Segregation kinetics in the rapid gravity flow of granular materials

An experimental analytical method for determining the kinetic segregation coefficient in the rapid gravity flow of a granular material down a rough incline is proposed. It is found that it is possible to predict the velocity of transverse displacement of individual large and small particles in the rapid gravity flow using a single kinetic segregation coefficient for different particle sizes and structural and kinematic characteristics of the flow. A previously proposed equation of segregation kinetics is refined, and its predictive power is analyzed.     

Rapid Gravity Flow of a Granular Medium

An experimental study is performed to analyze the equation of state of a granular medium, which relates its dilatancy, shear rate, and pressure by an analogy between a granular medium under rapid shear and a dense gas. A method is developed for the contactless determination of the solid-phase concentration distribution in the two-dimensional flow of a granular medium using x-ray analysis. The method is used to explore the concentration profiles in rapid gravity flows of ceramic particles down a rough incline. The adequacy of the equation of state of a granular medium under rapid shear and for unordinary properties of the gravity flow down a rough incline is directly confirmed.     

Phenomenological analysis of the interaction of nonelastic incoherent particles in a rapid gravity flow

Interaction of nonelastic incoherent spherical particles in a rapid gravity flow is analyzed. The analysis provides a refinement for the relationship between the pressure, dilatancy, and temperature of the granular medium (energy of mutual displacements of the particles). The equation of state obtained for the granular medium establishes the determined interrelation of the parameters of a rapid gravity flow of cohesionless nonelastic spherical particles and for the first time makes it possible to evaluate the effect of various forms of mutual displacement of particles on the dilatancy of the granular material during a rapid shift. The adequacy of the equation of state of the granular medium is confirmed with the use of the X-ray diffraction method.     

Density effect on mixing and segregation processes in a vibrated binary granular mixture

The mixing and segregation processes of binary granular mixture with identical sizes but different densities particles subjected to vertical oscillatory excitation are investigated in this study. The spatial distributions of vibrated binary steel-glass beads mixture are visualized by simulation and the results are similar to the experimental data. The time evolution of pattern formations show that the heavy particles first move toward the center of the bed and then concentrate near the centers of the two convection cells of the vibrated system. The mechanism causing the mixing and segregation is strongly dependent on the momentum exchange of each species which is related to the granular temperature gradients of mixture components. The influences of solid fraction and granular temperature profiles on the mixing of the mixture are examined under different operating conditions. The simulation results show that the granular temperatures of heavy particles are higher than those of light particles, indicating that the granular temperatures do not equilibrate for the mixture system. The convection motion also plays an important role in determining the mixing of the system. For understanding the extent of granular mixing, the segregation intensity was determined to quantify the mixing rate of binary mixtures. The segregation intensity shows that the mixing rate increases with the vibration strength, but decreases with the initial heights of mixture.     

Numerical analysis of density-induced segregation during die filling

In this study, segregation behaviour of binary granular mixtures with the same particle size but different densities during die filling in the presence of air was investigated using a combined discrete element method (DEM) and computational fluid dynamics (CFD) approach, in which the kinematics of particles was modelled using DEM, the motion of air was analysed using CFD and a two-way coupling of the particles and the air was incorporated. The depositions of powder from stationary and moving shoes into the die cavities of different geometries were simulated and the corresponding segregation behaviours were analysed. It has been found that, for die filling from a stationary shoe, the concentration distributions of the heavy and light particles along the die width mainly depend on the initial spatial distribution of the granular mixture in the shoe. For die filling from a moving shoe, a low concentration of light particles on the leading side of the die (referring to the direction of the shoe motion) is observed for die filling with a square die, in which the process is dominated by nose flow. The density difference can cause segregation along the die depth with a low concentration of light particles at the bottom. The presence of air enhances this segregation tendency by resisting the flow of light particles into the bottom of the die and causes a higher concentration of the light particles at the top. Finally, the segregation index, defined as the volume weighted root-mean-square deviation in the content of light particles, was introduced to quantify the degree of segregation in the horizontal and vertical directions. It has been found that the degree of segregation is determined by the presence of air and also the powder flow pattern.     

Granular and gas-particle flows in a channel with a bidisperse particle mixture

Steady state solutions of granular and gas-particle flows in a channel with a bimodal particle mixture have been computed using kinetic theory. For granular channel flows we find granular energy equipartition breaks down with an increase in the system inelasticity and the mass ratio of particles. The effect of the particle size ratio on breakdown of energy equipartition is very small if the two particle species have the same mass. The species segregation in the solid phase is enhanced with a decrease in the system inelasticity, an increase in the average solid fraction or an increase in the size ratio, due to the competition of three diffusion forces: the thermal diffusion force, the ordinary diffusion force, and the pressure diffusion force. In addition, we find a competition mechanism exists in the equal density case (particles with equal density but different sizes) since in the equal mass case (particles with equal mass but different sizes) small particles have a higher concentration in low granular energy regions, whereas in the equal size case (particles with equal size but different masses) heavy particles have a higher concentration in low granular energy regions. These findings are in agreement with the results for granular Couette flows. For equal density particles, the segregation of large particles has a transition from the walls to the center when the restitution coefficient (e_p) decreases from 1 to 0.99. This sensitivity is reduced when the system becomes more inelastic. For a given monodisperse granular system, we show that if larger particles are mixed in the system the sensitivity of the total solid distribution to the restitution coefficient is suppressed, while if smaller particles are added in the system the situation reverses. Lastly, we extend our work to gas-particle flows in a channel where particles are fluidized by gas flowing upwards, and find that for the kinetic theory models used in the present study, the solid fraction, the species segregation and the granular energy profiles are quite similar between the granular flows and the gas-particle flows.     

The influence of gravity on dynamic properties in sheared granular flows

The influences of gravity on the granular flow behavior and dynamic properties were experimentally studied in a vertical shear cell device where the shear dilation direction of granular materials was perpendicular to the gravity direction. The particle motions were recorded by a high-speed camera from three different observational views. By using image processing technology and the particle tracking method, the average velocities and granular temperatures in the streamwise and the transverse directions were successfully measured and analyzed. The results show that the anisotropic motions exist in sheared granular flows. The dynamic properties in the streamwise direction are larger than those in the transverse direction. Due to the gravity effect and bulk flow of granular materials, the local packing structure is not homogenous in the vertical shear cell. By comparing the three different observational views in the vertical shear cell, we find that the spatial average velocity and self-diffusion coefficient are the greatest but the shear rate and granular temperature are the smallest when the particles are co-flowing with gravity causing the most dilute packing structure due to the gravity effect. Similar experiments were also performed in a horizontal shear cell where the shear dilation direction of granular materials was against the gravity direction. The dynamic properties are smaller in the horizontal shear cell than those in the vertical shear cell. It is because the horizontal shear cell has the smaller shear rate with the shear dilation direction against the gravity direction.     

颗粒斜槽流的实验研究与数值模拟

从实验和理论两个方面对颗粒慢速斜槽流进行了研究。建立颗粒慢速斜槽流的实验装置 ,采用示踪颗粒法测定表面速度 ;通过测量表面速度和流层厚度 ,初步分析了流率及壁面状况对流动的影响。用有限元法对粗糙表面上的慢速斜槽流进行了数值模拟     

Segregation of cohesive powders in a vibrated granular bed

The effects of small amounts of added liquid on the segregation behavior of a granular system under vertical vibration by DEM simulation are investigated in this study. The cohesive forces of grains are incorporated into DEM simulations via a simplified dynamic liquid bridge force model. The simulation results show that capillary forces in addition to viscous forces have an important effect on the segregation phenomenon. The segregation rate of larger intruder rises to the top of the bed is found to depend on the liquid content. The segregation rate is sharply increased when a small amount of liquid is added to granular system. A transition to the reduction of segregation rate occurs at a critical liquid content. It has shown that this transition can be interpreted as the increase of attractive force between grains due to viscous force. The viscous forces make the particles stick more tightly to each other and retard the movement of particles, thus reducing the segregation rate. The segregation rate is also related to the convection motion of the granular system. The presence of convection enhances the segregation rate of wet granular materials.     

Development of a multi-fluid model for poly-disperse dense gas-solid fluidised beds, Part II: Segregation in binary particle mixtures

Particle mixing and segregation rates in a bi-disperse freely bubbling fluidised bed have been studied with a new multi-fluid model (MFM) based on the kinetic theory of granular flow for multi-component systems (see Part I). The MFM simulation results have been compared with digital image analysis experiments obtained by Goldschmidt et al. [2003. Digital image analysis of bed expansion in dense gas-fluidised beds. Powder Technology 138, 135-159] for bi-disperse mixtures of glass beads. In strong contrast to MFMs previously described in the literature, that strongly overestimate the segregation rates, the new MFM seems to underestimate the segregation rates at longer times. This underprediction of the segregation rate is probably related to the neglect of frictional stresses associated with long-term multiple-particle contacts resulting in an overestimation of the mobility of the emulsion phase, which is corroborated by discrete particle simulations without friction between the particles and the particles and the wall. The level of the granular temperature of the segregating system, as computed with the new MFM, compares reasonably well with the granular temperatures found in the DPM simulation.     

Electrostatic charging during the flow of grains from a cylinder

Electrostatic charging is ubiquitous in granular processing, leading to problems of safety, jamming and unwanted material segregation. To better understand the mechanics of granular charging, we focus here on flow through a metal cylinder, where we can isolate charging regions near the cylinder walls from noncharging regions further away. We confirm that monodisperse grains charge in proportion to the area of contact between grains and the cylinder walls, and so in large cylinders, most particles remain almost uncharged. Those particles that do charge reach a plateau charge density after filling the cylinder and flowing past the walls a distance of less than one and a half centimeters. For bidisperse granular blends, the net charge produced by the mixture is dominated by the component that comes into contact with the walls of the apparatus. This is found to be caused by segregation effects as well as the coating of the larger particles by the smaller ones. We make use of these results to predict the charge generated in mass flow hoppers, and we test these predictions. Finally we examine the effect of grounding the experimental apparatus, and we find that paradoxically, grounding does not prevent charge accumulation.     

Numerical Simulation of Particle Segregation in Bubbling Gas‐Fluidized Beds

A multi‐fluid Eulerian model incorporating the kinetic theory of granular flow is used for the simulation of bubbling fluidized beds containing a binary mixture of Geldart B particles at low gas velocities. The cases of density, size and combined density/size segregation are investigated using computational fluid dynamic simulations. Various expressions for the drag force are evaluated for predicting different segregations. The simulation results show that summation of the particle‐particle drag force, i.e., the “hindrance effect” term, and the Stokes drag of particles, which is modified based on the Wen‐Yu drag model can be used for accurate simulation of a binary mixture of particles differing in size, density, or both. Bed expansion and dimensionless axial segregation profiles of CFD results are compared with the experimental data and good agreement is found.     

Numerical simulation of the flow of a bidisperse granular material in a shaft reactor

The flow of a bidisperse granular material in a vertical cylindrical bunker with a cone discharger is numerically simulated. It is shown that the flow of the fraction of small particles shows different behaviors depending on the size of particles and their weight fraction in the granular material. It is found that there exists a boundary layer in which the flow velocity of the fraction of small particles exceeds its bulk flow velocity. It is also found that the flow velocity of large particles is higher in the presence of the fraction of small particles.     

Segregation under flow of objects suspended in a yield stress fluid and NMR imaging visualisation

This study demonstrates the segregation of spheres suspended in a gelled fluid, in laminar flow, in a sudden expansion. The flow conditions are such that gravity effects are negligible. The spheres are stable in the gel at rest. The upstream pipe diameter is in a ratio of 4:1 to the diameter of the spheres. In these circumstances, the medium is discrete, not continuous. It is shown that the initial conditions and flow kinematics lead to segregation of the matter in the downstream pipe. Nuclear magnetic resonance imaging reveals an organised distribution of the solid matter downstream of the expansion. The effects of volume concentration, geometry and flow velocity were assessed. A model of the phenomenon is proposed.     

Density segregation in vibrated granular beds with bumpy surfaces

Segregation of granular materials by virtue of density or size is a commonly encountered phenomenon in nature. Despite its widespread interest among many researchers in recent years, a complete and unified understanding of granular segregation remains elusive to date. Using molecular dynamics simulations, we report a novel technique of inducing density segregation in a binary mixture of granular materials subjected to vibrations by the use of a bumpy vibrating base. Density segregation in the vertical directions may be induced by oscillating the bumpy base composed of discrete solid particles vertically or horizontally. In both cases, lighter particles tended to rise to the top of the granular bed and form a layer above the heavier particles. We suggest that differences in granular temperature profiles arising from the two different modes of vibrations may play an important role in determining the extent of density segregation occurring in binary granular mixtures. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Shape dependence of resistance force exerted on an obstacle placed in a gravity‐driven granular silo flow

Resistance force exerted on an obstacle in a gravity‐driven slow granular silo flow is studied by experiments and numerical simulations. In a two‐dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate and resistance‐force decreasing rate. The dimensionless number is independent of flow rate. Rather, we find the weak shape dependence of the dimensionless number. This tendency is a unique feature for the resistance force in granular silo flow. It characterizes the effective flow width interacting with the obstacle in granular silo flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3849–3856, 2018     

Simulation study of the effect of wall roughness on the dynamics of granular flows in rotating semicylindrical chutes

A discrete element model (DEM) is used to investigate the behavior of spherical particles flowing down a semicylindrical rotating chute. The DEM simulations are validated by comparing with particle tracking velocimetry results of spherical glass particles flowing through a smooth semicylindrical chute at different rotation rates of the chute. The DEM model predictions agree well with experimental results of surface velocity and particle bed height evolution. The validated DEM model is used to investigate the influence of chute roughness on the flow behavior of monodisperse granular particles in rotating chutes. To emulate different base roughnesses, a rough base is constructed out of a square close packing of fixed spherical particles with a diameter equal to, smaller, or larger than the flowing particles. Finally, the DEM model is used to study segregation in a binary density mixture for different degrees of roughness of the chute. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2117–2135, 2015     

A perspective on vibration-induced size segregation of granular materials

Segregation of particulate mixtures is a problem of great consequence in industries involved with the handling and processing of granular materials in which homogeneity is generally required. While there are several factors that may be responsible for segregation in bulk solids, it is well accepted that nonuniformity in particle size is a fundamental contributor. When the granular material is exposed to vibrations, the question of whether or not convection is an essential ingredient for size segregation is addressed by distinguishing between the situation where vibrations are not sufficiently energetic to promote a mean flow of the bulk solid, and those cases where a convective flow does occur. Based on experimental and simulation results in the literature, as well as dynamical systems analysis of a recent model of a binary granular mixture, it is proposed that “void-filling” beneath large particles is a universal mechanism promoting segregation, while convection essentially provides a means of mixing enhancement.     

Mixing characteristics of wet granular matter in a bladed mixer

We performed numerical simulations of dry and wet granular flow inside a four-bladed mixer using the discrete element method (DEM). A capillary force model was incorporated to mimic the complex effects of pendular liquid bridges on particle flow. The simulations are able to capture the main features of granular flow, which is substantiated by the comparison of our results with experimental data.It was found that mean and fluctuating velocity fields for wet and dry particles differ significantly from each other. Our results indicate a strong increase in heap formation for wet particles and hence velocity fluctuations in the vertical direction become more pronounced. We observe that mixing in bladed mixers is strongly heterogeneous for wet granular matter due to the formation of different flow regimes within the mixer. The analysis of mixing quality shows that the spatial distribution of mixing intensity is influenced by the moisture content. This can lead to locally and even globally higher mixing rates for wet particles compared to dry granular matter.     

Segregation behavior of binary mixtures of cylindrical particles with different length ratios in the rotating drum

Particle shape impacts the flow behavior of granular material but this effect is still far from being fully understood. Using discrete element method, the current work explores the segregation phenomena of the binary mixtures of cylindrical particles (differing in length but with the same diameter) in the three-dimensional rotating drum operating in the rolling regime, with each cylindrical particle fully represented by the superquadric equation. The important characteristics and the effect of length ratio on the flow dynamics of the binary mixtures are discussed. Some trends are in sync with those of binary mixtures of spherical particles. Unique to nonspherical particles is the orientation of particles, with results indicating that the cylindrical particles align their major axes perpendicular to the drum axis and this behavior becomes more significant for large particles when the length ratio increases. The length-induced radial segregation causes the orientation of large cylindrical particles to be less uniform.