Influence of particle shape on mixing rate in rotating drums based on super-quadric DEM simulations

Fundamental research on the flow and mixing of non-spherical particles is critical for industrial production and design. In this paper, the Discrete Element Method (DEM) is used to study the flow and mixing of granular materials in the horizontal rotating drum, and the periodic boundary condition is employed to eliminate end wall effect. Super-quadric elements are adopted to describe spherical and non-spherical particles. The influences of rotating speed, blockiness, and aspect ratio on the mixing rate are investigated by the Lacey mixing index. The results show that the rotating speed has a primary effect on the mixing rate, whereas the effect of the particle shape on the mixing rate is a secondary factor for non-spherical granular systems. Moreover, the mixing rate of spherical and non-spherical particle systems is significantly different. The mixing rate of spheres is the lowest, and the cubes have a higher mixing rate than the cylinders. As the blockiness decreases or aspect ratio deviates from 1.0, the mixing rate decreases. Ordered face-to-face contacts and dense packing structures result in a higher mixing rate. The analysis of kinetic energy shows that particle shape affects the transfer efficiency of external energy to the granular systems. The translational kinetic energy of non-spherical particles is higher than that of spherical particles, and their rotational kinetic energy is lower than that of spheres. Meanwhile, the blockiness enhances the transfer efficiency of external energy to the non-spherical systems; in contrast, the aspect ratio reduces the energy conversion efficiency.     

Segregation behavior of particles with Gaussian distributions in the rotating drum with rolling regime

The mixing and segregation of granular materials are essential to provide valuable insights and references for practical industrial production. In this paper, the segregation behaviors of particles with Gaussian distributions and 40% filling level in the rotating drum with rolling regime were numerically studied by the discrete element method. The effects of rotation speed and particle size parameter λ (size ratio of the largest versus smallest particles) on the segregation behavior (mixing index, segregation rate), flow characteristics (particle velocity and trajectory, gyration degree and radius, particle size distributions) and the microscopic properties (collision, contact force, axial diffusion, and kinetic energy) of granular systems were systematically investigated. The results show that the segregation rate and degree of particles with Gaussian distributions gradually increase with the increase of the rotation speed and particle size parameter λ. The radial and axial segregation patterns become more obvious with the increase of λ. And the variation of the flow characteristics of particles with different sizes in the same system is also inconsistent. The microscopic properties of Gaussian-dispersed particles change with the rotation speed and λ. The rapid radial segregation depends on the larger pores existed in the granular system, which leads to a gradual increase of the axial dispersion coefficient of large particles and a gradual decrease of the axial dispersion coefficient of small particles.     

A device for measuring the concentration and dispersion quality ofmagnetic particle suspensions

A technique, called rheomagnetic measurement, for studying the concentration and orientation of magnetic particles through inductance measurement is presented. The particles are oriented in a predominantly extensional flow field, and, because they are magnetic, their orientation can be detected with a weak magnetic sensing field. Because flocs of magnetic particles orient differently in a flow field than primary particles do, this method can be useful in obtaining information about the particle flocculation aspect of dispersion quality. A magnetic sensing field can also be used to detect the particle concentration in a quiescent flow. Experimental data on the effects of particle concentration and milling for rod-like γ-Fe₂O₃ and plate-like Ba-ferrite suspensions are discussed. The results for Ba-ferrite magnetic markedly contrast with those for the rod-like magnetic particles but showed similarity with those for rod-like γ-Fe₂O₃     

Investigating the fluidization of disk-like particles in a fluidized bed using CFD-DEM simulation

Fluidization of monodispersed disk-like particles with different aspect ratios in the fluidized bed is simulated by CFD-DEM, with disk-like particles being modeled by the super-ellipsoids. The relatively comprehensive investigations are performed in order to understand the fluidization behaviors of disk-like particles and to evaluate how the aspect ratio influences the fluidization. The results obtained demonstrate that disk-like particles with a larger aspect ratio possess stronger particle movement and more apparent fluidization. Comparisons between spherical particles and disk-like particles elucidate their differences in the fluidization behavior. Particle orientation is also investigated in this paper due to its important influence on the fluidization. Particles possess different preferred orientations in the static bed and in the fluidization state, and a reduced aspect ratio can drive particles to be in the preferred orientation. The existence of the walls will prompt particles to align their cross sections to be parallel to the plane of the walls.     

Electro-orientation in particle light valves

Electro-orientation of rod-like particles in liquids, under the application of an external AC field, is analysed. A rod shape is suitable for particle light valve (PLV) applications. When they are aligned with their long axes parallel to the electric field (and the direction of light is assumed to be parallel to the applied electric field), then it can lead to good transmission of light. Various criteria to arrive at appropriate parameters for PLV applications are proposed. It is found that good electric conductors are excellent rod materials for PLV applications. They lead to an appropriate orientation of the rods and at the same time result in maximum orientational torque. Water-like liquids with higher values of permittivity are appropriate choices as suspending liquids since the Brownian dispersion in the presence of the electric field is minimized. The time it takes the rods to fully diffuse in the orientational space, once the electric field is turned off, decreases with decreasing liquid viscosity.     

Modeling the Dynamics of Fabric in a Rotating Horizontal Drum Using the Discrete Element Method

In order to provide a tool for designing more efficient methods of mixing fabric, a simplified discrete element computational model was developed for modeling fabric dynamics in a rotating horizontal drum. Because modeling the interactions between actual pieces of fabric is quite complex, a simplified model was developed where individual pieces of bundled fabric are represented by spherical particles. This model is essentially a ball mill. The simulations are used to investigate fabric bundle kinematics, the power required to drive the rotating drum, and the power dissipated through normal and tangential contacts. Parametric studies were performed to investigate the effects of fill percentage, baffles, rotation speed, friction coefficient, and coefficient of restitution. The simulation results indicate that fill percentage, drum rotation speed, and friction coefficient play significant roles in the fabric bundle dynamics. For example, the specific drum power increases by a factor of 600% to 800% as the fill percentage decreases from 75% to 25%. In addition, the maximum specific drum power occurs at a rotation speed just less than the speed at which centrifuging occurs. The friction coefficient does not play a significant role in the bundle dynamics for values greater than a critical value. The critical value decreases from a value of approximately 0.3 at a 25% fill percentage to 0.05 for a 75% fill percentage. For friction coefficients less than this critical value, the specific power decreases with decreasing friction coefficient. Drum baffles have a minor effect on the power dissipation and kinematics for fill percentages greater than 50%. Bundle size and coefficient of restitution have a relatively weak influence on the measured parameters.     

Modeling the Dynamics of Fabric in a Rotating Horizontal Drum Using the Discrete Element Method

In order to provide a tool for designing more efficient methods of mixing fabric, a simplified discrete element computational model was developed for modeling fabric dynamics in a rotating horizontal drum. Because modeling the interactions between actual pieces of fabric is quite complex, a simplified model was developed where individual pieces of bundled fabric are represented by spherical particles. This model is essentially a ball mill. The simulations are used to investigate fabric bundle kinematics, the power required to drive the rotating drum, and the power dissipated through normal and tangential contacts. Parametric studies were performed to investigate the effects of fill percentage, baffles, rotation speed, friction coefficient, and coefficient of restitution. The simulation results indicate that fill percentage, drum rotation speed, and friction coefficient play significant roles in the fabric bundle dynamics. For example, the specific drum power increases by a factor of 600% to 800% as the fill percentage decreases from 75% to 25%. In addition, the maximum specific drum power occurs at a rotation speed just less than the speed at which centrifuging occurs. The friction coefficient does not play a significant role in the bundle dynamics for values greater than a critical value. The critical value decreases from a value of approximately 0.3 at a 25% fill percentage to 0.05 for a 75% fill percentage. For friction coefficients less than this critical value, the specific power decreases with decreasing friction coefficient. Drum baffles have a minor effect on the power dissipation and kinematics for fill percentages greater than 50%. Bundle size and coefficient of restitution have a relatively weak influence on the measured parameters.     

Numerical study of size-driven segregation of binary particles in a rotary drum with lower filling level

Discrete element method (DEM) simulations of size-driven segregation of binary particles in a rotary drum were conducted to investigate the influence of filling level, size ratio, and rotation speed on the segregation performance. Segregation experiments with different filling levels were used to verify the DEM model and analyze the influence of filling levels on segregation. The granular bed was divided into five layers to study the axial segregation in the rotary drum. The total velocity fluctuation was used to discuss the granular behavior from a mesoscopic perspective. A segregation index was adopted to quantify the segregation performance with different parameters. It was found that binary particles in the drum with different filling levels have different segregation patterns. A core of small particles was formed in the middle of granular bed for the case with a higher filling level, while there is no core formed for the case with a lower filling level. Results obtained indicate that the size-driven segregation in the drum with lower filling level increases with the increase of size ratio. Within the rolling regime, the rotation speed has little influence on the final segregation index of particles.     

Numerical analysis of restitution coefficient,rotational speed and particle size effects on the hydrodynamics of particles in a rotating drum

Hydrodynamic behavior of two dimensional horizontal rotating drum was studied by using finite volume method and granular kinetic theory. In this work, the effects of the different parameters such as rotation speed, restitution coefficient and particle size on the hydrodynamic and especially on the granular temperature of particles were investigated. At first, the results of present work were verified with previous experimental results. Packing limit of 0.6 and restitution coefficient of 0.95 with Gidaspow inter-phase momentum coefficient showed the good agreement with experimental works. It is found that by increasing the restitution coefficient, the granular temperature at different depth of bed increased and affected the hydrodynamic behavior of the bed. Also, particle size and rotation speed directly changed the granular temperature. Moreover, augmentation of the rotation speed leads to increasing the repose angle which caused better mixing of bed, granular temperature rising and consequently particle velocity alteration in the bed.     

棒状SiO_2-TiO_2核壳结构粒子的制备和表征

通过液相法制备棒状SiO2颗粒,研究正硅酸乙酯的浓度和聚乙烯吡咯烷酮的相对分子质量对棒状SiO2颗粒的影响,利用液相沉积法在最优化条件下制备的棒状SiO2颗粒表面均匀包覆TiO2,制备棒状SiO2-TiO2核壳结构粒子,并采用X射线衍射、透射电镜和傅里叶红外光谱等手段对棒状SiO2-TiO2核壳粒子进行表征。结果表明,随着聚乙烯吡咯烷酮相对分子质量的增大,SiO2颗粒由大头针状转变为棒状,随着正硅酸乙酯浓度的增大,棒状SiO2颗粒的长径比变大并出现类球状颗粒;棒状SiO2表面包覆的TiO2为针状,晶型为锐钛矿,包覆厚度为80 nm左右。     

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.     

Experimental investigation on the packed bed of rodlike particles

Rodlike particles have been usually found in industrial applications, such as the straw and needle catalyst in energy and chemical engineering. Compared to spherical particles, rodlike particles exhibit different behaviour in the packing structure due to their rotational movement. In this work, we have experimentally explored the packing structure and its friction factor for fluid flow. The porosity of packing structure generated by two packing methods is measured for four kinds of rodlike particles. The experimental results show that the porosity of bed of rodlike particles in the poured packing is not a monotonic function of the aspect ratio of particles. This is due to the competition between the “self-fitting” effect and excluded effect. The porosity of bed of rodlike particles is more sensitive to the packing method than that of spherical particles. To describe the pressure drop of fluid flow through the packing structure, the Ergun equation is further modified by introducing the modified Reynolds number and Galileo number. By combing the experimental data for packed bed generated by the fluidised packing method, and other experimental work in current literature, a new empirical equation is proposed to predict the friction factor of the packing structure of rodlike particles, in which the effects of the particle orientation and particle shape are both considered by the equivalent sphericity. These experimental results would be of interest from applied standpoints as well as revealing fundamental effects of the aspect ratio of rodlike particles on the packing structure.     

Direct numerical simulation of particulate flows with heat transfer in a rotating cylindrical cavity

The purpose of this work was the direct numerical simulation of heat and fluid flow by granular mixing in a horizontal rotating kiln. To model particle behaviour and the heat and fluid flow in the drum, we solve the mass conservation, momentum and energy conservation equations directly on a fixed Eulerian grid for the whole domain including particles. At the same time the particle dynamics and their collisions are solved on a Lagrangian grid for each particle. To calculate the heat transfer inside the particles we use two models: the first is the direct solution of the energy conservation equation in the Lagrangian and Eulerian space, and the second is our so-called linear model that assumes homogeneous distribution of the temperature inside each particle. Numerical simulations showed that, if the thermal diffusivity of the gas phase significantly exceeds the same parameter of the particles, the linear model overpredicts the heating rate of the particles. The influence of the particle size and the angular velocity of the drum on the heating rates of particles is studied and discussed.     

Dynamic simulation of rod-like and plate-like particle dispersed systems

A particle simulation method (PSM) is presented to simulate the dynamics of rod-like and plate-like particle dispersed systems. In this method, the particle is modeled with arrays of spheres connected by three types of springs. The motion of particles in flow is followed by solving the translational and rotational equations of motion for each constituent sphere. The mobility matrix for each particle is calculated to obtain the hydrodynamic force and torque exerted on each sphere. For the hydrodynamic interaction among particles, the near-field lubrication force is considered. The method was applied to the simulation of the transient behavior of particles in a shear flow by dispersing them into a cell with periodic boundaries. In semi-dilute to concentrated systems, the overshoot of viscosity was observed for rigid rod-like particle dispersed systems, but not for flexible ones. This was due to the transient change of the microstructure from the flow-directional orientation to the planar one of particles. The normal stress appeared in the flexible particle dispersed systems because of the deformation of particles. In the rectangular plate-like particle dispersed system, the planar orientation of particles was observed and furthermore the orientation of the major axis of particles in the shear direction appeared.     

基于离散元法的双组份复合涂料搅拌螺杆参数优化

为了提高双组份复合涂料的混合均匀度，对搅拌螺杆的参数进行优化。以混合销钉式搅拌螺杆为对象，建立其三维模型后导入EDEM软件，然后基于离散元法对双组份复合涂料在该搅拌螺杆中的搅拌过程进行仿真分析，研究了螺杆的转速、螺距和长径比对混合均匀度的影响。最后通过单轴压缩实验对螺杆参数优化后的搅拌效果进行了对比验证。结果表明：螺杆转速、螺距和长径比分别通过改变颗粒抛撒程度、螺旋叶片间隙和螺杆长度来影响复合涂料的混合均匀度；稳定出料后，螺杆转速为200 r/min、螺距为80 mm、长径比为5.57∶1时的搅拌效果最佳；实验验证了利用优化后搅拌螺杆搅拌时复合涂料的力学性能优于手工搅拌时的。研究结果可为自动化搅拌螺杆的结构设计和参数优化提供理论依据。     

CdSe/Cd(x)Zn1-xS core/shell nanocrystals: core morphology and luminescent property

CdSe cores with rod (an aspect ratio of 1.8, d-5 nm) and spherical (an aspect ratio of 1, d-5 nm) morphologies were fabricated by two kinds of organic approaches through adjusting growth processes. Because of large difference of size and morphology, two kinds of cores revealed different absorption spectra. However, these cores exhibited almost same photoluminescence (PL) spectra with a red-emitting PL peak of around 625 nm. This is ascribed that they have a similar size in diameter. A graded Cd(x)Zn1-xS shell of larger band gap was grown around CdSe rods and spheres using oleic acid as a capping agent. Based on the growth kinetics of CdS and ZnS, interfacial segregation was created to preferentially deposit CdS near the core, providing relaxation of the strain at the core/shell interface. For spherical CdSe cores, the homogeneous deposition of the Cd(x)Zn1-xS shell created spherical core/shell nanocrystals (NCs) with a size of 7.1 nm in diameter. In the case of using CdSe cores with rod morphology, the anisotropic aggregation behaviors of CdS monomers on CdSe rods led to the size (approximately 10 nm in diameter) of spherical CdSe/Cd(x)Zn1-xS core/shell NCs with a small difference to the length of the CdSe rod (approximately 8.9 nm). The resulting spherical core/shell NCs created by the rod and spherical cores exhibited almost same PL peak wavelength (652 and 653 nm for using rod and spherical cores, respectively), high PL efficiency up to 50%, and narrow PL spectra (36 and 28 nm of full with at half maximum of PL spectra for the core/shell NCs with CdSe spheres and rods, respectively). These core/shell NCs provide an opportunity for the study of the evolution of PL properties as the shape of semiconductor NCs.     

Depolarization ratios of single ice particles assuming finite circular cylinders

Results of the depolarization ratio (delta) of single ice particles in fixed orientations are presented to determine whether discrimination between nonspherical ice crystals (causing depolarization) and spherical water droplets (inducing no depolarization) can be made. A T-matrix method is used to compute delta over a range of particle diameters from 0.13 to 4 microm and aspect ratios chi=d/h (d is the diameter and h the height of the particle) from 0.3 to 3, where ice crystals are assumed to have a circular cylindrical shape. The depolarization ratio is primarily dependent on the orientation of the particle. Some orientations return no depolarization, whereas others generate values reaching almost delta=1. Considering the depolarization averaged over all orientations, a dependence of delta with the particle size is observed where values close to 0.25 are reached. No strong influence of the aspect ratio on the depolarization for a given particle size of 2 mum is evident, as values remain in a range between 0.2 and 0.3.     

Resistive pulse sensing of analyte-induced multicomponent rod aggregation using tunable pores

Resistive pulse sensing is used to monitor individual and aggregated rod-shaped nanoparticles as they move through tunable pores in elastomeric membranes. By comparing particles of similar dimensions, it is demonstrated that the resistive pulse signal of a rod is fundamentally different from that of a sphere. Rods can be distinguished using two measurements: the blockade event magnitude (Δi(p) ), which reveals the particle's size, and the full width at half maximum (FWHM) duration, which relates to the particle's speed and length. While the observed Δi(p) values agree well with simulations, the measured FWHM times are much larger than expected. This increase in dwell time, caused by rods moving through the pore in various orientations, is not observed for spherical particles. These differences are exploited in a new agglutination assay using rod-shaped particles. By controlling the surface chemistry and location of the capture ligand, rods are made to form either long "end-on-end" or wide "side-on" aggregates upon the addition of an analyte. This observation will facilitate multiplexed detection in agglutination assays, as particles with a particular aspect ratio can be distinguished by two measurements. This is first demonstrated with a biotinylated target and avidin capture probe, followed by the detection of platelet-derived growth factor (PDGF-BB) using an aptamer capture probe, with limits of detection down to femtomolar levels.     

Numerical study of the mixing process of binary-density particles in a bladed mixer

Discrete element method (DEM) simulations of binary mixing of particles with different densities were conducted to study the influence of density ratio, blade speed, and filling level on the particle dynamics and mixing performance in a bladed mixer. Four particles with different densities at different locations were tagged to discuss the influence of three factors on the particle trajectory and velocity field in the mixer. A method based on cubic polynomial fitting of relative standard deviation was used to determine the critical revolution during the mixing process. It was found that the non-dimensional tangential velocity decreases with the increase of the blade speed and filling level, the fluctuation of vertical velocity increases with the radial location, blade speed, and filling level, and it is more pronounced than the fluctuation of tangential and radial velocity during the mixing process. Results obtained indicate that the mixing performance of particles with different density increases with the decrease of density ratio and filling level, while it increases with the increase of blade speed.     

Nanotoxicology: Advanced Optical Imaging Reveals the Dependence of Particle Geometry on Interactions Between CdSe Quantum Dots and Immune Cells (Small 3/2011)

The biocompatibility and possible toxicological consequences of engineered nanomaterials, including quantum dots (QDs) due to their unique suitability for biomedical applications, remain intense areas of interest. We utilized advanced imaging approaches to characterize the interactions of CdSe QDs of various sizes and shapes with live immune cells. Particle diffusion and partitioning within the plasma membrane, cellular uptake kinetics, and sorting of particles into lysosomes were all independantly characterized. Using high‐speed total internal reflectance fluorescence (TIRF) microscopy, we show that QDs with an average aspect ratio of 2.0 (i.e., rod‐shaped) diffuse nearly an order of magnitude slower in the plasma membrane than more spherical particles with aspect ratios of 1.2 and 1.6, respectively. Moreover, more rod‐shaped QDs were shown to be internalized into the cell 2‐3 fold more slowly. Hyperspectral confocal fluorescence microscopy demonstrates that QDs tend to partition within the cell membrane into regions containing a single particle type. Furthermore, data examining QD sorting mechanisms indicate that endocytosis and lysosomal sorting increases with particle size. Together, these observations suggest that both size and aspect ratio of a nanoparticle are important characteristics that significantly impact interactions with the plasma membrane, uptake into the cell, and localization within intracellular vesicles. Thus, rather than simply characterizing nanoparticle uptake into cells, we show that utilization of advanced imaging approaches permits a more nuanced and complete examination of the multiple aspects of cell‐nanoparticle interactions that can ultimately aid understanding possible mechanisms of toxicity, resulting in safer nanomaterial designs.