François Chevoir

Rheophysics of dense granular materials : Discrete simulation of plane shear flows

We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.

Experimental study of collisional granular flows down an inclined plane

The collisional flow of a slightly inelastic granular material down a rough inclined plane is usually described by kinetic theories. We present an experimental study aimed at analysing the assumptions and the quantitative predictions of such theories. A two-dimensional channel coupled to a model granular material and image analysis allow detailed and complete measurement of the kinematics and structure of the flows. We determine the range of inclination and particle flux for which the flow is stationary and uniform. The characteristic profiles of solid fraction, mean velocity and granular temperature are systematically measured. Both the true collisional and the dilute kinetic regimes are examined. We show that a quasi-hydrodynamic description of these regimes seems relevant, and that the pressure and the viscosity terms are in good qualitative agreement with the prediction of the kinetic theory. The profiles are well described by the kinetic theory near the top of the flow, at low solid fraction. Conversely there are large discrepancies near the rough plane, where the material is structured in layers

Dense flows of cohesive granular materials

Using molecular dynamic simulations, we investigate the characteristics of dense flows of model cohesive grains. We describe their rheological behaviour and its origin at the scale of the grains and of their organization. Homogeneous plane shear flows give access to the constitutive law of cohesive grains which can be expressed by a simple friction law similar to the case of cohesionless grains, but intergranular cohesive forces strongly enhance the resistance to the shear. Then we show the consequence on flows down a slope: a plugged region develops at the free surface where the cohesion intensity is the strongest. Moreover, we measure various indicators of the microstructure within flows which evidence the aggregation of grains owing to cohesion and we analyse the properties of the contact network (force distributions and anisotropy). This provides new insights into the interplay between the local contact law, the microstructure and the macroscopic behavior of cohesive grains. Movies are available with the online version of the paper.

Dense flows of bidisperse assemblies of disks down an inclined plane

Using discrete numerical simulations, we have studied the flow down a rough inclined plane of a bidisperse assembly of frictional cohesionless disks. Our study focuses on steady uniform flows, once a stable segregation has developed inside the flowing layer. The material is segregated in three layers: a basal layer (small grains), a superficial layer (large grains), and a mixed layer in the center, so that the average diameter of the grains increases from the bottom to the top. From the measurement of the profiles of velocity, solid fraction, and stress components, we show that the rheological law of such a polydisperse material may be described by a local friction law, which extends the result obtained for quasimonodisperse granular flows. This law states that the effective friction coefficient depends approximately linearly on a generalized inertial number, taking into account the average diameter of the grains.

Annular shear of cohesionless granular materials: from the inertial to quasistatic regime.

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches.

Calculation of phonon‐assisted tunneling and valley current in a double‐barrier diode

We have calculated the longitudinal optical phonon scattering contribution to electron tunneling through a double‐barrier diode. Our model takes into account the delocalization of the incident electron over the whole structure as well as the momentum transfer between electrons and phonons. Our results, obtained without fitting parameters, give considerably improved estimates of the experimentally observed valley current and its dependence on temperature.

Rheology of dense snow flows: Inferences from steady state chute-flow experiments

Good knowledge of snow rheology is useful for the mitigation of avalanches. However, experiments with snow are difficult and the few available data provide only a partial knowledge of snow flows. In this study we investigated the rheological behavior of a dense flow of dry snow, which often occurs in real avalanches. To this end, we carried out systematic small-scale in situ flows down a flume with natural snow. Over three winters, we performed approximately 100 experiments with various slopes and flow discharges and we characterized them by measuring the velocity profile and basal stress. This data set, unique in its extent, allows us to identify various generic characteristics of dense flow of dry snow, which are found to differ from common fluids. We point out that snow flows develop as a very viscous upper thick layer over a much less viscous thin layer. We interpret this heterogeneity as a consequence of a shear-induced evolution of the snow microstructure that gives rise to different materials betwe...

Dense flows of dry granular material

The behavior of dense assemblies of dry grains submitted to continuous shear deformation is still not well understood. Recently it has been the subject of several experiments and discrete particle simulations. For both confined and free surface geometries, we present the general features of such flows as well as grain-level information. We then describe the main rheological models and their predictions. c 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS granular media/ hydrodynamics/ rheology ecoulements de milieux granulaires secs

Photoluminescence and space-charge distribution in a double-barrier diode under operation

The low‐temperature photoluminescence of a double‐barrier diode under operation is studied. Its observation with exciting light above (as well as below) the quantum well absorption edge indicates that the tunneling of holes plays an important role. A new crossed transition identified to occur in the collector spacer layer shows a strong Stark shift with applied bias giving information on the potential distribution in the diode.

Rheology and structure of granular materials near the jamming transition

The shear stress of non-cohesive granular material in the vicinity of the jamming transition is supposed to be connected to the formation of transient rigid clusters of particles. The characteristics of these transient clusters are investigated as a function of the imposed pressure, the solid volume fraction and the shear rate. This is responsible for an increase of the shear stress for a vanishing shear rate, which leads to an instability close to the jamming transition. We discuss the consequences for stick-slip motion and flows down an inclined plane, in agreement with the observations. Then, the oscillation of the granular material between two jam-flow states generates fast velocity fluctuations which result in a mean frictional force proportional to the mean velocity relative to the jammed state in the flow direction. Accordingly the velocity field in a simple shear flow is governed by a Brinkman equation and any symmetry break favours a strain localization. This analysis might be extended to the case of granular pastes.