Entropy, entropy flux and entropy rate of granular materials

The aim of this work is to analyze the entropy, entropy flux and entropy rate of granular materials within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas that follows from the Boltzmann equation differs from the one of a simple fluid due to the presence of a term which can be identified as the entropy density rate. From the knowledge of a non-equilibrium distribution function-valid for processes closed to equilibrium-it is obtained that the entropy density rate is proportional to the internal energy density rate divided by the temperature, while the entropy flux is equal to the heat flux vector divided by the temperature. A thermodynamic theory of a granular material is also developed whose objective is the determination of the basic fields of mass density, momentum density and internal energy density. The constitutive laws are restricted by the principle of material frame indifference and by the entropy principle. Through the exploitation of the entropy principle with Lagrange multipliers, it is shown that the results obtained from the kinetic theory for granular gases concerning the entropy density rate and entropy flux are valid in general for processes close to equilibrium of granular materials, where linearized constitutive equations hold.     

Dynamic self-assembly and patterns in electrostatically driven granular media

We show that granular media, consisting of metallic microparticles immersed in a poorly conducting liquid in a strong dc electric field, self-assemble into a rich variety of novel phases. These phases include static precipitates: honeycombs and Wigner crystals; and novel dynamic condensates: toroidal vortices and pulsating rings. The observed structures are explained by the interplay between charged granular gas and electrohydrodynamic convective flows in the liquid.     

Avalanche dynamics in wet granular materials

We have studied the dynamics of avalanching wet granular media in a rotating drum apparatus. Quantitative measurements of the flow velocity and the granular flux during avalanches allow us to characterize novel avalanche types unique to wet media. We also explore the details of viscoplastic flow (observed at the highest liquid contents) in which there are lasting contacts during flow, leading to coherence across the entire sample. This coherence leads to a velocity-independent flow depth at high rotation rates and novel robust pattern formation in the granular surface.     

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.     

Granular Rayleigh-Taylor instability: experiments and simulations

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.     

Factors influencing the density profiles of granular flux in a two-dimensional inclined channel

The two-dimensional dilute granular flow on a smooth incline bounded by rough sidewalls is investigated experimentally, and the transverse density profiles of granular flux (ζ = ρ v) across the channel are measured. The results show that the transverse density profiles of granular flux are symmetric about the channel center and that the density of granular flux near the boundary is clearly lower than that of the center. There is a critical width of channel W _c for the transition of the density of granular flux. The density of granular flux near the boundary decays with the increasing of inclination (sinθ) of the channel. Supported by the National Natural Science Foundation of China (Grant No. 10274071) and the Department of Education of Zhejiang Province (Grant Nos. 20050916 and y200804093)     

Coarsening in granular systems

We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular media. Thereafter, dilute systems, the so-called “granular gases”, are discussed: idealized kinetic models, such as the gas of inelastic hard spheres in the cooling regime, are the optimal playground to study the slow growth of correlated structures, e.g., shear patterns, vortices, and clusters. In fluidized experiments, liquid–gas or solid–gas separations have been observed. In the case of monolayers of particles, phase coexistence and coarsening appear in several different setups, with mechanical or electrostatic energy input. Phenomenological models describe, even quantitatively, several experimental measures, both for the coarsening dynamics and for the dynamic transition between different granular phases. The origin of the underlying bistability is in general related to negative compressibility from granular hydrodynamics computations, even if the understanding of the mechanism is far from complete. A relevant problem, with important industrial applications, is related to the demixing or segregation of mixtures, for instance in rotating tumblers or on horizontally vibrated plates. Finally, the problem of compaction of highly dense granular materials, which is relevant in many practical situations, is usually described in terms of coarsening dynamics: there, bubbles of misaligned grains evaporate, allowing the coalescence of optimally arranged islands and a progressive reduction of the total occupied volume.     

分仓颗粒布居分聚现象的通量模型

置于以窗口连接的分隔仓中振动驱动的颗粒气体会出现颗粒在两仓中布居分聚现象,被形象地称为麦克斯韦妖现象.通量模型的建立是理解麦克斯韦妖现象的关键问题.Eggers以颗粒气体动力学为基础得出了简化的理论模型.该模型可以很好地得到分仓中颗粒的布居分聚现象,然而似乎无法用于预测两种颗粒在分仓体系中的布居振荡现象.通过实验研究,测量了颗粒气体的流通量曲线,改进了Eggers模型.改进的模型可以很好地得到两种颗粒在分仓体系中的布居振荡现象. 关键词： 颗粒气体 耗散 通量模型     

Phase Transition and Critical Phenomenon Occurring in Granular Matter

We investigate the granular flow states in a channel with bottleneck by molecular dynamics simulations.Our study is restricted only on a selected key area rather than on the whole system to focus on the flow properties of a single granular state.A random force field is introduced to control the granular temperature.It is also pointed out that the flow rate in the granular flow can be correlated with the pressure,which leads us to carry out a comprehensive study similar to the classical study for general liquid-gas phase transition.Our results show that the dilute flow state and the dense flow state of the granules are similar to the gas state and the liquid state of general substances,respectively,and the properties of phase transition and critical phenomenon are also similar to those occurring in general substances.     

二维斜面粗糙边界附近颗粒流量密度分布

以往的实验研究中，已经知道粗糙边界条件下，二维颗粒流的颗粒流量是以通道中心横向对称分布的，颗粒流横向分布既受通道宽度的影响，同时也受通道斜面倾斜角的影响，而且颗粒在通道两侧的分布明显少于通道中间. 主要研究粗糙边界附近颗粒分布随通道宽度以及通道斜面倾斜角的变化规律. 在稀疏流状态以及保持边界墙体的粗糙度不变的条件下，对应不同通道宽度，粗糙边界附近10d范围内的颗粒流量密度(ξ=ρv)随斜面倾斜角的增大而减小，颗粒流量密度随通道宽度的变化存在一临界宽度Wc；在通道宽度小于Wc时，粗糙墙体附近10d范围内颗粒流量密度ξ随sinθ呈指数衰减，通道宽度大于Wc时，颗粒流量密度ξ_sinθ曲线随θ增大几乎呈线性减小. 关键词： 二维颗粒流 颗粒物质 颗粒流量密度     

Evolution of Energy in Submerged Granular Column Collapse

The evolution of energy in subaerial and subaqueous granular column collapses is studied.Employing the refractive index matching method and planar laser-induced fluorescence technique,we obtain granular and liquid images simultaneously in a single experiment of subaqueous flow.Particle image velocimetry and particle tracking velocimetry are used to process the data for the fluid and granular phase.We find stepwise decreases in the total kinetic energy of the granular material.The stage of rapidl...     

剪切振动下湿颗粒的力学谱

在恒温25 ℃剪切振动条件下,测量不同水分含量的NaCl湿颗粒体系的力学谱（能量耗散tanφ和剪切模量G）.研究发现,随着剪切振幅增大,NaCl湿颗粒体系的剪切模量G和能量耗散tanφ都表现出类似于干颗粒体系的阻塞（Jamming）转变行为.随着体系中水含量的增大,湿颗粒体系的剪切模量G和能量耗散tanφ在质量分数约等于11%的临界水浓度下均出现一个峰值,且峰位与应变振幅无关,表明此时颗粒之间主要的作用力发生了变化.     

Directed segregation in compartmentalized bi-disperse granular gas

A bi-disperse granular gas in an asymmetrical two-compartment system is studied experimentally. The presence of asymmetry within the range of our experimental parameters results in a directed segregated state and a directed clustering state. This deterministic system does not depend on the initial conditions. A modified flux model based on Lohse's flux model for bi-disperse granular gases is derived. The modified flux model explains qualitatively the experimental results.     

通道宽度对二维粗糙边界斜面颗粒流的影响

在此之前已经报道了二维斜面颗粒流在通道中的分布规律以及二维斜面粗糙边界附近的颗粒 流量密度（ξ=ρ·ν）分布.本文则主要研究通道宽度W对边界附近颗粒流量密度(ξ=ρ· ν)分布的影响.结果表明，颗粒流量密度随通道宽度的变化（ξ W）存在一临界通道宽度W c.在本实验条件下临界通道宽度Wc=70d.当通道宽度小于临界宽度Wc时 ，通道中距边界20d—30d区间内的相对颗粒流量密度随斜面倾斜角的变化可描述为ξ∝( sinθ)α，α是与通道宽度W有关的参数，其数值在032至085之间. 关键词： 二维颗粒流 颗粒物质 颗粒流量密度     

Collective behavior in a granular jet: emergence of a liquid with zero surface tension

We perform the analog to "water bell" experiments with granular jets. Rebounding from cylindrical targets, wide granular jets produce sheets or cones with shapes that mimic a zero-surface-tension liquid. The jets' particulate nature appears when the number of particles in the cross section is decreased: the emerging structures broaden, gradually disintegrating into diffuse sprays. The experiment has a counterpart in the behavior of quark-gluon plasmas generated by colliding heavy ions. There, a high collision density gives rise to collective behavior also described as a liquid.     

双轴压缩下颗粒物质剪切带的形成与发展

本文采用离散元方法,研究了双轴压缩的颗粒体系在刚性边界约束下,局部剪切带的形成和发展过程,注重分析了细观的体积分数、配位数、颗粒旋转角度等参数以及力链结构形态的演变.并从颗粒体系jamming 相图中J点附近的边壁压强和配位数随体积分数的标度规律出发,分析了剪切带内外的体积分数和配位数的变化.结果表明:剪切带形成于颗粒体系的塑性变形开始阶段,此时体系发生剪胀,颗粒体积分数减小,颗粒体系抵抗旋转的能力降低,开始出现细小剪切带,随着轴向应变的继续,细小剪切带发生连接,最终导致贯穿性优势剪切带形成 关键词： 颗粒物质 力链 双轴压缩 剪切带     

Velocity correlations in dense granular flows observed with internal imaging

We show that the velocity correlations in uniform dense granular flows inside a silo are similar to the hydrodynamic response of an elastic hard-sphere liquid. The measurements are made using a fluorescent refractive-index-matched interstitial fluid in a regime where the flow is dominated by grains in enduring contact and fluctuations scale with the distance traveled, independent of flow rate. The velocity autocorrelation function of the grains in the bulk shows a negative correlation at short time and slow oscillatory decay to zero similar to simple liquids. Weak spatial velocity correlations are observed over several grain diameters. The mean square displacements show an inflection point indicative of caging dynamics. The observed correlations are qualitatively different at the boundaries.     

Periodic and disordered structures in a modulated gas-driven granular layer

Experiments with a thin gas-fluidized granular layer revealed a sequence of well-defined transitions as the amplitude and frequency of the gas flow modulation are varied. The observed patterns include subharmonic squares and stripes, quasiperiodic and disordered structures. The wavelength of subharmonic patterns increases with the mean flow rate and decreases with the modulation frequency.     

Collisional source of the second moment and pressure tensor for inhomogeneous rapid granular flows of highly inelastic spheres

By extending the constitutive theories for homogeneous granular flows of highly inelastic spheres by Richman (J. Rheol 33 (1989) 1293), Chou (J. CSME 16-6 (1995) 577), and Chou and Richman (Physica A 259 (1998) 430), the collisional source of the second moment of fluctuation velocity and pressure tensor were developed in this study for inhomogeneous rapid granular flows of identical smooth highly inelastic spheres. The important mean fields in this flow are the solid fraction, mean velocity, and full second moment of fluctuation velocity. The collisional source of second moment and the collisional flux of momentum are based upon an anisotropic Maxwellian velocity distribution function. The constitutive theory was combined with the experimental results measured by Hsiau and Jang (Exp. Thermal Fluid Sci. 17 (1998) 202) so as to determine the profiles of pressure tensor and collision source of second moment in the inhomogeneous rapid granular shear flows of inelastic spheres. The normal pressure discrepancies were also observed.     

Ripple formation in weakly turbulent flow

The formation of granular ripples under liquid shear flow in an annular channel is studied experimentally. The erodible granular bed is subject to weakly turbulent flows without a defined sharp boundary layer close to the granular bed. The flow field and the degree of turbulence is characterized quantitatively by using a particle image velocimeter and a laser-Doppler velocimeter, respectively. A new range of particle Reynolds numbers at the lower limit of the Shields diagram were explored. Quantitative measurements of the granular flow on the surface reveal that the threshold for particle motion coincides within the order of one percent with the threshold for ripple formation. In fully developed ripples it was found that on the leeward side of the ripples regions of low-velocity gradients exist where granular motion is scarce, indicating that the coupling between the ripples is mainly caused by the flow field of the liquid.