Eric Clément

Footprints in Sand: The Response of a Granular Material to Local Perturbations

We experimentally determine ensemble-averaged responses of granular packings to point forces, and we compare these results to recent models for force propagation in a granular material. We use 2D granular arrays consisting of photoelastic particles: either disks or pentagons, thus spanning the range from ordered to disordered packings. A key finding is that spatial ordering of the particles is a key factor in the force response. Ordered packings have a propagative component that does not occur in disordered packings.

Green's function measurements of force transmission in 2D granular materials

Abstract We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amounts of disorder, disks packed in a regular rectangular lattice with different frictional properties, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface, but this description is not as good for non-normal applied forces. These observations are consistent with recent predictions of Bouchaud et al. [Eur. Phys. J. E 4 (2001) 451] and Socolar et al. [Eur. Phys. J. E 7 (2002) 353] and with the anisotropic elasticity models of Goldenberg and Goldhirsch [Phys. Rev. Lett. 89 (2002) 084302]. At this time, it is not possible to distinguish between these two models. The data do not support a diffusive picture, as in the q-model, and they are in conflict with data by Da Silva and Rajchenbach [Nature 406 (2000) 708] that indicate a parabolic response for a system consisting of cuboidal blocks. We also explore the spatial properties of force chains in an anisotropic textured system created by a nearly uniform shear. This system is characterized by stress chains that are strongly oriented along an angle of 45°, corresponding to the compressive direction of the shear deformation. In this case, the spatial correlation function for force has a range of only one particle size in the direction transverse to the chains, and varies as a power law in the direction of the chains, with an exponent of −0.81. The response to forces is the strongest along the direction of the force chains, as expected. Forces applied in other directions are effectively refocused towards the strong force chain direction.

Fluidization of a Bidimensional Powder

We present experimental observations of a fluidized state in a 2d vertical packing of beads submitted to vertical vibrations. The density field and the velocity distributions are simultaneously measured. The system is shown to reach a steady density profile but the state of internal agitation is dependent on the phase of excitation.

Stresses in silos: comparison between theoretical models and new experiments

We present precise and reproducible mean pressure measurements at the bottom of a cylindrical granular column. If a constant overload is added, the pressure is linear in overload and nonmonotonic in the column height. The results are quantitatively consistent with a local, linear relation between stress components, as was recently proposed by some of us. They contradict the simplest classical (Janssen) approximation, and may rather severely test competing models.

Nonlocal rheology of granular flows across yield conditions.

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A nonlocal constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point.

SIMULATIONS OF PATTERN FORMATION IN VIBRATED GRANULAR MEDIA

We present simulations of peak pattern formation in vibrated two-dimensional (2D) granulates and measure the dispersion relation of the pattern for various frequencies, accelerations, cell sizes, and layer heights. We report the first quantitative data from numerical simulations showing an interesting dependence of the pattern wavelength on the acceleration and the system size. Our results are related to recent experimental findings and theoretical predictions for gravity waves.

Green's function probe of a static granular piling

We present an experiment which aims to investigate the mechanical properties of a static granular assembly. The piling is a horizontal 3D granular layer confined in a box. We apply a localized extra force at the surface and the spatial distribution of stresses at the bottom is obtained (the mechanical Greens function). For different types of granular media, we observe a linear pressure response whose profile shows one peak centered at the vertical of the point of application. The peaks width increases linearly with increasing depth. This Greens function seems to be in at least qualitative agreement with predictions of elastic theory.

Non-Newtonian viscosity of Escherichia coli suspensions.

The viscosity of an active suspension of E. coli bacteria is determined experimentally as a function of the shear rate using a Y-shaped microfluidic channel. From the relative suspension viscosity, we identify rheological thickening and thinning regimes as well as situations at low shear rate where the viscosity of the bacteria suspension can be lower than the viscosity of the suspending fluid. In addition, bacteria concentration and velocity profiles in the bulk are directly measured in the microchannel.

From the stress response function (back) to the sand pile “dip”

Abstract. We relate the pressure “dip” observed at the bottom of a sand pile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sand pile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing --albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.

Unjamming a granular hopper by vibration

We present an experimental study of the outflow of a hopper continuously vibrated by a piezoelectric device. Outpouring of grains can be achieved for apertures much below the usual jamming limit observed for non-vibrated hoppers. Granular flow persists down to the physical limit of one grain diameter, a limit reached for a finite vibration amplitude. For the smaller orifices, we observe an intermittent regime characterized by alternated periods of flow and blockage. Vibrations do not significantly modify the flow rates both in the continuous and the intermittent regime. The analysis of the statistical features of the flowing regime shows that the flow time significantly increases with the vibration amplitude. However, at low vibration amplitude and small orifice sizes, the jamming time distribution displays an anomalous statistics.