254 research outputs found
Long surface wave instability in dense granular flows
In this paper we present an experimental study of the long surface wave
instability that can develop when a granular material flows down a rough
inclined plane. The threshold and the dispersion relation of the instability
are precisely measured by imposing a controlled perturbation at the entrance of
the flow and measuring its evolution along the slope. The results are compared
with the prediction of a linear stability analysis conducted in the framework
of the depth-averaged or Saint-Venant equations. We show that when the friction
law proposed in Pouliquen (1999a) is introduced in the Saint-Venant equations,
the theory is able to predict quantitatively the stability threshold and the
phase velocity of the waves but fails in predicting the observed cutoff
frequency. The instability is shown to be of the same nature as the long wave
instability observed in classical fluids but with characteristics that can
dramatically differ due to the specificity of the granular rheology.Comment: 29 pages, 20 figures, to be published in Journal of Fluid Mechanic
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
The MESANGE model: re-estimation on National Accounts base 2000 / Part 2 Version with chained-linked volumes
Mesange is a medium-size quarterly macro-econometric model of the French economy (about 500 equations, three sectors). The model describes short-term Keynesian dynamics and its long-term equilibrium is driven by supply-side determinants. Its reestimation on data from the national accounts base 2000 with fixed-base volumes is presented in a recent working paper (Klein and Simon, 2010). This first version of the model has been optimized for simulation use. Other applications of the Mesange model (short-term forecasting, analyses of the past) required its adaptation to the published data from the quarterly accounts with chained-linked volumes, as well as the integration of the recent crisis episode. A second version of the Mesange model has, therefore, been developed for this purpose. This version is presented in this working paper. First, the problems raised for macroeconomic modelling by national accounts with chained-linked volumes are explained and the solutions chosen to adapt the model to these new conventions are discussed. The applications of the version of the model with chained-linked volumes are, then, explained and illustrated with examples. Last, the main reestimated equations are detailed. The differences with respect to the version of the model with fixed-base volumes are commented. They stem from estimations based on non-identical data, but also from the different uses made of the two versions of Mesange and the resulting various needs and constraints that have conditioned the methodological choices that have been made. As for the version of the model with chained-linked volumes, priority has been given to the quality of the adjustment to the data rather than to the underlying theoretical framework. Nonetheless, the philosophy and general structure of the two versions of the model remain very much alike.macroeconometric model, estimation, chained-linked volumes, short-term forecasting, contribution analysis
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
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
Slow dynamics and aging of a confined granular flow
We present experimental results on slow flow properties of a granular
assembly confined in a vertical column and driven upwards at a constant
velocity V. For monodisperse assemblies this study evidences at low velocities
() a stiffening behaviour i.e. the stress necessary to obtain
a steady sate velocity increases roughly logarithmically with velocity. On the
other hand, at very low driving velocity (), we evidence a
discontinuous and hysteretic transition to a stick-slip regime characterized by
a strong divergence of the maximal blockage force when the velocity goes to
zero. We show that all this phenomenology is strongly influenced by surrounding
humidity. We also present a tentative to establish a link between the granular
rheology and the solid friction forces between the wall and the grains. We base
our discussions on a simple theoretical model and independent grain/wall
tribology measurements. We also use finite elements numerical simulations to
confront experimental results to isotropic elasticity. A second system made of
polydisperse assemblies of glass beads is investigated. We emphasize the onset
of a new dynamical behavior, i.e. the large distribution of blockage forces
evidenced in the stick-slip regime
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
- …