Segregation due to particle shape of a granular mixture in a slowly rotating tumbler

Using DEM particle simulations we consider segregation of a binary granular particle mixture in a slowly rotating cylindrical tumbler where the particles differ only in their shape—spherical versus more cubical particles. We find that the more cubical particles segregate to the inner core of the particle bed while the spherical particles segregate to the curved walls of the tumbler. The main mechanism for this segregation is different energy dissipation rates for the different particle shape types when avalanching down along the free surface. The cubical particles, due to their sharper corners, dissipate energy much faster than the spherical particles. This results in spherical particles reaching the bottom end of the sloped, free surface which are then transported around the cylinder adjacent to the cylinder wall, as rigid body motion. In contrast to size or density segregation, the segregation due to shape is much weaker and takes longer to reach its equilibrium or steady state. In addition, the segregation occurs along the top surface rather than through the top surface (as occurs for size and density segregation). In general, in situations where two particles differ in their ease of flow (viz flowability) the more rapidly flowing particle will segregate to the base of the free surface (which in the case of the tumbler results in spherical particles near the periphery) and the more slowly flowing particle will segregate underneath.     

The effect of liquids on radial segregation of granular mixtures in rotating drums

The presence of liquids can significantly affect the dynamics of granular flow. This paper investigates the effect of liquids on radial segregation of granular mixture in a rotating drum using the discrete element method. The wet granular mixture, due to differences in particle size and density, segregates in a similar way to that of dry particles: lighter/larger particles move to the periphery of the bed while heavier/smaller particles stay in the centre. An index based on the variance of local concentration of one type of particles was proposed to measure the degree of segregation. While the liquid induced capillary force slows down the segregation process, its effect on the final state is more complicated: small cohesion shows no or even positive effect on segregation while high cohesion significantly reduces particle segregation. The effect can be explained by the change of flow regimes and the competing effects of mixing and segregation (un-mixing) in particle flow which are both reduced by the interparticle cohesion. A diagram is generated to describe the combined effect of particle size and density on segregation of wet particles. A theory is adopted to predict the segregation of particles under different density/size ratios.     

Dynamics of rotating paramagnetic particles simulated by lattice Boltzmann and particle dynamics methods

Novel biochemical sensors consisting of rotating chains of microscale paramagnetic particles have been proposed that would enable convenient, sensitive analyte detection. Predicting the dynamics of these particles is required to optimise their design. The results of lattice Boltzmann (LB) and particle dynamics (PD) simulations are reported, where the LB approach provides a verified solution of the complete Navier-Stokes equations, including the hydrodynamic interactions among the particles. On the other hand, the simpler PD approach neglects hydrodynamic interactions, and does not compute the fluid motion. It is shown that macroscopic properties, like the number of aggregated particles, depend only on the drag force and not on the total hydrodynamic force, making PD simulations yield reasonably accurate predictions. Relatively good agreement between the LB and PD simulations, and qualitative agreement with experimental data, are found for the number of aggregated particles as a function of the Mason number. The drag force on a rotating cylinder is significantly different from that on particle chains calculated from both simulations, demonstrating the different dynamics between the two cases. For microscopic quantities like the detailed force distributions on each particle, the complete Navier-Stokes solution, here represented by the LB simulation, is required.     

Particle screening phenomena in an oblique multi-level tumbling reservoir: a numerical study using discrete element simulation

Due to their wide usage in industrial and technological processes, granular materials have captured great interest in recent research. The related studies are often based on numerical simulations and it is challenging to investigate computational phenomena of granular systems. Particle screening is an essential technology of particle separation in many industrial fields. This paper presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shape particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level obliqued vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle–particle and particle–boundary collisions will appear under the tumbling motion of the rotating structure. A penalty method, which employs spring-damper models, will be applied to calculate the normal and frictional forces. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. The particle distribution, sifting rate of the separated particles and the efficiency of the segregation process have been studied. It is recognized that the screening phenomenon is very sensitive to the machines geometrical parameters, i.e. plate inclinations, shaft eccentricities and aperture sizes in the sieving plates at different levels of the structure. The rotational speed of the machine and the feeding rate of the particles flow have also a great influence on the transportation and segregation rates of the particles. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies for achieving optimal operation have been performed.     

Dynamics of bi-dispersed settling suspension of non-colloidal particles in rotating cylinder

Non-neutrally buoyant suspension of bi-dispersed non-colloidal particles in viscous fluid rotating in a horizontal cylinder displays in-homogeneities in particle distribution with alternate bands of high and low particle concentrations along the symmetric axis of the cylinder. Experiments were carried out to characterize the axial segregation in bi-dispersed suspension at various filling fraction and rotation speed of cylinder. The mixture of same particles in absence of any suspending fluid did not show any segregation. However, in case of particles suspended in water it was observed that the rate of segregation increases with increase in filling fraction. Once the particles get segregated along the full length of the cylinder, these bands start to migrate along the tube axis finally merging to give wider bands. For a given filling fraction the rate of segregation increases with the angular speed of the rotating cylinder. When the tube is partially filled the particle segregation is observed at higher angular speed, whereas in fully filled case the segregation starts at much lower rotation speed for the same concentration of particles. The segregation pattern changes as the rotation speed is increased. At higher speed the centrifugal force dominates over gravitational and viscous drag forces and this result into completely different segregation patterns. We have also analyzed the evolution of concentration profile from the image analysis of the particles.     

CFD simulation of particle segregation in a rotating drum. Part II: Effects of specularity coefficient

Segregation of binary particle mixture in a rotating drum is numerically studied using the Eulerian multiphase computational fluid dynamics (CFD) simulations coupling the solid phase kinetic theory of granular flow model. The corresponding solid kinetic viscosities of the two particulate phases are determined by the previous granular bed surface fitting (BSF) method. The effects of the specularity coefficients used in the simulations on the segregation patterns in the rotating drums are systematically studied by using the specularity coefficient values ranging from 0.15 to 1.0. When using a smaller specularity coefficient value in the simulation, the momentum transferring from the drum wall to the particulate phase is poorer, lowering the kinetic energy of the particulate phase. The lower particulate phase kinetic energy causes slower particle motion in the bed and hence delays the segregation core/band formation. At the same simulation time, the concentration of the smaller particles in the segregation core increases with the increasing of the specularity coefficient value used in the simulation. When the specularity coefficient values larger than 0.4 are used in our simulations, the realistic three-dimensional segregation structures are well predicted. A proper specularity coefficient value should be adopted in Eulerian multiphase CFD simulations of granular flows.     

Numerical study of forced axial segregation of binary density granular system in a split rotary drum

Driving and controlling the segregation in a rotary drum is both a theoretical and a practical challenge in powder technology. A novel horizontal split drum design composed of two reverse rotating sub-drums was explored to drive axial segregation of granular matter. DEM (Discrete Element Method) simulations were performed to study the particle dynamics and segregation performance of binary density particles in the split drum. Then, the effects of drum speed, the speed ratio of the two sub-drums, and the split position on the axial segregation were analyzed. It was found that true axial segregation occurred in the split drum and heavier particles tend to accumulate in the region near the split. An increase in drum speed can accelerate the segregation but it has no obvious influence on the final axial distribution of particles. The results obtained indicate when two sub-drums rotate at different speeds, the concentrated region of heavier particles moves towards the low-speed sub-drum. These findings could lead to new designs for a broad range of particle processing industries.     

Radial segregation of ternary granular mixtures in rotating cylinders

We carry out an experimental study of the equilibrium segregation of ternary granular mixtures in a rotating cylinder. In all the experiments, 50% of the volume of the cylinder is filled with the granular mixture and the rotational speed used ensures operation in the rolling regime of flow. Mixtures of spherical particles differing only in size and of spherical particles differing in size and density are considered, using steel balls and glass beads of different sizes. Volume fractions of the components (f{\phi}) are measured by sampling at different radial positions (r) to yield the radial volume fraction profiles (f(r){\phi(r)}). Results for mixtures differing only in size of the components indicate that the segregation process is nearly independent of the sizes of the large and middle size particles for the same size of small particles. In the case of mixtures with different size and density components, the segregation patterns depend on the direction of the resultant driving force. In many of the mixtures considered, the pattern of segregation can be qualitatively predicted by considering binary interactions between the components. However, in some mixtures, ternary interactions are found to determine the pattern obtained.     

Experimental study of density segregation at end walls in a horizontal rotating cylinder saturated with fluid: friction to lubrication transition

What is the effect of interstitial fluid viscosity on granular density segregation in a horizontal rotating cylinder? We conducted experiments in the rolling regime with equal amounts of equal sized high and low density, nearly spherical granular particles saturated with air, water, and water-glycerin mixtures. We held particle density, rotation rate and characteristic length scale constant to highlight differences due purely to the interstitial fluid. Images of the granular flow at an end wall were used to determine radial and axial density segregation rates and patterns. Over a four decade change in viscosity, segregation rates varied by only a factor of two. However, for ratios of lubrication to frictional stresses above one, segregation rates decreased by about 30%, and we observed several notable phenomena in the segregation pattern formation. These were a creeping mode of radial density segregation, a change in shape of the granular bed to kidney shaped from flat, and for cylinders more than half full the typically reported unsheared central portion of the granular bed (often referred to in the literature as a core region) was disrupted by a wavy instability where the rate of disappearance of the core region decreased as the fill level increased.     

Segregation of combined size and density varying binary granular mixtures in a slowly rotating tumbler

Granular mixtures composed of particles which differ in size or density readily segregate when there is relative motion between particles, such as in a slowly rotating tumbler. In the past, several studies have considered segregation due to different sized particles or different density particles. The physical mechanisms that lead to segregation are different in these two cases. Few studies have considered the important (practical) situation where particles differ both in size and density, which is what we consider here. Depending on particle sizes and densities the two mechanisms either oppose or enhance each other. We consider both cases here and find when the two mechanisms oppose each other size segregation is generally stronger than density segregation. We also determine stability regions for the various patterns that form. When the mechanisms enhance each other we find, under some specific conditions, streak patterns form. We argue that one requires a bed microstructure which fluctuates in strength which subsequently leads to avalanching. We find stable streaks only occur when the smaller, denser particles are blocky in shape while the larger, less dense particles are spherical.     

Radial segregation of multi-component granular media in a rotating tumbler

Segregation and mixing of granular mixtures are important to the minerals, food processing and pharmaceuticals industry to name just a few. It has recently been demonstrated that a rotating tumbler is a suitable device for separating out binary granular mixtures, i.e. mixtures composed of only two different particle types. However, most practical granular mixtures are composed of multi-component particle types. We therefore study the capability of this rotating tumbler to segregate mixtures composed of more than two components where the particles differ either in size or density. The general pattern of segregation involves the formation of an inner core of smallest or densest particles followed, at larger radii, by the next largest or densest particle type and so-on in an onion-like pattern. In the mixtures where particles differ in size we always get relatively pure inner cores of the smallest particles, while the other regions are less segregated. On the other hand for mixtures whose particles differ in density we get a relatively pure outer region (adjacent to cylinder wall) consisting of the least dense particles while the other regions are less segregated. We attempt to relate the simulation results to phenomenological theory and find that size segregation in a specific multi-component mixture can be suitably described by a recent theoretical model.     

The influence of end walls on the segregation pattern in a horizontal rotating drum

The influence of end walls on segregation of bidisperse granular beds in a short rotating horizontal drum is studied by a discrete element method. Whereas non-closed periodically continued drums segregate radially, all simulations of drums with end walls resulted in axial segregation with two bands at low friction between the particles and the end-wall, and three bands at high friction. Various simulations show irregular transitions between two approximately equally stable states, with rapid oscillations preceding the conversions. The formation of two axial bands decreases the energy dissipation by the bed, whereas neither radial segregation nor axial segregation into three bands reduced the power absorption at constant angular velocity. Roughening up the end-walls also increased the rate of axial segregation.     

Modelling axial dispersion of granular material in inclined rotating cylinders with bulk flow

The axial dispersion of approximately monosized particles in rolling mode in rotating cylinders with bulk flow is examined using a Monte Carlo model and discrete element method (DEM) simulations. The Monte Carlo model predicts that the mean square displacement relative to the mean axial displacement of the bed undergoes oscillations in time. The nature of these oscillations depends on the fill level of the cylinder and the extent of particle mixing during avalanches. When the cylinder is half full the Monte Carlo model predicts undamped oscillations, whereas a filling fraction of 0.26 produces oscillations whose amplitude decreases with time. If mixing during avalanches is assumed to be perfect then the oscillations occur about a linear increase with time. In contrast, if it is assumed that the particles do not mix during avalanching, the oscillations occur about an increase with time which has a gradient which increases with time. There is good qualitative agreement between the Monte Carlo model with perfect mixing and the DEM when the filling fraction is 0.26. For a filling fraction of 0.5 the DEM data show oscillations about a faster than linear increase with time.

     

Tangential velocity profiles of granular material within horizontal rotating cylinders modelled using the DEM

Flow regimes of granular materials in horizontal rotating cylinders are industrially important since they have a strong influence on the rates of heat and mass transfer within these systems. The tangential velocity profile, which describes how the average particle velocity in the direction parallel to the surface of the bed varies along a radius perpendicular to the surface of the bed, has been examined for many experimental and simulated systems. This paper is concerned with tangential velocity profiles within rotating cylinders simulated using the discrete element method. For high fill levels good agreement is found between the simulated velocity profiles and the equation proposed by Nakagawa et al. (Exp Fluids 16:54–60, 1993) based on magnetic resonance measurements. At lower fill levels slip is observed between the cylinder wall and the particles in contact with it and also between the outer layer of particles and the bulk of the bed. It is demonstrated that this slip occurs when the particles in contact with the wall are able to rotate and that it may be prevented either by using non-spherical particles or by attaching “lifters” to the cylinder wall.     

基于离散元方法的RDX-Al颗粒混合数值模拟分析

基于离散元方法,以旋转筒内RDX-Al二元颗粒体系的搅拌过程为研究对象进行模拟。采用离散元软件(EDEM),首先研究RDX-Al二元颗粒各自随转速的变化趋势,并进一步得出二元颗粒变化率的特点,做出分布上的拟合,得出最吻合模拟试验的函数为指数函数。然后,将旋转筒细分为多个单元空间,考察旋转轴与单元空间之间的距离对二元颗粒混合效果的影响。结果表明:单元空间离旋转轴越远,即旋转半径越大,颗粒之间的变化率也就越快,越容易达到均匀状态。最后,考察加入抄板的影响,结果表明:RDX-Al二元颗粒趋于的稳定值分别发生了改变。     

Axial particle diffusion in rotating cylinders

We study the interface dynamics of a binary particle mixture in a rotating cylinder numerically. By considering only the particle motion in axial direction, it is shown that the initial dynamics can be well described by a one-dimensional diffusion process. This allows us to calculate a macroscopic diffusion constant and we study its dependence on the inter-particle friction coefficient, the rotation speed of the cylinder and the density ratio of the two components. It is found that radial segregation reduces the drift velocity of the interface. We then perform a microscopic calculation of the diffusion coefficient and investigate its dependence on the position along the cylinder axis and the density ratio of the two particle components. The latter dependence can be explained by looking at the different hydrostatic pressures of the two particle components at the interface. We find that the microscopically calculated diffusion coefficient agrees well with the value from the macroscopic definition when it is measured in the middle of the cylinder.     

Segregation pattern of binary-size mixtures in a double-walled rotating drum

Size-induced granular segregation was performed systematically and experimentally in an almost fully filled double-walled rotating drum at 10 different rotation speeds and two different side wall types. The motion of the granular materials was recorded using a high-speed camera for image analysis of particle segregation development in the drum. With continual tracking of the particle movements, the velocity, fluctuations, and granular temperatures were measured. The experimental results indicate that both rotation speeds and friction coefficient of side walls significantly affect segregation phenomena in binary-size mixture granular flows. The results demonstrate similar situations to the Brazil-nut effect and its reverse in the radial direction at either high or a low rotational speed (where the Froude number (Fr) is far from 1). At these instances, the maximum granular temperature occurs near the side walls. Specifically, a double segregation effect (DSE) is found at Froude number (Fr) close to 1. These results can be used in many industrial processes, for example, size grading of materials, screening of impurities, and different structures of functionally graded materials. Moreover, the maximum granular temperature occurs in the middle of the ring space. It causes small particles to move toward both side walls as it pushes bigger particles to accumulate in the middle of the ring space of rotating drum.     

Simulations for dynamics of granular mixtures in a rotating drum

We present a simple model and carry out simulations to investigate the dynamics of mixtures of granular material within a rotating drum. On the basis of the commonly held belief (supported by considerable experimental evidence) that segregation is due to motion of particles on the active layer, the bulk playing little or no role, we introduce a 2d lattice gas model which takes into account the rotational frequency, frictional forces, and the gravitational field, and represents segregation tendencies via activated effective grain-grain interactions. Our results include the onset of segregation perpendicular to the drum axis, the appearance and subsequent coarsening of bands and peculiarities of the effects of periodic modulation of the drum. Observed effects such as the segregation of rougher (smoother) particles into the bellies (necks) of the modulation are reproduced by our simulation. Received: 30 March 2000     

Experimental investigation and numerical modelling of density-driven segregation in an annular shear cell

Granular materials segregate spontaneously due to differences in particle size, shape, density and flow behaviour. In this paper we experimentally investigate density-difference-driven segregation for a range of density ratios and a range of heavy particle concentrations. The experiments are conducted in an annular shear cell with rotating bumpy bottom that yields an exponential shear profile. The cell is initially filled with a layer of light particles and an upper layer of heavier grains and, on top, a load provides confinement. The segregation process is filmed through the transparent side-wall with a camera, and the evolution of particle concentration in space and time is evaluated by means of post-processing image analysis. We also propose a continuum-approach to model density-driven segregation. We use a segregation-diffusion transport equation, constitutive relations for effective viscosity and friction coefficient, and a segregation velocity analogous to the Stokes’ law. The model, which is validated by comparison with experimental findings, can successfully predict density-driven segregation at different density ratios and volumetric fraction.     

Effects of scale and inertia on granular banding segregation

We report that the formation of much reported axial segregation bands in rotating cylinders loaded with different sized particles depends critically on scale and inertia. Specifically, when the ratio, , of the diameter of the cylinder to the average diameter of the particles is large, axial bands invariably appear, when is small, bands never appear, and between these extremes lies a reversible state where the presence or absence of bands depends on container rotation speed. Our results indicate that banding is associated with a Rayleigh-like instability of a granular core of fine particles, and that this instability is controlled by the inertia of the larger species – and consequently on scale.KeywordsGranular, Segregation, Mixing, Banding, ScalePACS number(s): 05.40.+j, 46.10.+z, 83.10.Hh.