Luc Oger

Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres

The motion of non‐Brownian spheres settling in the midst of a suspension of like spheres has been experimentally studied under creeping flow conditions. A few glass spheres, marked with a thin coating of silver, were tracked in a suspension of unmarked glass spheres, made optically transparent by matching the index of refraction of the suspending fluid to that of the glass spheres. Particles were tracked with a real time digital imaging processing system. Particle trajectories were examined in the bulk region of the suspension for particle volume fractions ranging from 0% to 40% in 5% steps. Statistical analyses of local particle velocities yield the mean settling velocity, the RMS of the fluctuations of the vertical and horizontal particle velocity and the particle velocity autocorrelation functions. The long time fluctuating particle motion is demonstrated to be diffusive in nature. Vertical and horizontal correlation times and self‐diffusivities are found as a function of particle volume fraction, and a strongly anisotropic diffusion noted.

Pulsed gradient NMR measurements and numerical simulation of flow velocity distribution in sphere packings

The displacement of water molecules associated with the flow of water inside a nonconsolidated packing of 800 μm OD glass spheres has been measured by a pulsed gradient NMR technique. Using a stimulated spin‐echo sequence, mean displacements of up to 300 μm corresponding to measurement times of up to 200 ms can be analyzed. The measurement can be quantitatively calibrated using the pure molecular self‐diffusion of water at zero flow conditions. For molecular displacements much smaller than the pore size, the distribution of the flow velocity component along the mean flow direction is determined at Reynolds numbers high enough so that longitudinal molecular diffusion is negligible. An exponential decay of the probability distribution of the displacements is observed at large distances. The results are very similar to those obtained by numerical solution of the Stokes equation in random sphere packings. At longer displacement distances, a secondary peak of the displacement distribution is observed: It is in...

Voronoi tessellation of packings of spheres: Topological correlation and statistics

Abstract We describe three-dimensional froths obtained by the Voronoi tessellation of monosize packings of spheres at different packing fractions C from C = 0 toC = 0·58. The packings are built numerically. The distribution p(f) of the number f of faces of a cell is well approximated by a Gaussian. The average number m(f) of faces of the neighbours of a f-faceted cell follows the three-dimensional equivalent of the Aboav-Weaire law. The Lewis and the Deschlaws can be generalized to the three-dimensional case to describe the metricproperties of the froths. The distribution of the volumes of the cells is wellfitted by a gamma law at low packing fractions but becomes narrower and more symmetric at higher concentrations.

Yield and deformation of an assembly of disks subjected to a deviatoric stress loading

The deformation of an assembly of particles is examined using a discrete element method (DEM) numerical model. The particles are modeled as random-sized, rough, inelastic, circular two-dimensional disks. The simulations keep track of the displacements, velocities and contact forces of each particle in order to examine the local rearrangements of the particles during the deformation and to determine the bulk stress states. The behavior of cohesive materials can be examined by introducing tensile forces between particles. The tests are done by applying constant confining pressures on two parallel flexible boundaries and a constant displacement rate on the two other flat frictionless walls. During the loading, the axial stress on the moving walls reaches a peak value and afterwards remains essentially constant for large strains. Stress–strain curves are obtained for a large range of confining pressures. They show that the yield envelopes follow the linear Mohr–Coulomb criterion. The global angle of friction is determined for a large range of particle–particle friction angles and particle size distributions. It was found that the global friction angle φcv increased with interparticle friction angle φi for φi<6°; for larger values of φi, the global friction angle is essentially constant. As the spread in the particle size distribution increased, the magnitude of the internal angle of friction was found to increase for a given interparticle friction angle.

Properties of disordered sphere packings I. Geometric structure: Statistical model, numerical simulations and experimental results

Abstract This paper presents a study of the characterisation of topological disorder in packings and the resulting effects on the mechanical and electrical properties of binary packings of spheres. It is shown that the contacts between spheres as predicted by an idealised statistical model are different from those found by computer simulations and from experimental results. These differences depend on the assumptions used in the model and the method of packing, sphere by sphere in computer simulations and collectively in experiments. The consequences of these differences are interpreted in terms of cooperative effects and local arching in real packings. Finally, we give a range of 4.75 to 6 for the mean co-ordination number for the stability of sphere packings under gravity. The minimum value of 4.75 is determined by an analysis of local arching and the maximum value of 6 by the stability of a single sphere.

Smoothed particle hydrodynamics for cohesive grains

Abstract A rheology based on the Mohr–Coulomb yield criterion for cohesive materials is implemented in the framework of Smoothed Particle Hydrodynamics (SPH). We enhance the classical SPH approaches by using some conservative renormalization techniques and a new smoothing kernel which improves the stability of the code near discontinuities. We apply this approach to the simulation of broken-ice fields floating on the water surface and moving under the effect of wind forces. When broken-ice fields are regarded as a continuum, their rheological behavior can be described by a model known as viscous-plastic. The ice field is modeled as a viscous fluid for very small strain rates and is assumed to flow plastically otherwise. In the plastic regime the stress states are described in terms of the Mohr–Coulomb yield criterion.

Tessellation of binary assemblies of spheres

We describe three-dimensional froths obtained by radical tessellation of random binary assemblies of spheres at different packing fractions C from C=0 to C∼0.60 and for large ranges of composition. The packings are built numerically using different algorithms: collective reorganization, random deposition or molecular dynamics interaction. Both topological and metric properties show deviations from those of a totally random froth. The results are qualitatively similar to those obtained previously on 2D binary mixtures of disks.

Voronoi and Radical Tessellations of Packings of Spheres

The Voronoi tessellation is used to study the geometrical arrangement of disordered packings of equal spheres. The statistics of the characteristics of the cells are compared to those of 3d natural foams. In the case of binary mixtures or polydisperse assemblies of spheres, the Voronoi tessellation is replaced by the radical tessellation. Important differences exist.

Properties of disordered sphere packings II. Electrical properties of mixtures of conducting and insulating spheres of different sizes

Abstract Reproducible results have been obtained for the electrical conductivity of packings of spheres after they had been subjected to cycles of pressure. The percolation properties of mixtures of conducting and non-conducting spheres are investigated by comparison with a numerical simulation. In a mixture where the two kinds of sphere have different sizes, the numerical simulation gives a higher threshold value than is found in the experiments, which we attribute to the higher coordinance of the latter. At the threshold, the critical volume fraction occupied by the conducting species depends on the diameter ratio of the spheres.

Transport of small particles through a 3D packing of spheres: experimental and numerical approaches

In this paper, we study the transport of particles through a porous structure. Experimentally, we focus our attention on the dependence of the mean transit time on some parameters like the number of small particles injected in the structure, and the height of the packing. We have developed a numerical model, based on a DEM method, to simulate the experiment. This model is useful for accessing the internal structure of the packing and for analysing precisely the influence of the restitution coefficient and the size ratio between spheres.