which propagates with
invariant profile orthogonally to a fixed wind direction. Here we show
numerically and with a linear stability analysis that transverse dunes are
unstable with respect to along-axis perturbations in their profile and decay on
the bedrock into barchan dunes. Any forcing modulation amplifies exponentially
with growth rate determined by the dune turnover time. We estimate the distance
covered by a transverse dune before fully decaying into barchans and identify
the patterns produced by different types of perturbation.Comment: 4 pages, 3 figures; To appear in Physical Review Letter
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
Modelling formation and evolution of transverse dune fields
We model formation and evolution of transverse dune fields. In the model,
only the cross section of the dune is simulated. The only physical variable of
relevance is the dune height, from which the dune width and velocity are
determined, as well as phenomenological rules for interaction between two dunes
of different heights. We find that dune fields with no sand on the ground
between dunes are unstable, i.e. small dunes leave the higher ones behind. We
then introduce a saturation length to simulate transverse dunes on a sand bed
and show that this leads to stable dune fields with regular spacing and dune
heights. Finally, we show that our model can be used to simulate coastal dune
fields if a constant sand influx is considered, where the dune height increases
with the distance from the beach, reaching a constant value.Comment: 18 pages including 9 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
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
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
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