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.     

Surface flows of granular mixtures: II. Segregation with grains of different size

We present the generalization of a theoretical model for segregation of granular mixtures due to surface flows, published in J. Phys. I France 6, 1295 (1996). Our generalized model is valid for grains differing by their size and/or their surface properties; in the present paper, we describe the case of two species with the same surface properties but two different sizes. The rolling stream is assumed to be homogeneous. Exchanges between the grains at rest and the rolling stream are modelized via binary collisions. The model predicts that during the filling of a two-dimensional silo, continuous segregation appears inside the static phase: small (respectively large) grains tend to stop uphill (respectively downhill), although both species remain present everywhere. This fits the observations when the size difference between the species is small. When the size difference is large, a different regime is observed. We argue that in this case, segregation occurs directly inside the rolling stream. Received: 25 February 1998 / Received in final form and Accepted: 6 July 1998     

A molecular dynamics simulation of segregation behaviours of horizontally vibrated binary granular mixture

This paper performs the two-dimensional, soft-sphere molecular dynamics simulations to study the granular segregation in a binary granular mixture with the same size but different density in the container with the sawtooth base under horizontal vibration. The segregation phase diagram is presented in the acceleration-frequency space. When the acceleration is high enough to result in relative motions of the particles, the system can be in various states (mixed state, vertical and horizontal segregation state), which depend on both acceleration and frequency. Due to the sawtooth base there is stratified flow effect besides density effect. The density effect raises the light particles. The stratified flow drives the particles in the upper levels to the right and the particles in the lower particles to the left, those fact results in the appearance of the left segregation state. The left segregation state can be changed to the right segregation by changing the shape of the sawtooth. As the vibration frequency increases, the stratified flow effect becomes weaker and weaker, so at high vibration frequencies the vertical segregation state appears instead of the left segregation state.     

Kinematic segregation of granular mixtures in sandpiles

We study the segregation of granular mixtures in two-dimensional silos using a recently proposed set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this dynamical segregation process, called kinematic sieving, free-surface segregation or percolation, into the theoretical formalism and calculate the profiles of the rolling species and the concentration of grains in the bulk in the steady state. Our solution shows the segregation of the mixture with the large grains being found at the bottom of the pile in qualitative agreement with experiments. Received: 6 July 1998 / Revised and Accepted: 13 August 1998     

Gas-driven subharmonic waves in a vibrated two-phase granular material

Vibrated powders exhibit striking phenomena: subharmonic waves, oscillons, convection, heaping, and even bubbling. We demonstrate novel rectangular profile subharmonic waves for vibrated granular material, that occur uniquely in the two-phase case of grains, and a fluid, such as air. These waves differ substantially from those for the gas-free case, exhibit different dispersion relations, and occur for specific shaking parameters and air pressure, understandable with gas-particle flow models. These waves occur when the gas diffusively penetrates the granular layer in a time comparable to the shaker period. As the pressure is lowered towards P =0, the granular-gas system exhibits a Knudsen regime. This instability provides an opportunity to quantitatively test models of two-phase flow.     

Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected. Received 4 June 1999 and Received in final form 28 September 1999     

Segregation effect in symmetric cellular automata model for two-lane mixed traffic

Segregation effects commonly exist in granular mixtures with difference in size, shape or density. In mixed traffic flow, slow vehicle and fast vehicle, as two types of particles, have different desired speed. We investigate the segregation along the road in mixed traffic flow by using a symmetric two-lane cellular automata model. A parameter D, which quantifies the degree of segregation, is defined. We study the density dependency of the parameter at different randomization probability. Simulation results show that segregation is more obviously in free flow region. We argue that the overtaking maneuvers have similar effect as percolation in granular flow.     

Surface flows of granular mixtures

We present the generalization of the minimal model for surface flows of granular mixtures, proposed by Boutreux and de Gennes [J. Phys. I France 6, 1295 (1996)]. The minimal model was valid for grains differing only in their surface properties. The present model also takes into account differences in the size of the grains. We apply the model to study segregation in two-dimensional silos of mixtures of grains differing in size and/or surface properties. When the difference in size is small, the model predicts that a continuous segregation appears in the static phase during the filling of a silo. When the difference in size is wide, we take into account the segregation of the grains in the rolling phase, and the model predicts complete segregation and stratification in agreement with experimental observations. Received 9 September 1998 and Received in final form 4 November 1998     

The song of dunes as a wave-particle mode locking

Singing dunes, which emit a loud sound as they avalanche, constitute a striking and poorly understood natural phenomenon. We show that, on the one hand, avalanches excite elastic waves at the surface of the dune, whose vibration produces the coherent acoustic emission in the air. The amplitude of the sound (approximately 105 dB) saturates exactly when the vibration makes the grains take off the flowing layer. On the other hand, we show that the sound frequency (approximately 100 Hz) is controlled by the shear rate inside the sand avalanche, which for granular matter is equivalent to the mean rate at which grains make collisions. This proves the existence of a feedback of elastic waves on particle motion, leading to a partial synchronization of the avalanching sand grains. It suggests that the song of dunes results from a wave-particle mode locking.     

Competition of Brazil nut effect,buoyancy, and inelasticity induced segregation in a granular mixture

It has been recently reported that a granular mixture in which grains differ in their restitution coefficients presents segregation: the more inelastic particles sink to the bottom. When other segregation mechanisms as buoyancy and the Brazil nut effect are present, the inelasticity induced segregation can compete with them. First, a detailed analysis, based on numerical simulations of two dimensional systems, of the competition between buoyancy and the inelasticity induced segregation is presented, finding that there is a transition line in the parameter space that determines which mechanism is dominant. In the case of neutrally buoyant particles having different sizes the inelasticity induced segregation can compete with the Brazil nut effect (BNE). Reverse Brazil nut effect (RBNE) could be obtained at large inelasticities of the intruder. At intermediate values, BNE and RBNE coexist and large inelastic particles are found both near the bottom and at the top of the system.     

Segregation in arch formation

We report new segregation phenomena in the clogging arches formed during the discharge of granular piles. Results from molecular dynamics simulations show segregation effects with respect to both size and density ratios used in piles built with bidisperse mixtures of grains. The clogging arch is preferentially constituted of large grains when size bidisperse piles were discharged, whereas for density bidisperse mixtures there is a predominance of light grains in the arch for large orifice widths but, for small widths, an inversion in the preference is observed, with a slightly higher incidence of heavy grains forming the arches. We present arguments based on the reverse buoyancy effect and the statistics collected for the avalanche size distributions to explain how these effects can be understood as a crossover between two different segregation mechanisms acting independently at small and large orifice width limits.     

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.     

不同振动模式下颗粒分离行为的数值模拟

利用三维离散元法对垂直方向上的直线、圆和椭圆振动模式颗粒分离过程进行了数值模拟研究,对直线振动时上层大颗粒的波动及圆和椭圆振动时出现的聚集、循环等现象的形成机理进行了分析,并讨论了振动强度对各振动模式下颗粒分离形态的影响规律. 研究表明,综合运用空隙填充、侧面驱动的颗粒运动和能量非均匀分布三种机理,并结合颗粒群的速度矢量分布情况能够较好地解释各振动模式下的颗粒分离行为. 振动强度对圆和椭圆振动模式的分离形态具有显著的影响,并在振动强度约为3时,各种振动模式均具有良好的颗粒分离效果和稳定的颗粒运动状态. 关键词： 振动模式 颗粒分离 离散元法 数值模拟     

不同振动模式下颗粒分离行为的数值模拟

利用三维离散元法对垂直方向上的直线、圆和椭圆振动模式颗粒分离过程进行了数值模拟研究,对直线振动时上层大颗粒的波动及圆和椭圆振动时出现的聚集、循环等现象的形成机理进行了分析,并讨论了振动强度对各振动模式下颗粒分离形态的影响规律. 研究表明,综合运用空隙填充、侧面驱动的颗粒运动和能量非均匀分布三种机理,并结合颗粒群的速度矢量分布情况能够较好地解释各振动模式下的颗粒分离行为. 振动强度对圆和椭圆振动模式的分离形态具有显著的影响,并在振动强度约为3时,各种振动模式均具有良好的颗粒分离效果和稳定的颗粒运动状态.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.     

振动颗粒物质中倍周期运动对尺寸分离的影响

实验研究了竖直振动颗粒床中,倍周期运动对尺寸分离的影响.实验中,当振动加速度足够大时,系统中出现稳定的对称对流,进一步增大振动加速度到某个临界值时,还会出现倍周期运动.观察表明,背景颗粒的对流运动对分离过程起主导作用,对流速度决定着分离过程的快慢,而在2倍周期和4倍周期分岔之后,分离时间有所减慢.对引起对流运动的起因进行了分析,以此为基础分析了倍周期运动产生影响的物理机理,并对分离时间进行了定量计算,结果与实验值符合很好. 关键词： 颗粒物质 “巴西果”效应 倍周期分岔 对流     

振动颗粒混合物中的三明治式分离

在竖直振动两种颗粒的混合物的实验中，观察到了一种新的分离现象——“三明治”式分离，即大而重的颗粒被夹在两层小的轻颗粒之间.这不同于“巴西果”效应导致的大而重的颗粒在上的两层有序结构.实验表明当振动加速度大于某个临界值时这种三层有序将取代两层结构，而且是稳定的.实验中观察到导致“三明治”式分离的两种不同的分离过程.对这两种过程的物理机理及其与振动加速度、振动频率及颗粒尺寸等因素的关系做了研究，并给出了相图. 关键词： 颗粒物质 振动 有序结构 三明治式分离 巴西果效应     

振动颗粒物质“巴西果”分离效应实验和理论研究

本文通过实验和理论研究了影响"巴西果"分离的因素及其物理机理. 分析了振动加速度、大小颗粒尺寸和密度对分离时间的影响, 并利用流体模型对分离时间作估算, 对实验结果进行定性解释. 结果表明在振动频率固定时, 调节振动加速度是控制"巴西果"分离的一个主要手段. 振动加速度存在一个临界值, 当高于此临界值时, "巴西果"分离的主要物理机理由对流机理转变为几何填空机理, 且振动加速度对分离影响变小, 大颗粒尺寸对分离的影响增大. 可通过调节大颗粒的尺寸来改变分离效果. 当大、 小颗粒密度比为1时, 仍会出现"巴西果"分离现象. 增大小颗粒尺寸或密度可以促进"巴西果"分离.     

垂直振动作用下二元混合颗粒分层的动态循环反转

在对垂直振动下的铜颗粒和氧化铝颗粒混合物的研究中,除了观测到巴西果分层和混合分层外,还发现了一种新的随时间周期变化的分离形态. 此分离形态可随着时间的演化,在巴西果、反巴西果和三明治这几种分层构型之间进行动态的循环反转. 给出了这种反转态出现的相区,并且观测了其动态转变的规律. 根据碰撞、磨擦及空气的耗散作用所产生的耗散结构对循环反转态的出现给出了定性的解释,并通过实验证实这种分层构型与空气的存在有密切的关系. 关键词： 颗粒物质 巴西果效应 相分离     

Experimental evidence for molecular chaos in granular gases

We present measurements showing the presence and the absence of molecular chaos in a two-layer vertically vibrated granular media where a plate drives a horizontal layer of massive grains, which, in turn, drives a second horizontal layer of lighter grains above the first. In the first layer driven by the plate, the velocities are spatially correlated. In the second layer, we find uncorrelated velocities consistent with the presence of molecular chaos. In this experiment, energy injection that is randomized in both space and time throughout the shaking cycle is necessary for observing molecular chaos and "kinetic theory"-like behavior. At higher densities, excluded volume effects force velocity correlations in the system which is no longer "gaslike" in behavior.