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.     

RESEARCH ON AN AERODYNAMIC PARTICLE SEPARATOR (THE EPS)

This report presents an account of the research work carried out in support of the development of a new particle separator.* The EPS, as it is designated, produces multiple fractions simultaneously at a high throughput rate. The cut sizes are roughly in the range 10 to 200 µm. The principle is that particles dissimilar with respect to any of size, density, or shape will follow different and distinct trajectories when injected into a uniform laminar flow of air.

The report outlines the theoretical analyses and experimental measurements made to verify the design concepts. A detailed model of the flow field permits the calculation of particle trajectories, and hence the prediction of coarse grade efficiency and sharpness of cut. The measurements made with glass spheres and other irregular particles (e.g., carbon, cement) provide a general verification of the analytical results.

Sharpness of cut values better than 0.8 are achieved down to cut points of about 10µm. Maximum throughput rates are not yet known, but separations have been made at 480 kg/hr in a separation zone 100 mm wide. Scale-up to larger capacity is straightforward.     

Real-time shape-based particle separation and detailed in situ particle shape characterization

Particle shape is an important attribute in determining particle properties and behavior, but it is difficult to control and characterize. We present a new portable system that offers, for the first time, the ability to separate particles with different shapes and characterize their chemical and physical properties, including their dynamic shape factors (DSFs) in the transition and free-molecular regimes, with high precision, in situ, and in real-time. The system uses an aerosol particle mass analyzer (APM) to classify particles of one mass-to-charge ratio, transporting them to a differential mobility analyzer (DMA) that is tuned to select particles of one charge, mobility diameter, and for particles with one density, one shape. These uniform particles are then ready for use and/or characterization by any application or analytical tool. We combine the APM and DMA with our single-particle mass spectrometer, SPLAT II, to form the ADS and demonstrate its utility to measure individual particle compositions, vacuum aerodynamic diameters, and particle DSFs in two flow regimes for each selected shape. We applied the ADS to the characterization of aspherical ammonium sulfate and NaCl particles, demonstrating that both have a wide distribution of particle shapes with DSFs from approximately 1 to 1.5.     

Effect of shape of HZ liquid bridge on particle accumulation structure (PAS)

We focus on the dynamic particle accumulation structure (PAS) due to thermocapillary effect in a half-zone liquid bridge. Effects of shape of liquid bridge upon shape of the PAS itself and motion of particle on the PAS are discussed in the present study by tracking particles in the liquid bridge and by measuring temperature over the free surface. It is found that the variation of the shape of the liquid bridge leads to a significant variation of the temperature gradient on the free surface, which results in difference of the shape of the PAS. The variation of the PAS shape is mainly explained by drastic change of the axial velocity of the particle and less change of its azimuthal velocity near the free surface.     

Orientation dependence in near-field scattering from TiO(2) particles

This scattering of light by small particles embedded in a continuous transparent medium is influenced not only by the bulk optical properties of the particles and the medium but also by the size, shape, and spatial arrangement of the particles-that is, by the microstructure. If the particles are close together, as in agglomerated coatings or stereolithographic suspensions, interactions between the radiation fields of adjacent particles can lead to variations in the magnitude and spatial arrangement of the scattered light in the near and the far field, which can affect the color and hiding power of a coating, the cure depth and homogeneity in stereolithography, and the threshold intensity for stimulated emission in random lasers. Our calculations of the near- and the far-field scattering distribution for 200-nm TiO(2) spheres in pairs of various orientations and in an ordered array of five particles show that, depending on the orientation of the particles with respect to the incident light, these interactions can either increase or decrease the scattering efficiency, the isotropy of the scattering, and the magnitude of the electric field strength within the matrix and the particles. In the mid-visible range, two particles in line increase the backscattering fraction by 28% and the scattering strength by 38% over that of a single particle, whereas if the particles are in the diagonal configuration the backscattering fraction and scattering strength are actually reduced by addition of the second particle. At shorter or longer wavelengths the backscattering fraction is reduced regardless of the location of the second particle, by as much as 60% when five particles are arranged in the zigzag configuration. These results are surprising in that it is generally assumed that multiple scattering enhances backscattering. Simple models of multiple scattering or scattering of two particles as a single, larger particle are inadequate to explain these results.     

3D analytical mathematical models of random star-shape particles via a combination of X-ray computed microtomography and spherical harmonic analysis

To compute any physical quantity for a random particle, one needs to know the mathematical shape of the particle. For regular particles like spheres and ellipsoids, the mathematics are straightforward. For random particles, with realistic shapes, mathematically characterizing the shape had not been generally done. But since about the year 2002, a method has been developed that combines X-ray computed tomography and spherical harmonic analysis to give analytical, differentiable mathematical functions for the three-dimensional shape of star-shape particles, which are a wide class of particles covering most industrial particles of interest, ranging from micrometer scale to millimeter scale particles. This review article describes how this is done, in some detail, and then gives examples of applications of this method, including a contact function that is suitable for these random shape particles. The purpose of this article is to make these ideas widely available for the general powder researcher who knows that particle shape is important to his/her applications, and especially for those researchers who are just starting out in their particle science and technology careers.     

Mesoscopic particulate system assembled from three-dimensional irregular particles

Particles around us are generally in the form of irregular characteristics in shape and size. Establishing rational mesoscale models that are suitable for different types of particles is of great significance to comprehensively evaluate the mechanical properties of particulate systems assembled from irregular particles. The preponderances of previous works are mainly focused on particle simulations using regular-shaped geometries or simple polyhedrons, and little is known about quantitative characterization for the particles with complex shape characteristics. In this paper, a series of novel and efficient algorithms are presented to generate three-dimensional particulate systems assembled from particles with irregular characteristics in shape and size. According to the developed particle generation algorithm and vector-growth algorithm, the convex- and concave particles with different shape- and size configurations are obtained. Parametric analysis of corresponding algorithm parameters on the shape- and size configurations of particles are quantitatively investigated in terms of different indexes, such as sphericity, angularity and size, which provides an important guidance for the shape- and size control of irregular particles. Based on the generated irregular particles, a series of algorithms are proposed to generate the particulate systems with random spatial characteristics as well. Employing the developed compaction algorithm, mesoscopic particulate systems with different particle gradations and compactness are generated precisely. To sum up, the present particle model provides insights into capturing and studying the meso-structure characteristics and macroscopic mechanical properties of particulate systems.     

Discrete element model study into effects of particle shape on backfill response to cyclic loading behind an integral bridge abutment

The discrete element method, implemented in a modular GPU based framework that supports polyhedral shaped particles (Blaze-DEM), was used to investigate effects of particle shape on backfill response behind integral bridge abutments during temperature-induced displacement cycles. The rate and magnitude of horizontal stress build-up were found to be strongly related to particle sphericity. The stress build-up in particles of high sphericity was gradual and related to densification extending relatively far from the abutment. With increasing angularities, densification was localised near the abutment, but larger and more rapid stress build-up occurred, supported by particle reorientation and interlock developing further away.     

The smooth piecewise polynomial particle shape functions corresponding to patch-wise non-uniformly spaced particles for meshfree particle methods

In the previous papers (Kim et al. Submitted for publication, Oh et al. in press), for uniformly or locally non-uniformly distributed particles, we constructed highly regular piecewise polynomial particle shape functions that have the polynomial reproducing property of order k for any given integer k ≥ 0 and satisfy the Kronecker Delta Property. In this paper, in order to make these particle shape functions more useful in dealing with problems on complex geometries, we introduce smooth-piecewise-polynomial Reproducing Polynomial Particle shape functions, corresponding to the particles that are patch-wise non-uniformly distributed in a polygonal domain. In order to make these shape functions with compact supports, smooth flat-top partition of unity shape functions are constructed and multiplied to the shape functions. An error estimate of the interpolation associated with such flexible piecewise polynomial particle shape functions is proven. The one-dimensional and the two-dimensional numerical results that support the theory are resented. June G. Kim is Visiting Professor of the University of North Carolina at Charlotte.     

SiCp／Al基复合材料中增强颗粒统计特征的定量化研究

基于微观组织对SiC颗粒增强铝基复合材料中SiC颗粒的特征做统计性的定量分析,研究了SiC颗粒的形状、光滑度以及粒度等特征分布规律。结果表明：增强颗粒的形状因子在正方形（1：1）与长方形（1：2）之间,且表面光滑程度相似。粒径范围为1-12μm之间,大小分布规律可用GaussAmp函数表示,位置分布带有明显的团聚特征。根据所获得的颗粒统计特征规律建立了基于视场的胞元模型,其视场范围为295μm×190μm。颗粒的形状视作长方形,边长分别为5μm和7．5μm,颗粒的面积百分数为19．09％,颗粒呈带状分布,所划分的四个区域内颗粒的个数分别为29、126、105、25。     

Effects of bottom profile on the circulation and classification of particles in cylindrical hydrocyclones

The cylindrical hydrocyclone has been increasingly used in coarse classification due to its reduced fine particle entrainment, but the loss of coarse particles to overflow remains an intractable problem. Based on the notion that the strong circulation flow caused by the flat bottom structure bears primary responsibility for the problem, this study designs eight unique bottom profiles to regulate the particle circulating flow and attempts to correlate particle circulation flow with classification performance. The effects of the bottom profile on flow field characteristics, particle spatial distribution, circulation flow rates, and grade efficiency are explored in detail using validated models in a Φ200 mm cylindrical hydrocyclone. The findings suggest that bottom profiles have the greatest effect on the axial velocity near the bottom and the grade efficiency of intermediate and coarse particles, while all unique designs have the potential to lower turbulence intensity. An ascending segment near the wall or a descending segment near the axis can help to mitigate the misplacement of coarse particles by reducing particle circulation flow without affecting the entrainment of fines appreciably. Additionally, two circles are found on each side of the cut plane, which is conducive to releasing coarse particles from the circulation flow. Regulation of particle circulation flow by adjusting bottom profile parameters can improve separation performance.     

Influence of pile shape and pile interaction on the crushable behavior of granular materials around driven piles: DEM analyses

This study presents an analysis and a visualization of the effect that the pile shape has on the penetration resistance of driven piles in crushable granular materials. Discrete Element Method (DEM) simulations of single piles with different shapes (flat tip, open pile, triangular tip) being driven into a previously compacted uniform crushable soil are presented. The results from the DEM simulations showed that the shape of the driven piles has a significant influence on the development of penetration resistance and particle crushing. This study also presents the penetration resistance and particle crushing results when a second flat tip pile was driven in a region near a pre-existing single flat tip pile. It was found that considerable high crushing was induced by the second pile. The second pile induced crushing not only on the particles surrounding itself but also on the particles surrounding the pre-existing pile, showing that particle crushing around a driven pile not only takes place when the pre-existing pile is being driven, but it also occurs during the installation of a second pile, in a region closely located to the first one.     

Experimental and numerical investigation of effects of particle shape and size distribution on particles’ dispersion in a coaxial jet flow

In this study, an experimental and a numerical investigations are performed to investigate the effect of particle’s shape and size distribution on its dispersion behavior. Firstly, particle dispersion of pulverized coal and spherical polymer particles is observed by Particle Image Velocimetry (PIV) technique in the experiment. Secondly, a simulation is performed to analyze the particle dispersion in detail. Spherical and spheroidal motion models are applied to particle’s movement to investigate the shape effect. Furthermore, monodisperse and polydisperse for particles are applied to investigate the size distribution effect on the dispersion. Experimental results show that in the jet turbulence flow, pulverized coal particles, which have complex shapes and various sizes, have quite different dispersion behavior compared to spherical particles. In terms of the results of the simulation, this difference is mainly caused by the size distribution effect. Although particle’s shape affects the dispersity, it is weakened by the size distribution effect.     

Micromagnetic investigation by a simplified approach on the demagnetization field of permanent magnets with nonmagnetic phase inside

A simplified analysis method based on micromagnetic simulation is proposed to investigate effects of nonmagnetic particles on the demagnetizing field of a permanent magnet. By applying the additivity law of the demagnetizing field, the complicated demagnetizing field of the real magnet could be analyzed by only focusing on the stray field of the reserved magnet. For a magnet with nonmagnetic particles inside, the particle size has no significant effect on the maximum value of the demagnetization field, but the area of the affected region by the particle is proportional to the particle size. A large particle produces a large affected area overlapped with those influenced by other particles, which leads to the large demagnetization field. With increasing the length of the particle along the magnetization direction, the demagnetization field on the pole surface increases. The pole surface with a convex shape will increase the demagnetization field. The demagnetizing field near the nonmagnetic particle will be further increased by the large macroscopic demagnetizing field near the pole surface. This work suggests some practical approaches to optimize the microstructure of permanent magnets.     

Particle Shape Discrimination Using Slotted Sieves

A set of sieves having rectangular apertures has been used, with a set of square-mesh sieves, to separate powder particles according to their shape. A free-flowing granular material, sodium perborate tetrahydrate, was shape-sorted using the slotted sieves and also using an inclined, vibrating deck.

The length, width, thickness, projected area diameter and equivalent volume diameter were determined for each shape-fraction and these data were used to calculate shape factors to assess the performances of the two methods

It was found that both methods were capable of sorting the material according to particle shape. The deck was capable of a slightly higher throughput, but the sieves were more selective as well as being quantitative with respect to two of a particle's three principal dimensions.     

A terminal-velocity model for super-ellipsoidal particles

The prediction of the terminal velocity of non-spherical particles, such as sediments and microplastics, is essential for understanding their transport processes in rivers or marine environments. However, most of the existing models have been proposed based on specific particle materials, and there is a lack of systematic research on the effects of different shape factors on terminal velocity. In this study, super-ellipsoidal particles were selected as test particles for settling experiments, and a particle–velocity tracking code was developed to measure their terminal velocities during falling through glycerin–water mixtures. A terminal–velocity model for super-ellipsoidal particles was proposed based on the measured data. Owing to the new model, multivalued predictions of the terminal velocity based on a single shape factor, such as sphericity and Corey shape factor, were disclosed, and the prediction errors were evaluated. The results of this study can provide a basis for establishing a general terminal–velocity model that considers the influence of particle shape.     

A pi-shaped ultrasonic tweezers concept for manipulation of small particles

A pi-shaped ultrasonic actuator is proposed for the noncontact trapping, extraction, and transportation of small particles. In this actuator, two metal plates clamp a multilayer piezoelectric vibrator by a small bolt, and the metal plates are tapered in their lower parts so that a vibration gradient can be obtained. The flexural vibration of the metal plates is used to generate a sound field in the gap between the two tapered metal plates. At a driving frequency of about 152.8 kHz, shrimp eggs, grass seeds, thyme seeds, rice powder, fine salt, and fine sugar, which have an average diameter from several tens of micrometers to several hundreds of micrometers, can be trapped stably without contact with the actuator, and the particles insoluble in water can be extracted from water and transported in water by the actuator. In the noncontact trapping of small particles, the positions of trapped particles as well as the relationship among the number of trapped particles, vibration velocity, and input power are investigated. The number of trapped particles increases as the vibration velocity or input power increases. However, when the vibration velocity or input power is too large, the particles may be ejected out of the actuator and, therefore, cannot be stably trapped. The minimum vibration velocity to trap small particles increases as particle density increases for the particles that have the shape near to a sphere and a proper density. In the extraction of small particles from water, the relationship between the number of extracted thyme seeds and the input power is investigated. Increasing the input power can increase the extracted thyme seeds. However, there is a maximum particle number that can be extracted from water. In the transportation of thyme seeds in water, the dependence of the particle loss during the transportation on the speed and distance of transportation and the input power is experimentally estimated. As the distance and speed of transportation increase, the particle loss during the transportation increases. Increasing the input power increases the trapping effect and, therefore, decreases the particle loss.     

Monitoring particle adsorption by use of laser reflectometry near the critical angle

We investigate the use of laser reflectometry near the critical angle to monitor particle adsorption onto a flat glass surface. Experimental results show that positive particles are adsorbed onto the glass surface and that their adsorption kinetics depend strongly on the volume fraction occupied by the particles in suspension but not appreciably on the particle size. The reflectance near the critical angle is dominated by the particles on the surface, with the contribution of the particles in suspension being very low. We compare the reflectance change near the critical angle with the change in reflectance near the Brewster angle when particles are adsorbed onto the glass surface. We find that reflectometry near the critical angle is 3000 times more sensitive than it is near the Brewster angle. Some optical images are presented to validate our results.     

Numerical study of the motion behaviour of three-dimensional cubic particle in a thin drum

The motion of three-dimensional cubic particles in a thin rotating drum is simulated by the SIPHPM method. The drums with frictional or smooth front and rear walls, and the particles of cubic and spherical shapes, and different particle numbers are considered to study the effect of cubic particle shape, end-wall frictions and filling levels. Different flow patterns of cubic particles are observed, which are significantly dominated by the friction from the end-walls. The probability density function of velocity components, the flatness factors are used to analyze the motion behaviour of cubic particle. The Froude number, ensemble mean and time averaged particle velocities are also analyzed. A primary and secondary mode of driving from the end-wall frictions are indicated and the mechanisms on the influences of wall friction, particle shape and filling levels are fully explained.