The response of 2D foams to continuous applied shear in a Couette rheometer

The continuum model that has reproduced the experimental observation of exponential shear localisation for straight-edge boundary conditions is adapted to the case of circular geometry. Essentially the same effect is found. However, the scenario of possible velocity profiles is much richer. Our calculations elucidate many recent experiments qualitatively and suggest further extensions of them. Various limits are analysed. In particular, the localisation length vanishes as the inner-boundary velocity tends to zero.     

Numerical simulation of the sedimentation of a sphere in a sheared granular fluid: a granular Stokes experiment

We study, computationally, the sedimentation of a sphere of higher mass in a steady, gravity-driven granular flow of otherwise identical spheres, on a rough inclined plane. Taking a hydrodynamic approach at the scale of the particle, we find the drag force to be given by a modified Stokes law and the buoyancy force by the Archimedes principle, with excluded volume effects taken into account. We also find significant differences between the hydrodynamic case and the granular case, which are highlighted.     

Solid-fluid transition in a granular shear flow

The rheology of a granular shear flow is studied in a quasi-2D rotating cylinder. Measurements are carried out near the midpoint along the length of the surface flowing layer where the flow is steady and nonaccelerating. Streakline photography and image analysis are used to obtain particle velocities and positions. Different particle sizes and rotational speeds are considered. We find a sharp transition in the apparent viscosity (eta) variation with rms velocity (u). Below the transition depth we find that the rms velocity decreases with depth and eta proportional to u(-1.5) for all the different cases studied. The material approaches an amorphous solidlike state deep in the layer. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The results indicate a sharp transition from a fluid to a fluid + solid state with decreasing rms velocity.     

Compaction of a granular material under cyclic shear

In this paper we present experimental results concerning the compaction of a granular assembly of spheres under periodic shear deformation. The dynamics of the system is slow and continuous when the amplitude of the shear is constant, but exhibits rapid evolution of the volume fraction when a sudden change in shear amplitude is imposed. This rapid response is shown to be uncorrelated with the slow compaction process. Received 31 March 2000     

Interrupted shear of granular media

The response of a granular material during a stop-and-go shear experiment is investigated using an annular shear cell and silicagel powders of different particle sizes. The experimental results are examined on the basis of the Dieterich-Rice-Ruina model for solid friction. In addition to making this analogy with solid friction, we describe a new instability that is observed when restarting shear, where the powder bed is found to slip and compact for short hold times but only dilates for long hold times. The minimum hold time to restore a non-slip behaviour has been investigated for different size particles and normal loadings. The observed dependencies show analogies between this behaviour and the sliding rearrangements seen above the stick-slip threshold.     

Numerical simulation of 2D granular particles and its analyses by means of the micropolar fluid model

Numerical simulations of two-dimensional granular flows under uniform mean shear and external body torque were performed following the setting of the authors’ previous study [10]. Convergence of the stresses with the increase of coarse-graining length is investigated. Difference R between vorticity field and spin field is controlled by the external torque and the stresses for the region R > 0 is obtained as well as those for R < 0. The symmetry of the stresses under the change of the sign of R is discussed.     

Transient and oscillatory granular shear flow

The forces and particle motion during transient and oscillatory shear of granular material are investigated experimentally. In a shear cell of Taylor-Couette-type we find that how a granular shear flow starts depends strongly on the prior shear direction. If the shear direction is reversed, the material goes through a transient period during which the material compacts, the shear force is small, and the shear band is wide. Three-dimensional confocal imaging of particle rearrangements during shear reversal shows that bulk and surface flows are comparable. Repeated reversals, or oscillations of the shear direction, lead to additional compaction, which can be described by a stretched exponential, similar to compaction induced by tapping.     

Breakdown of energy equipartition in a 2D binary vibrated granular gas

We report experiments on the equipartition of kinetic energy in a mixture of pairs of different types of grains vibrated in two dimensions. In general, the two types of grains do not attain the same granular temperature, T(g) = 1/2m. However, the temperature ratio is constant in the bulk of the system and independent of the vibration velocity. The ratio depends strongly on the ratio of mass densities of the grains, but not on their inelasticity. Also, the temperature ratio is insensitive to compositional variables such as the number fraction of each component and the total number density. We conclude that a single granular temperature, as traditionally defined, does not characterize a multicomponent mixture.     

类固态颗粒物质的剪切弹性行为测量

利用能以极慢变形率直接剪切颗粒固体的实验装置,测量了(玻璃珠)样品对大幅度循环剪切的力-位移曲线,以及一个循环周期后的塑性位移残留.发现随着循环频率的降低,样品会从有限塑性残留的弹塑行为转变到几乎没有塑性的纯弹性行为,同时伴随有率相关性.该转变在剪切力幅度高达样品破坏值的90%时依然存在,但需要极小的变形率(10~(-5)Hz)或惯性数(10~(-8)).这意味着无论是高频小幅度的声波扰动,还是极低频大幅度的直接剪切,静态颗粒固体都可做出纯弹性的力学响应.在足够慢的状态变化范围里,它仍是属于经典弹性理论范畴的一类材料.这个弹性区域一直未被报道和关注,可能是观测它时需要样品的变形率远比通常此类研究中所采用的慢变形还要小许多(大约两个数量级)的缘故.理论上本文测量结果支持描述颗粒固体宏观动力学的基本方程组,不能只有弹塑和率无关行为,它们必须在极慢变形极限下退化为经典弹性理论,并且在这个转变过程中表现出率相关特性.     

A new solver for granular avalanche simulation: Indoor experiment verification and field scale case study

A new solver based on the high-resolution scheme with novel treatments of source terms and interface capture for the Savage-Hutter model is developed to simulate granular avalanche flows. The capability to simulate flow spread and deposit processes is verified through indoor experiments of a two-dimensional granular avalanche. Parameter studies show that reduction in bed friction enhances runout efficiency, and that lower earth pressure restraints enlarge the deposit spread. The April 9, 2000, Yigong avalanche in Tibet, China, is simulated as a case study by this new solver. The predicted results, including evolution process, deposit spread, and hazard impacts, generally agree with site observations. It is concluded that the new solver for the Savage-Hutter equation provides a comprehensive software platform for granular avalanche simulation at both experimental and field scales. In particular, the solver can be a valuable tool for providing necessary information for hazard forecasts, disaster mitigation, and countermeasure decisions in mountainous areas.     

Refraction of shear zones in granular materials

We study strain localization in slow shear flow focusing on layered granular materials. A heretofore unknown effect is presented here. We show that shear zones are refracted at material interfaces in analogy with refraction of light beams in optics. This phenomenon can be obtained as a consequence of a recent variational model of shear zones. The predictions of the model are tested and confirmed by 3D discrete element simulations. We found that shear zones follow Snell's law of light refraction.     

二维颗粒体系单轴压缩形成的力链结构

从接触力、能量分布和接触网络结构特点出发,提出了强力链的力大小(Fc)判据(Fc大于平均接触力〈F〉)和角度θc判据(θc=180/〈Z〉,其中〈Z〉是平均配位数),指出强力链和弱力链是本质不同的两类结构存在于颗粒体系中,其中强力链网络与体系的宏观性质直接相关.以二维颗粒体系的单轴压缩为例,计算发现了强力链长度的幂率分布规律,分析了侧向压力系数与相应强力链网络结构的关系:当内部强力链网络充分发育而不再变化时,侧向压力系数趋于稳定数值.     

Velocity fluctuations in a homogeneous 2D granular gas in steady state

We have measured the spectrum of velocity fluctuations in a granular system confined to a vertical plane and driven into a homogeneous, steady state by strong vertical vibration. The distribution of horizontal velocities is not Maxwell-Boltzmann and is given by P(v) = Cexp[-beta(|v|/sigma)(alpha)] where alpha = 1.55+/-0.1 at all frequencies and amplitudes investigated, and also for varying boundary conditions. The deviation from Maxwell-Boltzmann statistics occurs in the absence of spatial clustering and does not result from an inhomogeneous average over regions of varying local density. Surprisingly, P(v) has the same shape over a wide range of densities.     

颗粒流电磁垂直输运装置物理设计

为满足中国加速器驱动的次临界系统(C-ADS) 对于可靠性的要求, 计划采用基于螺线管的电磁垂直输运方案, 将经过质子束辐照后下落的散裂靶颗粒球再次输运至初始高度。基于解析方法对颗粒流垂直输运装置进行了分析和设计, 通过基于螺线管散热、径轴向颗粒流聚散焦效应和互感损耗等方面的考虑, 得到了适合于垂直输运颗粒流的螺线管驱动方式和螺线管构型及排布。利用基于本文解析方法的模拟程序, 对不同输运管道内径、不同螺线管驱动电流和不同螺线管构型和排布下的颗粒流垂直输运装置进行了模拟, 并从中筛选出了该装置的优化设计。模拟表明, 采用该优化设计的输运装置可将质量流量为19.6kg/s的颗粒流垂直输运至40m高度, 并满足颗粒球出口速度足够大的要求。     

Global nature of dilute-to-dense transition of granular flows in a 2D channel

The dilute-to-dense transition of granular flow of particle size d(0) is studied experimentally in a two-dimensional channel (width D) with confined exit (width d). Our results show that with fixed d and D there is a maximum inflow rate Q(c) above which the flow changes from dilute to dense and the outflow rate drops abruptly from Q(c) to a dense rate Q(d). A rescaled critical rate q(c) is found to be a function of a scaling variable lambda only: q(c) approximately F(lambda), where lambda identical with d/d(0) d/D-d. This form of lambda suggests that the dilute-to-dense transition is a global property of the flow, unlike the jamming transition which depends only on d/d(0). Furthermore, the transition is found to occur when the area fraction of particles near the exit exceeds a critical value which is close to 0.65+/-0.03.     

Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas

We report and discuss the results of a direct Monte Carlo simulation of the flow of a rarefied gas flowing between two parallel plates when one of them moves in its own plane. The boundary conditions are assumed to be of the bounceback type and the molecules to be Maxwell's. Under this condition the moments can be computed exactly, following a method used by Ikenberry and Truesdell in the unbounded case. This allows a comparison of the Monte Carlo methods with the exact solution and an evaluation of its accuracy.     

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     

Numerical simulations in granular matter: The discharge of a 2D silo

In this paper I give a short and elementary review of numerical simulations in granular assemblies, giving the process of discharge of a 2D silo as an example. The strengths and limitations of different approaches are discussed, together with some comments on the specific issues related to the numerics of discontinuous dissipative collisions.