颗粒材料上运动物体所受摩擦力的数值模拟

通过数值模拟,考察一定重量的平板在水平颗粒物质层上做匀速运动所引起的剪切颗粒流,并关注其与平板的摩擦力及等效摩擦系数.数值结果表明,等效摩擦系数不是常数,与平板的运动速度有关.这与通常的固体与固体之间剪切作用时所满足的摩擦定律不同,体现了颗粒系统的特殊力学行为.     

Numerical simulation of two-dimensional granular shearing flows and the friction force of a moving slab on the granular media

This paper studies some interesting features of two-dimensional granular shearing flow by using molecular dynamic approach for a specific granular system.The obtained results show that the probability distribution function of velocities of particles is Gaussian at the central part,but diverts from Gaussian distribution nearby the wall.The macroscopic stress along the vertical direction has large fluctuation around a constant value,the non-zero average velocity occurs mainly near the moving wall,which forms a shearing zone.In the shearing movement,the volume of the granular material behaves in a random manner.The equivalent friction coefficient between moving slab and granular material correlates with the moving speed at low velocity,and approaches constant as the velocity is large enough.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.     

基于离散元方法的颗粒材料缓冲性能及影响因素分析

在冲击荷载作用下, 颗粒材料通过颗粒间的摩擦及非弹性碰撞可有效进行能量耗散实现缓冲作用. 本文采用离散元方法对冲击载荷下颗粒材料的缓冲过程进行数值分析, 研究不同厚度下颗粒材料的缓冲性能. 计算结果表明: 颗粒层厚度H是影响颗粒材料缓冲性能的关键因素, 并存在一个临界厚度H_c. 当H < H_c时, 冲击力随H的增加而降低; 当H > H_c时, 冲击力对H的变化不敏感并趋于稳定值. 此外, 在不同颗粒摩擦系数和初始密集度下对缓冲过程的离散元分析表明, 光滑和疏松颗粒材料具有更好的缓冲性能. 最后, 对颗粒材料在冲击过程中的力链结构和底板的压力分布进行了讨论, 以揭示颗粒材料缓冲性能的内在机理.     

DEM simulation of small particles clogging in the packing of large beads

The percolation of small particles through a periodic random loose packing of large beads is studied numerically with the Distinct Element Method. The representativity of periodic mono-sized sphere packing of varying system size was first studied by comparing their pore size distributions and tortuosities with those of a larger system, considered as an infinite medium. The results show that a periodic packing of size as low as 4-grain diameters gives a reasonable representation of the porous medium and allows reducing considerably the number of particles that has to be used in the simulations. The flow and clogging of small particles of varying concentrations and friction coefficients flowing through the former packing are then studied numerically. Results show that a steady state is rapidly reached where the mean velocity and mean vertical velocity of small particles are both constant. These mean velocities decrease with an increase in friction coefficient and in small particle concentration. The influence of the friction coefficient μ is much less marked for values of μ larger than or equal to 0.5. The distribution of small particles throughout the crossed packing becomes rapidly heterogeneous. Small particles concentrate in some pores where their velocity vanishes and where the density can reach values larger than the density of the random loose packing. The proportion of particles blocked in these pores varies linearly with concentration. Finally, the narrow throats of the porous medium responsible for blocking are identified and characterized for different values of the friction coefficient.     

Numerical simulation of particle size effects on contact electrification in granular systems

Based on the contact charge transfer model between two particles due to a single collision proposed by Apodaca, the contact charges carried on a particle is derived due to multiple collisions, including the repeat collisions between two particles and the collisions with different particles, in mixed-size granular system of identical material. The effect of the particle size on the charges carried on the particle is simulated. The results indicate that for a mixed-size granular system, due to multiple collisions among particles, there exists a threshold particle radius, the particles with radius higher than which and the particles with radius lower than which carry opposite charges. The threshold particle radius is equal to mean value of particle size in the mixed-size granular system. Basically, the polarity of the charges carried on the largest particle is same as the polarity of the transfer charge carrier, and in case of the positive charge transferred, the largest particle will be positively charged and the smallest particle will be negatively charged, and vice versa. In the same size region, the more dispersive the particle size is, the more the net charges can be produced. In normal-distributed granular system, the magnitude of contact charge is determined mainly by the particle size distribution, size region, total particle number and the relative impact velocity.     

Stability and bifurcations of a stationary state for an impact oscillator

The motion of a vibroimpacting one-degree-of-freedom model is analyzed. This model is motivated by the behavior of a shearing granular material, in which a transitional phenomenon is observed as the concentration of the grains decreases. This transition changes the motion of a granular assembly from an orderly shearing between two blocks sandwiching a single layer of grains to a chaotic shear flow of the whole granular mass. The model consists of a mass-spring-dashpot assembly that bounces between two rigid walls. The walls are prescribed to move harmonically in opposite phases. For low wall frequencies or small amplitudes, the motion of the mass is damped out, and it approaches a stationary state with zero velocity and displacement. In this paper, the stability of such a state and the transition into chaos are analyzed. It is shown that the state is always changed into a saddle point after a bifurcation. For some parameter combinations, horseshoe-like structures can be observed in the Poincare sections. Analyzing the stable and unstable manifolds of the saddle point, transversal homoclinic points are found to exist for some of these parameter combinations. (c) 1994 American Institute of Physics.     

Steady State Properties of One-Dimensional Non-uniform Granular Gases Subjected to Gaussian White Noise Driving

We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time T of the Brownian process is greater than the mean collision time To, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state： the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.     

Brownian motion in granular gases of viscoelastic particles

A theory is developed of Brownian motion in granular gases (systems of many macroscopic particles undergoing inelastic collisions), where the energy loss in inelastic collisions is determined by a restitution coefficient ɛ. Whereas previous studies used a simplified model with ɛ = const, the present analysis takes into account the dependence of the restitution coefficient on relative impact velocity. The granular temperature and the Brownian diffusion coefficient are calculated for a granular gas in the homogeneous cooling state and a gas driven by a thermostat force, and their variation with grain mass and size and the restitution coefficient is analyzed. Both equipartition principle and fluctuation-dissipation relations are found to break down. One manifestation of this behavior is a new phenomenon of “relative heating” of Brownian particles at the expense of cooling of the ambient granular gas.     

Asymptotic Behavior of the Velocity Distribution of Driven Inelastic Gas with Scalar Velocities: Analytical Results

Journal of Statistical Physics - We determine the asymptotic behavior of the tails of the steady state velocity distribution of a homogeneously driven granular gas comprising of particles having a...     

Starting to move through a granular medium

We explore the process of initiating motion through a granular medium by measuring the force required to push a flat circular plate upward from underneath the medium. In contrast with previous measurements of the drag and penetration forces, which were conducted during steady state motion, the initiation force has a robust dependence on the diameter of the grains in the medium. We attribute this dependence to the requirement for local dilation of the grains around the circumference of the plate, as evidenced by an observed linear dependence of the initiation force on the plate diameter.     

Forcing and velocity correlations in a vibrated granular monolayer

The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anticorrelation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a Gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the plate.     

Collisional granular flow as a micropolar fluid

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.     

Rheology of dense granular mixtures: boundary pressures

Models for dense sheared granular materials indicate that their rheological properties depend on particle size, but the representative size for mixtures is not obvious. Here, we computationally study pressure on a boundary due to sheared granular mixtures to determine its dependence on particle size distribution. We find that the pressure does not depend monotonically on average particle size. Instead it has an additional dependence on a measure of the effective free volume per particle we adapt from an expression for packing of monosized particles near the jammed state.     

Nonequilibrium fluctuation relation for sheared micellar gel in a jammed state

We show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress, and in all cases show similar symmetry properties as predicted by the Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear-rate fluctuations increase with the decrease of the system size.     

Coexistence of two granular temperatures in binary vibrofluidized beds

An investigation into the granular temperature distributions of a binary vibrofluidized granular bed has been conducted using positron emission particle tracking. By repeating each experiment with the tracer selected in turn from the two size components, the granular temperature and packing fraction distributions for each phase were determined. It was found that, for a range of size fractions, the granular temperature of the larger particles was higher than that of the smaller diameter grains, a result which was supported by a simple theoretical analysis based on the steady state energy equation.     

Hydrodynamic model for particle size segregation in granular media

We present a hydrodynamic theoretical model for “Brazil nut” size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local “granular temperature”. The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.     

Simulation of nanopowder compaction in terms of granular dynamics

The uniaxial compaction of nanopowders is simulated using the granular dynamics in the 2D geometry. The initial arrangement of particles is represented by (i) a layer of particles executing Brownian motion (isotropic structures) and (ii) particles falling in the gravity field (anisotropic structures). The influence of size effects and the size of a model cell on the properties of the structures are studied. The compaction of the model cell is simulated with regard to Hertz elastic forces between particles, Cattaneo-Mindlin-Deresiewicz shear friction forces, and van der Waals-Hamaker dispersion forces of attraction. Computation is performed for monodisperse powders with particle sizes ranging from 10 to 400 nm and for “cohesionless” powder, in which attractive forces are absent. It is shown that taking into account dispersion forces makes it possible to simulate the size effect in the nanopowder compaction: the compressibility of the nanopowder drops as the particles get finer. The mean coordination number and the axial and lateral pressures in the powder systems are found, and the effect of the density and isotropy of the initial structure on the compressibility is analyzed. The applicability of well-known Rumpf’s formula for the size effect is discussed.     

Dynamic properties of the two-dimensional density-driven segregation

We discuss some dynamic properties of the segregation in vertically vibrated binary granular mixtures with the same size. We present a method that can accurately calculate the order parameter in the simulation. By use of the time evolution of the order parameter, we have found that the convergence of the segregated state depends at least on the vibration amplitude, the total mass of the particles, and also the density difference between the lighter and heavier particles.The convergence is quicker for larger vibration amplitude, lighter total mass of the particles and more density difference between the lighter and heavier particles. We have also found that thefluctuation is larger even after the steady state is reached for lighter total mass of the particles and less density difference between the lighter and heavier particles.