We report on experimental studies of the collision process between an incident bead and a three-dimensional granular packing (made of particles identical to the impacting one). The understanding of such a process and the resulting ejection of particles is, in particular, crucial to describe eolian sand transport. We present here an extensive experimental analysis of the collision and ejection process. The analysis is two dimensional in the sense that we determined only the vertical component V{z} of the ejection velocity of the splashed particles and the horizontal component V{x} lying in the incident plane. We extracted in particular the distribution of the ejection velocities for a wide range of impact angles theta{i} and incident velocity V{i} . We show that the mean quadratic horizontal velocity of the splashed particles is almost insensitive to changes in the impact angle and velocity, while the mean quadratic vertical velocity slightly increases with increasing impact velocity (as V{i}{1/2}). Moreover, the mean number of splashed particles per collision is found to be dependent on both the impact angle and velocity, and to scale with the impact speed as V{i}{3/2}. A consequence of these outcomes is that the sum of the kinetic energy of the splashed particles is directly proportional to the kinetic energy of the incident particle. Finally, we provide the bivariate probability distribution function P(V{x},V{z}) of the ejection velocities and show that it can be approximated by the product of a log-normal distribution and a circular normal one.

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 fuctuations of the vertical and horizontal particle velocity and the particle veloci[y autocorrelation functions. The long time fluctuating particle motion is demonstrated to be diffus&e 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. 0 199.

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 interpreted as the first step toward the transition toward classical dispersion at displacements much larger than the pore size. The influence of molecular diffusion and of the heterogeneities of the magnetic permeability also are discussed.

We present results of the collision process of a bead onto a static granular packing. We provide, in particular, a three-dimensional (3D) extensive characterization of this process from a model experiment that allows us to propel a spherical bead onto a granular packing with a well-controlled velocity and impact angle. A collision typically produces a high-energy particle (rebound particle) and several low-energy grains (ejected particles). The collision process is recorded by means of two fast video cameras. The sequence of images from both cameras are then analyzed via image processing and the trajectories of all particles are reconstructed in 3D space. We show that the incident particle does not remain in the vertical incident plane after the rebound and that the deviation angle increases with increasing impact angle. Concerning the ejected particles, we demonstrated that the ejection angle (measured with respect to the horizontal plane) is surprisingly independent of both the impact angle and velocity of the incident particle, and is very close to 60 degrees . The horizontal component of the ejection speed of the splashed particles is found to be weakly dependent on the incident speed and impact angle, and is relatively isotropic (no particular horizontal direction is favored). This last feature suggests that the bead packing acts as a perfect diffusive medium with respect to energy propagation.

The collision of a spherical grain with a granular bed is commonly parametrized by the splash function, which provides the velocity of the rebounding grain and the velocity distribution and number of ejected grains. Starting from elementary geometric considerations and physical principles, like momentum conservation and energy dissipation in inelastic pair collisions, we derive a rebound parametrization for the collision of a spherical grain with a granular bed. Combined with a recently proposed energy-splitting model [Ho et al., Phys. Rev. E 85, 052301 (2012)PLEEE81539-375510.1103/PhysRevE.85.052301] that predicts how the impact energy is distributed among the bed grains, this yields a coarse-grained but complete characterization of the splash as a function of the impact velocity and the impactor-bed grain-size ratio. The predicted mean values of the rebound angle, total and vertical restitution, ejection speed, and number of ejected grains are in excellent agreement with experimental literature data and with our own discrete-element computer simulations. We extract a set of analytical asymptotic relations for shallow impact geometries, which can readily be used in coarse-grained analytical modeling or computer simulations of geophysical particle-laden flows.

By using molecular dynamics simulations on a large number of hard spheres and the Voronoï tessellation we characterize hard-sphere systems geometrically at any packing fraction eta along the different branches of the phase diagram. Crystallization of disordered packings occurs only for a small range of packing fraction. For the other packing fractions the system behaves as either a fluid (stable or metastable) or a glass. We have studied the evolution of the statistics of the Voronoï tessellation during crystallization and characterized the apparition of order by an order parameter (Q(6)) built from spherical harmonics.

We performed numerical simulations of one-bead collision on the surface of a static granular medium. The simulations have been done for two- and three-dimensional packings of beads. The effect of the incident bead velocity, the shot angle, the mechanical parameters and the packing structure are analyzed for ordered and disordered 2D packings and only disordered 3D packings. The 2D results are in good agreement with experimental available data. The 3D simulations give good preliminaries results about the shock-wave propagation through the stacking and provides new insights in the ejection process ("Splash function").

The Voronoi network is known to be a useful tool for the structural description of voids in the packings of spheres produced by computer simulations. In this article we extend the Voronoi-Delaunay analysis to packings of nonspherical convex objects. Main properties of the Voronoi network, which are known for systems of spheres, are valid for systems of any convex objects. A general numerical algorithm for calculation of the Voronoi network in three dimensions is proposed. It is based on the calculation of the trajectory of the imaginary empty sphere of variable size, moving inside a system (the Delaunay empty sphere method). Analysis of voids is presented for an ensemble of random straight lines and for a molecular dynamics model of liquid crystal. The spatial distribution of voids and a simple percolation analysis are obtained. The distributions of the bottleneck radii and the radii of spheres inscribed in the voids are calculated.