Chaotic granular mixing

Several models for convective mixing of coarse, freely flowing in granular tumblers have been proposed over the past decade. Powders of practical interest, by contrast, are frequently fine and cohesive, and cannot be analyzed with these models. Moreover, even in the freely flowing regime, mixing transverse to the dominant, convective, direction is typically slow and inefficient. In this paper, we examine two chaotic mixing mechanisms, the first of which can be intentionally applied to increase transverse mixing rates severalfold, with new prospects for further improvements in three-dimensional mixing through judicious process design. The second mechanism occurs spontaneously in fine grains, resulting in mixing rates overwhelmingly exceeding what would be possible in freely flowing grains. Finally, we show that the same chaotic mixing mechanisms seen in simple drum mixers are also found to be at work in more complex blender configurations widely used in batch industrial operations. (c) 1999 American Institute of Physics.     

A dynamical systems approach to mixing and segregation of granular materials in tumblers

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.     

滚筒内非等粒径二元颗粒体系增混机理研究

提出了在圆形滚筒内设置十字形内构件的增混方式,并采用离散单元方法对设置不同大小内构件的滚筒内非等粒径二元颗粒体系的混合进行了数值模拟试验.通过模拟结果重点分析了内构件对混合的影响,讨论了内构件的尺寸对混合效果的作用,分析和探讨了滚筒内构件对二元颗粒体系的增混机理.研究发现,当滚筒内无内构件时,对流、扩散和离析三种作用机制对颗粒体系的混合和分离都起到了重要作用;当滚筒内含内构件时,颗粒的混合则只受到颗粒对流和扩散机制的作用,而颗粒的离析效应得到了很大程度的抑制.十字形内构件很大程度上会破坏滚筒内的自由表面流,从而使发生在自由表面流中的颗粒分离不能发生,最终可有效地增加颗粒之间的混合.对于采用在滚筒内设置十字形内构件的方式来增加颗粒间的混合,存在一个最优的内构件尺寸,内构件过小或过大都不利于颗粒间的混合. 关键词： 分离 混合 离散单元法     

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.     

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.     

Discrete particle simulation of radial segregation in horizontally rotating drum: Effects of drum-length and non-rotating end-plates

The radial segregation phenomena of a mixture of two different size grains in a horizontal rotating drum are studied by DEM simulations. The grano-dynamics of radial segregation phenomena is examined as a function of the axial length and the friction between grains and not-rotating end-plates of the drum. The results indicate that, in the longer drums, the radial segregation ratio is higher and the friction on the end-plates shows little effect. Whereas in the shorter drums, the radial segregation is very slow or negligible; however, decreasing the friction on non-rotating end-plates increases the segregation ratio. If we increase the friction further (greater than the frictions between the grain-grain and the grains and the inner wall), the segregation ratio drops in the longer drums while in the shorter drums mixing is seen instead. The cause of these phenomena lies in the mechanism of diffusion in granular flows due to shearing strain by the end-plates. For more roughened end-plates, this shearing activity increases the granular temperature of the system and only the mixing can be observed instead of the segregation.     

Air-Driven Segregation in Binary Granular Mixtures with Same Size but Different Densities

We investigate the segregation effect of binary granular mixtures with the same size but different densities under vibration at different air pressures. Our experiments show that the segregation state is seriously dependent on the air pressure and there is a new type of partially segregated state at high air pressure, which has the characteristic that the lighter grains tend to stay at the bottom and form a pure layer, while heavier grains and remained lighter ones tend to rise and to form a mixed layer on the top of the system. We redefine the order parameter to study the variation of the segregation effect with the air pressure and vibration parameter in detail. Finally, the mechanism of the air-driven segregation is illustrated by the faster acceleration due to the airflow through the granular bed for lighter particles.     

Multiscale clustering in granular surface flows

We investigate steady granular surface flows in a rotating drum and demonstrate the existence of rigid clusters of grains embedded in the flowing layer. These clusters appear to be fractal and their size is power law distributed from the grain size scale up to the thickness of the flowing layer. The implications of the absence of a characteristic length scale on available theoretical models of dense granular flows are discussed. Finally, we suggest a possible explanation of the difference between velocity profiles observed in surface flows and in flows down a rough inclined plane.     

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.     

离散颗粒层被横向推移过程中的力学行为研究

研究发现,颗粒物质层被匀速推移挤压过程中,所需推移力先以线性规律增加,在某一确定点后,则会以指数规律增加.而颗粒物质是由众多离散颗粒组成的软凝聚态物质,其宏观上反映的是离散颗粒的个体性质和凝聚态物质的集体效应.颗粒与颗粒之间以及颗粒与边界之间的细观尺度接触力链的构成以及演变规律将会直接影响各种宏观受力情况,其摩擦力与挤压力便是力链的主要构成形式.围绕着定量描述细观力链特征,从而揭示力的变化规律这一目标,采用计算机模拟的方法,依照球形颗粒Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论,对重力作用下不同数目的三维等径球体颗粒层的推移情况进行了离散元仿真模拟,量化分析了推移力变化规律、各摩擦力变化规律以及力链分布规律,发现摩擦力与挤压力在颗粒堆积的不同阶段对力链的构成起到了不同的主次作用,使得力链发生强弱演变,从而发现了推移颗粒物质层时推移力的变化规律及原因.这些结果有利于从力链角度揭示颗粒内部和颗粒与各边界之间的受力情况.     

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.     

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.     

椭球颗粒搅拌运动及混合特性的数值模拟研究

为探讨在强制搅拌下同属性颗粒由分层到分布均匀状态的运动特征及规律, 本研究利用三维离散单元法模拟不同转速下U形罐体内等粒径椭球颗粒的混合过程. 从单颗粒随机运动轨迹、宏观颗粒流运动矢量图的角度分析颗粒混合过程的宏观混合规律及局部混合特征, 定量描述混合度与搅拌叶片旋转圈数的数学关系. 结果表明, 强制搅拌下同属性分层颗粒的混合是在对流混合及四个局部混合共同作用下实现的; 分层颗粒的混合度与搅拌轴的转速无关, 而与搅拌轴旋转圈数直接相关; 混合度与圈数的关系符合指数增长模型. 研究结果可为散体物料增混行业的设备改进及操作控制提供依据和参考.     

The search for a quantum KAM theorem

The complex mechanisms by which nonlinear classical conservative systems undergo a transition from quasiperiodic to chaotic behavior are now fairly well understood. This transition is associated with a breakdown of quasi-constants of motion (KAM surfaces). There is growing evidence that similar mechanisms may govern the behavior of quantum systems. While K-type mixing behavior has not yet been found, there does appear to be a transition associated with the destruction of a quantum quasi-constant of motion (quantum KAM states) which changes qualitatively the spectrum of quantum systems.     

Chaotic mixing of granular materials in two-dimensional tumbling mixers

We consider the mixing of similar, cohesionless granular materials in quasi-two-dimensional rotating containers by means of theory and experiment. A mathematical model is presented for the flow in containers of arbitrary shape but which are symmetric with respect to rotation by 180 degrees and half-filled with solids. The flow comprises a thin cascading layer at the flat free surface, and a fixed bed which rotates as a solid body. The layer thickness and length change slowly with mixer rotation, but the layer geometry remains similar at all orientations. Flow visualization experiments using glass beads in an elliptical mixer show good agreement with model predictions. Studies of mixing are presented for circular, elliptical, and square containers. The flow in circular containers is steady, and computations involving advection alone (no particle diffusion generated by interparticle collisions) show poor mixing. In contrast, the flow in elliptical and square mixers is time periodic and results in chaotic advection and rapid mixing. Computational evidence for chaos in noncircular mixers is presented in terms of Poincare sections and blob deformation. Poincare sections show regions of regular and chaotic motion, and blobs deform into homoclinic tendrils with an exponential growth of the perimeter length with time. In contrast, in circular mixers, the motion is regular everywhere and the perimeter length increases linearly with time. Including particle diffusion obliterates the typical chaotic structures formed on mixing; predictions of the mixing model including diffusion are in good qualitative and quantitative (in terms of the intensity of segregation variation with time) agreement with experimental results for mixing of an initially circular blob in elliptical and square mixers. Scaling analysis and computations show that mixing in noncircular mixers is faster than that in circular mixers, and the difference in mixing times increases with mixer size. (c) 1999 American Institute of Physics.     

阻尼对水平滚筒内二元颗粒体系径向分离模式形成的影响

采用离散单元数学模型对一充装量为50%的水平薄滚筒内S形二元颗粒体系的分离模式进行了数值模拟试验,研究了不同碰撞阻尼参数下的分离过程,分析了阻尼对分离过程及分离模式的影响.模拟结果表明阻尼对滚筒内颗粒的分离过程及分离模式影响很大,在S形二元颗粒体系水平薄滚筒内,阻尼可控制渗透和离析的协同作用以及自由表面层的流动形式,最终影响分离模式的形成;当阻尼太大时分离模式只能形成月亮模式,阻尼太小时可形成不明显的花瓣模式,只有当阻尼在适当的范围内,自由表面流动层形成雪崩流型式时,分离模式才会呈现规则的花瓣模式,试验结 关键词： 滚筒 模式形成 径向分离 离散单元法     

Kink-induced transport and segregation in oscillated granular layers

We use experiments and molecular dynamics simulations of vertically oscillated granular layers to study horizontal particle segregation induced by a kink (a boundary between domains oscillating out of phase). Counterrotating convection rolls carry the larger particles in a bidisperse layer along the granular surface to a kink, where they become trapped. The convection originates from avalanches that occur inside the layer, along the interface between solidified and fluidized grains. The position of a kink can be controlled by modulation of the container frequency, making possible systematic harvesting of the larger particles.     

Time-of-flight variant to image mixing of granular media in a 3D fluidized bed

This paper describes a variant of time-of-flight magnetic resonance (MR) imaging that provides a method of measuring the inherent mixing in a fluidized bed without the introduction of tracer particles. The modifications to conventional time-of-flight imaging enable the measurement of the axial mixing of a precisely controlled initial particle distribution, thereby providing measurements suitable for a direct comparison with models of solids mixing in granular systems. The imaging sequence is applied to characterize mixing, over time scales of 25-1000 ms, in a gas-fluidized bed of Myosotis seed particles; mixing over short timescales, inaccessible using conventional tracer techniques, is studied using this technique. The mixing pattern determined by this pulse sequence is used in conjunction with MR velocity images of the motion of the particles to provide new insight into the mechanism of solids mixing in granular systems.     

Flowing Sand—A Possible Physical Realization of Directed Percolation

A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches, leading to a crossover from compact to ordinary directed percolation. Thus, systems of flowing granular matter on an inclined plane could serve as a first physical realization of directed percolation.     

Segregation behavior of magnetic ions in continuous flowing solution under gradient magnetic field

The research of magnetic separation starts from magnetic solid particles to nanoparticles, and in the research progress,particles become smaller gradually with the development of application of magnetic separation technology. Nevertheless,little experimental study of magnetic separation of molecules and ions under continuous flowing conditions has been reported. In this work, we designed a magnetic device and a "layered" flow channel to study the magnetic separation at the ionic level in continuous flowing solution. A segregation model was built to discuss the segregation behavior as well as the factors that may affect the separation. The magnetic force was proved to be the driving force which plays an indispensable role leading to the segregation and separation. The flow velocity has an effect on the segregation behavior of magnetic ions,which determines the separation result. On the other hand, the optimum flow velocity which makes maximum separation is related to the initial concentration of solution.