Coefficient of tangential restitution for viscoelastic spheres

A Numerical Research on the Relationship between Aeolian Sand Ripples and the Sand Flux

Theoretically, the sand flux will not change after the wind-driven sand particle transport reaches the saturated state. However, it has been found in many wind-tunnel experiments that the sand flux will gradually decrease with time in long-term particle transport duration and will eventually reach a new stable state. In this work, we used numerical simulations to study the source of this kind of decrease and found it is caused by the sand ripple on the bed surface. The ripple index showed a strong correlation to the sand flux, and it decreased during the initial stage of the ripple formation. With a simplified theoretical model, we found the linear relationship between the Shields number and the particle transport load holds. However, the slope of this relationship and the dynamic threshold of particle entrainment decreased with the ripple index. As the sand flux scales linearly with the particle transport load, we finally derived an expression that describes how the sand flux on the ripple bedform varies with the wind strength. From this expression, we found the sand flux increases with ripple index, and it was easier to be influenced by the ripple bed form in small wind strength.

An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments

The angle between the sloping side of a heap of particles and the horizontal, called angle of repose, is often used to characterize the flowability of granular materials on Earth and planetary environments, such as sand, dust aerosols, and powders. In planetary research, this angle provides an excellent proxy for particle size. The smaller the particle is, the larger the effect of attractive forces between atoms and molecules on the surface of the particles relative to particle weight, the less flowable the material, and the steeper, thus, the angle of repose. We present a model that accurately predicts the angle of repose as a function of particle size, both on Earth and under extraterrestrial gravity.

The angle of repose—i.e., the angle θr between the sloping side of a heap of particles and the horizontal—provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts θr as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle–particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as θr obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology.

Incorporation of velocity-dependent restitution coefficient and particle surface friction into kinetic theory for modeling granular flow cooling

Kinetic theory (KT) has been successfully used to model rapid granular flows in which particle interactions are frictionless and near elastic. However, it fails when particle interactions become frictional and inelastic. For example, the KT is not able to accurately predict the free cooling process of a vibrated granular medium that consists of inelastic frictional particles under microgravity. The main reason that the classical KT fails to model these flows is due to its inability to account for the particle surface friction and its inelastic behavior, which are the two most important factors that need be considered in modeling collisional granular flows. In this study, we have modified the KT model that is able to incorporate these two factors. The inelasticity of a particle is considered by establishing a velocity-dependent expression for the restitution coefficient based on many experimental studies found in the literature, and the particle friction effect is included by using a tangential restitution coefficient that is related to the particle friction coefficient. Theoretical predictions of the free cooling process by the classical KT and the improved KT are compared with the experimental results from a study conducted on an airplane undergoing parabolic flights without the influence of gravity [Y. Grasselli, G. Bossis, and G. Goutallier, Europhys. Lett. 86, 60007 (2009)10.1209/0295-5075/86/60007]. Our results show that both the velocity-dependent restitution coefficient and the particle surface friction are important in predicting the free cooling process of granular flows; the modified KT model that integrates these two factors is able to improve the simulation results and leads to better agreement with the experimental results.

Effective potentials in a bidimensional vibrated granular gas

We present a numerical study of the spatial correlations of a quasi-two-dimensional granular fluid kept in a nonstatic steady state via vertical shaking. The simulations explore a wide range of vertical accelerations, restitution coefficients, and packing fractions, always staying below the crystallization limit. From the simulations we obtain the relevant pair distribution functions (PDFs), and effective potentials for the interparticle interaction are extracted from these PDFs via the Ornstein-Zernike equation with the Percus-Yevick closure. The correlations in the granular structures originating from these effective potentials are checked against the originating PDF using standard Monte Carlo simulations, and we find in general an excellent agreement. The resulting effective potentials show an increase of the spatial correlation at contact with the decreasing values of the restitution coefficient, and a tendency of the potentials to display deeper wells for more dissipative dynamics. A general exception to this trend appears for a range of values of the forcing, which depends on the restitution coefficient, but not on the density, where resonant bouncing increases correlations, resulting in deeper potential wells. The nature of these resonances is explored and shown to be the result of synchronization in the parabolic flights of the particles.

Helical inner-wall texture prevents jamming in granular pipe flows

Granular pipe flows are characterized by intermittent behavior and large, potentially destructive solid fraction variations in the transport direction. By means of particle-based numerical simulations of gravity-driven flows in vertical pipes, we show that it is possible to obtain steady material transport by adding a helical texture to the inner-wall of the pipe. The helical texture leads to a more homogeneous mass flux along the pipe, prevents the emergence of large density waves and substantially reduces the probability of plug formation thus avoiding jamming of the particulate flow. We show that the granular mass flux Q through a pipe of diameter D with a helical texture of wavelength λ follows the equation Q = Q0·{1 - B sin[arctan(2πD/λ)]}, where Q0 is the flow without helix, predicted from the well-known Beverloo equation. Our new expression yields, thus, a modification of the Beverloo equation with only one additional fit parameter, B, and describes the particle mass flux with the helical texture with excellent quantitative agreement with simulation results. Future application of the method proposed here has the potential to improve granular pipe flows in a broad range of processes without the need for energy input from any external source.

Attractive particle interaction forces and packing density of fine glass powders

We study the packing of fine glass powders of mean particle diameter in the range (4-52) μm both experimentally and by numerical DEM simulations. We obtain quantitative agreement between the experimental and numerical results, if both types of attractive forces of particle interaction, adhesion and non-bonded van der Waals forces are taken into account. Our results suggest that considering only viscoelastic and adhesive forces in DEM simulations may lead to incorrect numerical predictions of the behavior of fine powders. Based on the results from simulations and experiments, we propose a mathematical expression to estimate the packing fraction of fine polydisperse powders as a function of the average particle size.

Stochastic behavior of the coefficient of normal restitution

We consider the collision of a rough sphere with a plane by detailed analysis of the collision geometry. Using stochastic methods, the effective coefficient of restitution may be described as a fluctuating quantity whose probability density follows an asymmetric Laplace distribution. This result agrees with recent experiments by Montaine et al. [Phys. Rev. E 84, 041306 (2011)].

Coefficient of restitution as a fluctuating quantity

The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice nontrivial (non-Gaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, p(ɛ), is formed by two exponential functions (one increasing, one decreasing) of different slope. This behavior may be explained by a certain roughness of the particle which leads to energy transfer between the linear and rotational degrees of freedom.

Viscoelastic behaviors in polymeric nanodroplet collisions

Viscoelastic behaviors in the head-on collisions of polymeric nanodroplets are reported. We propose a new model for normal forces between two colliding droplets. By decomposing the force into an elastic component and a dissipative component and carefully analyzing the equation of motion, we obtain some conditions on the model parameters imposed by the thermodynamic arguments. By employing molecular dynamics simulations, we can explicitly determine the corresponding model parameters by fitting. We compare the model predictions with the simulation results.

Negative normal restitution coefficient found in simulation of nanocluster collisions

The oblique impacts of nanoclusters are studied theoretically and by means of molecular dynamics. In simulations we explore two models--Lennard-Jones clusters and particles with covalently bonded atoms. In contrast with the case of macroscopic bodies, the standard definition of the normal restitution coefficient yields for this coefficient negative values for oblique collisions of nanoclusters. We explain this effect and propose a proper definition of the restitution coefficient which is always positive. We develop a theory of an oblique impact based on a continuum model of particles. A surprisingly good agreement between the macroscopic theory and simulations leads to the conclusion that macroscopic concepts of elasticity, bulk viscosity, and surface tension remain valid for nanoparticles of a few hundred atoms.