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.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

Fluctuating velocity and momentum transfer in dense granular flows

We show experimentally that in a free-surface granular flow the fluctuating velocity brings about momentum transfer at a considerable rate only very close to the free surface. Away from the free surface, where the flow is dense and stratified (or laminar), the fluctuating velocity plays no prominent dynamic role and stems passively from a kinematic constraint: The strata of particles must shake laterally as they slip past one another in the direction of the mean flow. Based on this insight, we formulate a simple model for the fluctuating velocity of dense granular flows. The predictions of the model agree well with our experimental measurements.     

Turbulentlike fluctuations in quasistatic flow of granular media

We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their different physical origins: (i) scale-dependent probability distribution with non-Gaussian broadening at small time scales; (ii) spatial power spectrum of the velocity field showing a power-law decay, reflecting long-range correlations and the self-affine nature of the fluctuations; and (iii) superdiffusion of particles with respect to the mean background flow.     

Creep motion in a granular pile exhibiting steady surface flow

We investigate experimentally granular piles exhibiting steady surface flow. Below the surface flow, it has been believed that a "frozen" bulk region exists, but our results show no such frozen bulk. We report here that even the particles in layers deep in the bulk exhibit very slow flow and that such motion can be detected at an arbitrary depth. The mean velocity of the creep motion decays exponentially with depth, and the characteristic decay length is approximately equal to the particle size and is independent of the flow rate. It is expected that the creep motion we have seen is observable in all sheared granular systems.     

Collisional granular flow as a micropolar fluid

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.     

稠密颗粒射流倾斜撞击颗粒膜特征

采用高速摄像仪对稠密颗粒射流倾斜撞击形成的类液体颗粒膜特征进行实验研究,考察了颗粒粒径、射流速度以及射流含固率等因素对颗粒膜形态及动态特征的影响.结果表明:随着颗粒粒径增大,稠密颗粒倾斜撞击流由颗粒膜向散射模式转变;随着射流速度增加,气固不稳定增强,射流流量出现脉动,正面与侧面分别表现为颗粒膜的非轴对称振荡和表面波纹结构;颗粒膜非轴对称振荡的振荡频率和振荡幅度随射流速度的增大而增大;表面波纹速度和波长沿传播方向增大,波纹间存在叠加现象.颗粒膜出现非轴对称振荡主要是因为喷嘴出口由气固不稳定性引起的射流流量脉动,射流流量脉动频率与撞击面振荡频率基本相当.     

Velocity and diffusion imaging in dynamic NMR microscopy

The imposition of resolution gradients in a pulsed-gradient spin-echo (PGSE) NMR sequence induces motionally dependent phase and amplitude modulation in the image, a technique which we have termed dynamic NMR microscopy. Fourier analysis of this modulation gives a dynamic displacement profile for each pixel which can then be analyzed to obtain velocity and diffusion maps. The application of this method at high spatial resolution is motivated by a desire to measure vascular flow in living plants and variations in molecular self-diffusion under the influence of velocity shear in narrow capillaries. The theory of dynamic NMR microscopy is presented and potential artifacts discussed, including the effect of slice selection gradients, PGSE gradient nonuniformity, and specific problems associated with the measurement of self-diffusion in the presence of velocity gradients. It is demonstrated that a double-echo PGSE pulse sequence can be used to restore coherent phase shifts associated with steady-state flow, and examples of self-diffusion maps and signed velocity maps from sequences of phase-encoded images obtained by projection reconstruction are given. This method has been applied at 20,um transverse resolution in laminar capillary flow.     

A quantitative analysis on the energy dissipation mechanism of the non-obstructive particle damping technology

The non-obstructive particle damping (NOPD) technology has been recently developed from particle damping and impact damping technologies. In this paper, a quantitative analysis of the dissipation mechanism of NOPD based on a statistical theory is investigated for the first time to our knowledge. Under high-frequency vibrations, the dense granular motion of NOPD is very similar to turbulence. Thus, Kolmogorov's hypothesis in turbulence is adopted to describe the energy spectral density and velocity correlation function of the particles in the NOPD technology. It is shown that the NOPD's mean energy dissipation (per unit mass) increases with either the granular diameter or the volume ratio of the dense granular flow. The quantitative model for the NOPD technology presented in the paper should be useful in possible engineering applications of vibration reduction.     

Granular gas of viscoelastic particles in a homogeneous cooling state

Kinetic properties of a granular gas of viscoelastic particles in a homogeneous cooling state are studied analytically and numerically. We employ the most recent expression for the velocity-dependent restitution coefficient for colliding viscoelastic particles, which allows us to describe systems with large inelasticity. In contrast to previous studies, the third coefficient a₃ of the Sonine polynomials expansion of the velocity distribution function is taken into account. We observe a complicated evolution of this coefficient. Moreover, we find that a₃ is always of the same order of magnitude as the leading second Sonine coefficient a₂; this contradicts the existing hypothesis that the subsequent Sonine coefficients a₂,a₃…, are of an ascending order of a small parameter, characterizing particles inelasticity. We analyze evolution of the high-energy tail of the velocity distribution function. In particular, we study the time dependence of the tail amplitude and of the threshold velocity, which demarcates the main part of the velocity distribution and the high-energy part. We also study evolution of the self-diffusion coefficient D and explore the impact of the third Sonine coefficient on the self-diffusion. Our analytical predictions for the third Sonine coefficient, threshold velocity and the self-diffusion coefficient are in a good agreement with the numerical finding.     

Statistics of particle velocities in dense granular flows

We present measurements of the particle velocity distribution in the slow flow of granular material through vertical channels. The velocities of particles adjacent to the smooth, transparent front face of the channel were determined by video imaging and particle tracking. We find that the mean velocity changes sharply in shear layers near the side walls, but remains constant in a substantial core. The velocity distribution is non-Gaussian, is anisotropic, and follows a power law at large velocities. Remarkably, the distribution is identical in the shear layer and the core. We show evidence of spatially correlated motion, and propose a mechanism for the generation of fluctuational motion in the absence of shear.     

Granular flows in a rotating drum: the scaling law between velocity and thickness of the flow

The flow of dry granular material in a half-filled rotating drum is studied. The thickness of the flowing zone is measured for several rotation speeds, drum sizes and beads sizes (size ratio between drum and beads ranging from 47 to 7400). Varying the rotation speed, a scaling law linking mean velocity vs. thickness of the flow, v∼h^m, is deduced for each couple (beads, drum). The obtained exponent m is not always equal to 1, the value previously reported for a drum in litterature, but varies with the geometry of the system. For small size ratios, exponents higher than 1 are obtained due to a saturation of the flowing zone thickness. The exponent of the power law decreases with the size ratio, leading to exponents lower than 1 for high size ratios. These exponents imply that the velocity gradient of a dry granular flow in a rotating drum is not constant. More fundamentally, these results show that the flow of a granular material in a rotating drum is very sensible to the geometry, and that the deduction of the “rheology” of a granular medium flowing in such a geometry is not obvious.     

颗粒速度在颗粒流稀疏流-密集流转变中的作用

用实验和计算模拟的方法研究了颗粒流中的颗粒速度与颗粒流特性的关系.实验研究发现当入口流量固定时，在出口上方高速运动的颗粒会使颗粒流由稀疏流向密集流转变的临界出口尺寸变小.当颗粒流转变为密集流后，颗粒速度的作用被出口上方的颗粒堆积区所消耗，最终变得与颗粒速度无关.二维分子动力学模拟计算得到了与实验相同的结论.通过二维分子动力学模拟计算，还给出了不同颗粒速度下体系的密度和速率在空间的分布图.这些分布图显示随着颗粒到达出口上方的瞬间速度的不同，颗粒堆积区的密度和高度均会改变，并最终导致颗粒流流动状态的改变. 关键词： 颗粒流 颗粒气体 分子动力学模拟     

Rolling velocity and relative motion of particle detector in local granular flow

The velocity of a particle detector in granular flow can be regarded as the combination of rolling and sliding velocities. The study of the contribution of rolling velocity and sliding velocity provides a new explanation to the relative motion between the detector and the local granular flow. In this study, a spherical detector using embedded inertial navigation technology is placed in the chute granular flow to study the movement of the detector relative to the granular flow. It is shown by particle image velocimetry (PIV) that the velocity of chute granular flow conforms to Silbert's formula. And the velocity of the detector is greater than that of the granular flow around it. By decomposing the velocity into sliding and rolling velocity, it is indicated that the movement of the detector relative to the granular flow is mainly caused by rolling. The rolling detail shown by DEM simulation leads to two potential mechanisms based on the position and drive of the detector.     

Numerical Simulation of the Formation of Granular Shock Wave Over Cylindrical Obstacle

A two dimensional (2‐D) stream of granular flow with zero initial granular temperature passing over a cylindrical obstacle is simulated by means of both molecular dynamics (MD) simulation and finite volume method (FVM). In experiments, a bow‐shaped shock wave with higher area fraction forms in front of the obstacle that was reproduced in our simulations. Due to the different circumstances to which particles are subjected, the granular flow is divided in two zones. One is undisturbed where quantities, such as space fraction (volume fraction for 3‐D and area fraction for 2‐D geometries), velocity and granular temperature are uniformly distributed and the other is called the shock wave zone. In this region, the values of the space fraction increases and the velocity of particles changes. From the MD simulation, it is found that the area fraction of the shock wave depends on surface roughness, coefficient of restitution (COR) of particles, the obstacle diameter as well as velocity of the granular stream, and a triangular region forms with almost zero velocity, and granular temperature forms in front of the cylindrical obstacle. The bigger is the size of the obstacle, the more stable this region is. In FVM simulations solid phase velocity and area fraction distributions similar to the MD simulation results are obtained for proper parameters.     

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.     

稠密颗粒射流撞击壁面颗粒膜表面波纹特征

采用高速摄像仪对稠密颗粒射流撞击有限尺寸壁面的流动过程进行了实验研究,重点研究了颗粒膜及其表面波纹特征,考察了颗粒粒径、射流速度和固含率等因素对颗粒膜形态和表面波纹的影响.研究结果表明,随着颗粒粒径增大,稠密颗粒撞壁流由颗粒膜向散射模式转变.与液体射流撞壁液膜相比,颗粒膜扩展角较大,射流速度对其影响不显著.稠密颗粒射流撞壁颗粒膜表面波纹存在明显的叠加现象,颗粒膜表面波纹频率比液膜大约低一个数量级.颗粒膜表面波纹主要由射流脉动引起,表面波纹频率与射流脉动频率具有相同的数量级.     

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in [#!bcre!#] to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We relate the critical wave vector to the mean hopping length and to the ratio of the flight time to the `stick' time. We provide an intuitive interpretation of the instability. Received: 30 January 1998 / Revised: 12 May 1998 / Accepted: 8 June 1998     

对颗粒物质运动的一致性进行控制的随机力场

在颗粒流的研究中引入了一个正态分布的随机力场, 并通过计算机模拟研究了该力场对均匀颗粒流的影响. 结果发现: 随机力场基本上不改变均匀颗粒流的平均密度和速度, 对颗粒流密度的涨落也影响很小. 随机力场对均匀颗粒流的影响主要体现在它可提高速度的涨落, 它与颗粒体系的耗散性质相抗衡, 使颗粒流维持一定的波动能量. 研究结果还显示: 通过随机力场所获得的波动能量并没有均匀分布到各个自由度上, 由于颗粒体系的耗散性质颗粒体系难以达到能均分状态. 关键词： 颗粒物质 随机力 分子动力学模拟     

开口角度对二维颗粒流稀疏流-密集流转变的影响

用计算机模拟的方法研究了开口角度对二维颗粒流稀疏流—密集流转变的影响.在固定入口流量和固定颗粒数两种条件下,均发现当开口角度大于零时,开口角度的增大可以提高颗粒流由稀疏流向密集流转变的最大出口流量.在稀疏流状态下,出口流量与开口角度无关;而在密集流状态下,出口流量随开口角度的增大而增大.进一步的计算还发现增加开口角度可以提高颗粒流出开口的流动速度,且最大出口流量与颗粒的流动速度呈线性关系. 关键词： 颗粒物质 颗粒流 分子动力学模拟