Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.     

Probability distribution of inherent states in models of granular media and glasses

The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a “tap dynamics” analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new “thermodynamical” parameters, called “configurational temperatures” (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single “configurational temperature”. Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed. Received 19 March 2002 and Received in final form 14 June 2002     

Volume fluctuations and geometrical constraints in granular packs

I study the structural organization and correlations in very large packings of equally sized spheres, reconstructed in three dimensions with x-ray computed tomography. I show that the geometrical structure can be conveniently studied as a packing of irregular tetrahedra with volume distribution that must decay exponentially with parameters controlled by the conditions of mechanical stability, nonoverlapping, and space filling. I argue that the system's structure can be described as constituted of two phases: (1) an "unconstrained" phase which freely shares the volume and (2) a "constrained" phase which assumes configurations accordingly with the geometrical constraints. It results that the granular system exploits heterogeneity maximizing freedom and entropy while constraining mechanical stability.     

Rheology of sheared monodisperse granular suspensions

Sheared granular suspensions can either flow or be jammed. They show as well a ‘melting’ transition: partially ordered flowing states are found which can be melted into fully disordered arrangements of grains by sufficient shear. While these are well documented phenomena, the underlying mechanisms and their control parameters are still far from clear. Via Molecular Dynamics simulations, we study the rheology of a model system of sheared frictional monodisperse granular materials [7, 8]. In particular, we aim to understand the nature of a critical line separating crystallised and melted states and the “jammed” region in the phase diagram. We outline as well connections and differences with thermal glass formers and colloidal suspensions.     

Preavalanche instabilities in a granular pile

We investigate numerically the transition between static equilibrium and dynamic surface flow of a 2D cohesionless granular system driven by a continuous gravity loading. This transition is characterized by intermittent local dynamic rearrangements and can be described by an order parameter defined as the density of critical contacts, i.e., contacts where the friction is fully mobilized. Analysis of the spatial correlations of critical contacts shows the occurrence of "fluidized" clusters which exhibit a power-law divergence in size at the approach of the stability limit. The results are compatible with recent models that describe the granular system during the static/dynamic transition as a multiphase system.     

Hysteretic transition between avalanches and continuous flow in rotated granular systems

Experiments in drums or cylinders partly filled with a granular system and rotated constantly about their horizontally aligned axis of symmetry show a hysteretic transition from discrete avalanches to continuous flow if the rotation rate is adiabatically changed. Herein, we show that this hysteresis can be explained by the impact of global Langevin-type fluctuations in a recently proposed minimal model for surface flow along granular piles. For too large magnitudes of the fluctuations corresponding to almost elastic grains, the hysteresis vanishes. This might explain why molecular dynamical simulations were not yet able to detect the hysteretic transition. (c) 1999 American Institute of Physics.     

Dynamics of freely cooling granular gases

We study dynamics of freely cooling granular gases in two dimensions using large-scale molecular dynamics simulations. We find that for dilute systems the typical kinetic energy decays algebraically with time, E(t) approximately t(-1), and velocity statistics are characterized by a universal Gaussian distribution in the long time limit. We show that in the late clustering regime particles move coherently as typical local velocity fluctuations, Deltav, are small compared with the typical velocity, Deltav/v approximately t(-1/4). Furthermore, locally averaged shear modes dominate over acoustic modes. The small thermal velocity fluctuations suggest that the system can be heuristically described by Burgers-like equations.     

Study of the shear-rate dependence of granular friction based on community detection

In this study, computer simulations are performed on three-dimensional granular systems under shear conditions. The system comprises granular particles that are confined between two rigid plates. The top plate is subjected to a normal force and driven by a shearing velocity. A positive shear-rate dependence of granular friction, known as velocity-strengthening, exists between the granular and shearing plate. To understand the origin of the dependence of frictional sliding, we treat the granular system as a complex network, where granular particles are nodes and normal contact forces are weighted edges used to obtain insight into the interiors of granular matter. Community structures within granular property networks are detected under different shearing velocities in the steady state. Community parameters, such as the size of the largest cluster and average size of clusters, show significant monotonous trends in shearing velocity associated with the shear-rate dependence of granular friction. Then, we apply an instantaneous change in shearing velocity. A dramatic increase in friction is observed with a change in shearing velocity in the non-steady state. The community structures in the non-steady state are different from those in the steady state. Results indicate that the largest cluster is a key factor affecting the friction between the granular and shearing plate.     

Unifying suspension and granular rheology

Using an original pressure-imposed shear cell, we study the rheology of dense suspensions. We show that they exhibit a viscoplastic behavior similarly to granular media successfully described by a frictional rheology and fully characterized by the evolution of the friction coefficient μ and the volume fraction ? with a dimensionless viscous number I(v). Dense suspension and granular media are thus unified under a common framework. These results are shown to be compatible with classical empirical models of suspension rheology and provide a clear determination of constitutive laws close to the jamming transition.     

颗粒样品形变对声波传播影响的实验探究

为了更好地理解颗粒间接触结构的变化对通过颗粒介质中的声波的影响,本文利用单轴压缩实验,通过一系列增加的轴向压力使样品塑性应变不断增大,这在颗粒尺度上对应于颗粒间接触结构的改变.我们测量了此过程中通过颗粒样品的声波变化,结果表明颗粒体系内接触结构的变化对声波波形中的非相干波部分和频率有明显的影响,并且在样品接触结构变化的初始阶段声速是偏离有效介质理论的预测的.     

YBCO颗粒膜的非平衡微波响应与Koterlitz-Thouless相变

报道了Yba₂Cu₃O_7-δ(YBCO)颗粒膜的微波辐射(λ＝8mm)响应的特征.实验结果表明：YBCO颗粒膜的微波响应行为不能用辐射热效应来描述,而应当属于非平衡响应行为.在超导转变温度T_∞以下温区,非平衡微波响应信号电平随样品电阻R趋于零而消失,并且对弱的外磁场十分灵敏.在对样品的直流I-V特性进行了仔细测量后发现,样品的电输运行为具有准二维结构特征,可以用Kosterlitz-Thouless(K-T)相变模型加以描述.在此基础上,分析结果表明:YBCO颗粒膜中的非平衡微波响应机制可能与磁通“涡旋-反涡旋”束缚对的激发态有关. 关键词：     

Equipartition of rotational and translational energy in a dense granular gas

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's law with a van?der?Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to nonequilibrium systems.     

冲击荷载下颗粒物质缓冲性能的试验研究

颗粒物质是一种复杂的能量耗散体系. 颗粒间的摩擦和黏滞作用可使冲击荷载引起的能量有效衰减, 颗粒间的力链结构又可将瞬时局部冲击荷载进行空间扩展和时间延长, 达到良好的缓冲效果. 为研究颗粒物质对冲击荷载的缓冲性能, 本文采用重力作用下球体冲击筒内颗粒物质的试验系统, 研究了筒体底部作用力在颗粒材料、颗粒厚度等因素影响下的变化规律. 试验结果表明: 非规则颗粒具有更加良好的缓冲性能, 粗颗粒的缓冲性能略高于细颗粒. 颗粒厚度H是影响缓冲性能的重要因素, 并存在一个临界厚度H_c. 当H<H_c时, 缓冲性能随H的增加而增强; 当H>H_c时, H对缓冲效果的影响不再显著. 以上研究是在同一冲击能量下进行的, 而对于不同冲击能量下的H_c还需要深入开展. 通过颗粒物质对冲击荷载缓冲性能的试验研究, 可揭示颗粒材料的基本物理力学行为, 为其在缓冲减振领域中的应用提供依据.     

Dynamically induced effective interaction in periodically driven granular mixtures

We show that a granular mixture subject to horizontal oscillations can be reduced to a monodisperse system of particles interacting via an effective interaction. This interaction is attractive at short distances and strongly anisotropic, and its features explain the system rich phenomenology, including segregation and stripe pattern formation. Finally, we show that a modified Cahn-Hilliard equation, which takes into account the characteristics of the effective interaction, is capable of describing the dynamics of the mixture.     

Density Waves in One-Dimensional Granular Flows Driven by Non-Uniform Force Field

We introduce a non-uniform gravity-like force field to control the granular flow state in a quasi-one-dimensional system, and study the system by the molecular dynamics simulation. We find that the granular flow under non-uniform force field can be well described by a density wave with fixed time period if a fixed particle number condition is used. The base frequency of the density wave does not depend on the position of the flow, while both the average density and oscillation amplitude of the flow vary continuously with the position. The formation of the density wave results from the aggregation of the granules in the decelerated region and the feed-back mechanism in the fixed particle number condition.     

Density Waves in One-Dimensional Granular Flows Driven by Non-Uniform Force Field

We introduce a non-uniform gravity-like force field to control the granular flow state in a quasi-onedimensional system, and study the system by the molecular dynamics simulation. We find that the granular flow under non-uniform force field can be well described by a density wave with fixed time period if a fixed particle number condition is used. The base frequency of the density wave does not depend on the position of the flow, while both the average density and oscillation amplitude of the flow vary continuously with the position. The formation of the density wave results from the aggregation of the granules in the decelerated region and the feed-back mechanism in the fixed particle number condition.     

二维颗粒堆积中压力问题的格点系统模型

为了便于从理论上探究粮仓效应产生的机理,处理筒仓中颗粒介质的应力分布等问题,将二维颗粒堆积简化为格点系统,并且以随机堆积为物理背景提出了一个由吸收系数p及侧向传递系数q决定的力传递模型.给出了矩阵形式的力传递方程,提出基于二阶差分方程的方法同时求解传递系数矩阵的特征值和特征向量,从理论上导出了一种典型情况下容器底部压力分布与顶部压力分布的关系式.对有效质量随总质量变化关系的理论分析表明,该模型可以给出与Janssen模型类似的结果.对无负载情况下的底部应力分布进行了理论计算,结果表明容器底部中央应力最大,离中央越远应力越小.运用数值计算讨论了p与q对容器底部压力随堆积高度变化曲线的影响.     

The Thermal Conductivity Theory of Non-uniform Granular Flow and the Mechanism Analysis

According to the fractal characteristics appearing in non-uniform granular system, we found the fractalmodel to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bringforward the fractal velocity probability distribution function. The equipartition of energy is employed to the non-uniform granular system, and the granular temperature is derived. We investigate the thermal conductivity in granularflow due to the movement of the particles, namely the heat transfer induced by the streaming mode only. The thermalconductivity in the mixed system changes with the fractal parameters such as the solid fraction v, structural characterparameter η, and fractal dimension D of size distribution. These parameters depict the characteristics of the thermalconductivity in the actual complex granular system. Comparing our conclusion with the correlative experimental dataand the theoretical conclusion of binary mixture of granular materials, the results can qualitatively confirm the generalityof our prediction on the granular system.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

The Thermal Conductivity Theory of Non-uniform Granular Flow and the Mechanism Analysis

According to the fractal characteristics appearing in non-uniform granular system, we found the fractal model to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bring forward the fractal velocity probability distribution function. The equipartition of energy is employed to the non-uniform granular system, and the granular temperature is derived. We investigate the thermal conductivity in granular flow due to the movement of the particles, namely the heat transfer induced by the streaming mode only. The thermal conductivity in the mixed system changes with the fractal parameters such as the solid fraction v, structural character parameter η, and fractal dimension D of size distribution. These parameters depict the characteristics of the thermal conductivity in the actual complex granular system. Comparing our conclusion with the correlative experimental data and the theoretical conclusion of binary mixture of granular materials, the results can qualitatively confirm the generality of our prediction on the granular system.