Modeling of the “fish-hook” effect in a classifier

On the basis of the kinematic model of entrainment of small particles by large ones the abnormally nonmonotonic dependence of the separation curve on the particle size is explained. The influence of the particle density, the classifier length, the split-parameter, and the average size of particles on the depth of the “fish-hook” effect has been investigated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 1, pp. 60–69, January–February, 2007.     

Motion of a “drift island” in a toroidal magnetic confinement device with Coulomb scattering of the particles

A resonant drift trajectory of a charged-particle in a magnetic field (a “drift island”) can be used to remove high-energy impurities from a thermonuclear plasma and to introduce (inject) high-energy particles into the plasma. As a rule, these effects are studied neglecting the Coulomb scattering, i.e., in the collisionless approximation. In the present letter, the effect of Coulomb scattering of a particle with a resonant trajectory by plasma particles is studied. The conditions under which the drift resonance is maintained are found, i.e., the plasma densities and plasma density profiles for which the “drift island” can still move over the transverse section of the plasma are determined. Pis’ma Zh. Tekh. Fiz. 25, 19–27 (September 26, 1999)     

Generation of porous particle structures using the void expansion method

The newly developed “void expansion method” allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller “void-particles”. Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles’ mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.     

Impact of powder composition on processing-relevant properties of pharmaceutical materials: An experimental study

In this work, we studied the influence of powder composition on packing density and other processing-relevant properties of binary mixtures, including powder flowability. Binary mixtures of pharmaceutical powders with different particle size ratios, α and varying fractions of large and small particles were analyzed systematically. Mixtures of three excipients and one API with different composition (2, 5, 10, 30, 50, 70, 90, 95 and 98 wt%) were prepared in a Turbula mixer. Powders with different properties and particle size distribution were chosen, in order to obtain three binary mixtures with different size ratios. Then, macroscopic powder properties including bulk (poured) and tapped density (BD and TD) were measured. A powder rheometer was used to measure the flow function coefficient (ffc), cohesion, compressibility and permeability of the binary mixtures. We considered experimentally three classes of binary mixtures, which are characterized by two critical ratios of particle diameter: the critical size ratio of entrance (α_c) and the critical size ratio of replacement (α_r), where α_c = 0.154 and α_r = 0.741. Below the critical size ratio of entrance (α_c), the particle asymmetry (ratio between large and small particle diameters) is high and small particles can fill the voids between larger ones. Between α_c and the critical size ratio of replacement (α_r), the smaller particles are too large to fit in the voids between larger particles (packing structure changes). Above α_r, the particles are more or less symmetric in size and overall packing structure does not change by mixing the particles. Our experiments show that there is a non-linear and non-monotonic dependence of all relevant properties on composition for powder mixtures that have an α < α_r. This non-linear behavior is even more significant for strongly asymmetric binary mixtures with α < α_c. We argue that this behavior is related to the composition dependence of random packing of particulate systems. Our results have relevance to pharmaceutical particle processing operations where constant powder mixture properties are needed to ensure quality standards are met; such operations include capsule or die filling during tableting, and the continuous feeding of powders via screw feeders. Our results suggest that for pharmaceutical particle processing operations, where constant powder mixture properties are a prerequisite for process robustness, the size ratio of API and excipient particles, α should not be smaller than α_r = 0.741.     

Effect of the particle size ratio on the structural properties of granular mixtures with discrete particle size distribution

In this study, the discrete element method was used to examine the structural properties and geometric anisotropy of polydisperse granular packings with discrete uniform particle size distributions. Confined uniaxial compression was applied to granular mixtures with different particle size fractions. The particle size fraction (class) was defined as the fraction of the sample composed of particles with a certain size. The threshold value of number of particle size fractions (i.e., the value above which structural properties of assemblies remain constant) was determined. The effect of heterogeneity in particle size on the critical value of number of particle size fractions was investigated for packings with different ratios between diameters of the largest and smallest grains. The threshold number of particle size classes decreased from five to three as the diameter ratio between the largest and smallest grains increased. Regardless of the diameter ratio, the critical number of particle size fractions (above which the packing density and coordination number of the granular mixtures remained constant) was determined to be five. The study has also shown an increase in packing density of binary mixtures with particle size ratio increasing up to 2.5, which was followed by decrease in density of mixtures with larger particle size ratios, which has not so far been reported in the literature.     

A packing algorithm for three-dimensional convex particles

Simulation of granular particles is an important tool in many fields. However, simulation of particles of complex shapes remains largely out of reach even in two-dimension. One of the major hurdles is the difficulty in representing particles in an efficient, flexible, and accurate manner. By representing particles as convex polyhedrons which are themselves the intersection of a set of half spaces, we develop a method that allows one to efficiently carry out key operations, including particle–particle and particle–container wall overlapping detection, precise identification of the overlapping region, particle shifting, particle rotation, and others. The simulation of packing 1,000 particles into a container takes only a few minutes with this approach. We further demonstrate the potential of this approach with a simulation that re-generates the “Brazil nut” phenomenon by mixing and shaking particles of two different sizes.     

粉体堆积密度的理论计算

考察了紧密堆积时多级理想球形颗粒混合粉体的堆积密度的理论值与粒级组分数的关系,紧密堆积时颗粒的粒度分布特征,以及堆积密度的理论值与单一粒径粉体空隙体积分数、颗粒干扰宽度的相关关系。研究表明,原始堆积密度越大,多粒级理想球形颗粒混合粉体达到相同的堆积密度所需的粒级数越少,各粒级的体积含量随着粒级的增加呈指数下降,且原始堆积密度越大,下降速度越快;其粒度分布符合对数正态分布;堆积密度的理论值与单一粉体空隙体积分数、颗粒干扰宽度的符合二元二次非线性关系。     

Light penetration through a single-row layer of dielectric particles

Light penetration through a layer of cubic dielectric particles was studied by the method of microwave physical modeling. The effect of an increase in the layer transmission (“clarification”) with increasing particle packing density was observed. Conditions for which the coefficient of directed transmission of a singlerow layer turns zero are determined.     

The role of friction in mixing and segregation of granular material

We use discrete element modelling to investigate the processes of mixing and size segregation in a polydisperse mixture of spherical particles in a three-dimensional rectangular box and analyze the influence of friction between the particles on segregation. The packed bed is stirred by a rectangular bar moving periodically in the horizontal direction. The parameters were introduced to characterise the segregation and mixing intensities, and a differential equation was proposed to describe the evolution of segregation intensity approaching exponentially a certain steady state value. It was found that the dynamic friction coefficient has a non-monotonous influence on the processes of mixing and size segregation in poly-disperse granular systems. Critical value of the dynamic friction coefficient μ_crit was identified. For the values of friction μ > μ_crit, behaviour of granular material can be characterised as a “laminar” flow with dominating convective motion of packed bed. For values of friction μ < μ_crit, behaviour of granular mattter can be characterised as “turbulent” flow with dominating “local” mixing inside the packed bed.     

Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

The term “discrete element method” (DEM) in engineering science comprises various approaches to model physical systems by agglomerates of free particles. While shapes, sizes and properties of particles may vary, in most DEM models, particles are not confined by constraints, but subject to applied forces derived from potential fields and/or contact laws. This general approach allows for widespread use of DEM models for physical phenomena including gas dynamics, granular flow, fracture and impact analysis. However, its characteristic feature, combining particle restraints and forces into applied forces, does not only provide for flexible adaption of DEM to different physics, but also creates the most limiting restriction: Evaluation of the applied forces for each particle is computational expensive restraining the time sequence and sample size for numerical analyses. As an ansatz to circumvent this obstacle for a class of DEM models, we propose a model order reduction method based on coherency in the dynamics of particles. While initial flexibility of DEM is conserved, computational effort can be reduced significantly.     

A particle packing model for sand–silt mixtures with the effect of dual-skeleton

The study of particle packing models for binary mixtures is important in the field of granular materials, from both theoretical and practical perspectives. A number of particle packing models have been developed for predicting packing density (or void ratio) of a binary mixture. However, the measured results and the predicted values do not always agree with each other, particularly in the range of fines content between 25 and 50%. It is postulated herein that the discrepancies between the measured results and the predicted values are primarily due to the incorrect assumptions used in the existing models. In the existing models, the packing density is determined from one of the following two assumed mechanisms of particle mixing: (1) the mixed packing has a dominant large-particle skeleton and the small particles fill the voids of the large-particle skeleton, or (2) the mixed packing has a dominant small-particle skeleton and the large particles are embedded in the small-particle skeleton. It is obvious that the first assumed mechanism is only applicable for mixtures with low fines content, whereas the second assumed mechanism is only applicable to mixtures with high fines content. Therefore, the predictions from existing models are unsuitable for mixtures with medium fines content, such as a mixture of fines content between 25 and 50%. In this study, a 3-D discrete element simulation is carried out to show that, for a mixture of medium fines content, the packing structure has a dual-skeleton, which is neither dominated by a large nor small-particle skeleton. Then, we postulate that, in the mixed packing, both mechanisms can take place: filling of small particles and embedment of large particles. The concepts of “dual-skeleton index” and “index size” are proposed to account for the interactive effects of filling and embedment. Based on this postulation, we develop an analytical method, which has the capability of predicting minimum void ratio for sand–silt mixtures with various fines contents. The developed model is then validated by the experimental results obtained from 16 types of sand–silt mixtures.     

A comparison of data structures for the simulation of polydisperse particle packings

Simulation of particle packings is an important tool in material science. Polydisperse mixtures require huge sample sizes to be representative. Simulation, in particular with iterative packing algorithms, therefore requires highly efficient data structures to keep track of particles during the packing procedure. We introduce a new hybrid data structure for spherical particles consisting of a so‐called loose octree for the global spatial indexing and Verlet lists for the local neighbourhood relations. It is particularly suited for relocation of spheres and contact searches. We compare it to classical data structures based on grids and (strict) octrees. It is shown both analytically and empirically that our data structure is highly superior for packing of large polydisperse samples. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental study on the packing densification of mixtures of spherical and cylindrical particles subjected to 3D vibrations

To identify the dense packing of cylinder–sphere binary mixtures (spheres as filling objects), the densification process of such binary mixtures subjected to three-dimensional (3D) mechanical vibrations was experimentally studied. Various influential factors including vibration parameters (such as vibration time t, vibration amplitude A, frequency ω, vibration acceleration Γ) as well as particle size ratio r (small sphere vs. large cylinder), composition of the binary mixtures X_L (volume fraction of cylinders), and container size D (container diameter) on the packing density ρ were systematically investigated. The results show that the optimal vibration parameters for different binary cylinder–sphere mixtures are different. The smaller the size ratio, the less vibration acceleration is needed to form a stable dense packing. For each binary mixture, high packing density can be obtained when the volume fraction of large cylindrical particles is dominant. Meanwhile, increasing the container size can decrease the container wall effect and get higher packing density. The proposed analytical model has been proved to be valid in predicting the packing densification of current cylinder–sphere binary mixtures.     

牙科复合树脂中无机填料双峰混合体的堆积性能

通过测定用作牙科复合树脂中无机填料的粉体的振实密度 ,使用Mathematica和SAS/STAT软件 ,用统计学的方法得到了双组分粉体混合物的粒度分布与堆积体比容之间关系的经验公式。说明可以使用引入了粒度分布宽度作为变量的改良线性堆积模型预测双峰粉体的堆积密度。结论为双组分粉体大小粒径比相差越大 ,混合物堆积密度越高。该结论为优化牙科复合树脂的组成提供了理论依据     

On close relations of local likelihood density estimation

Summary Recent papers of Copas (1995), Hjort and Jones (1996) and Loader (1996) have developed closely related methods for “local likelihood” density estimation. In various places, however, a more “simple-minded” and explicit analogue of local polynomial fitting in regression has been proposed for density estimation. By introducing the usual kind of binning procedure into Hjor and Jones' method, it is shown how the more and less sophisticated versions can be reconciled. Also, we attempt to understand better the role of the attractive subclass of local likelihood methodology proposed by Loader. Finally, we look at a further subset of methods and make some theoretical comparisons between members of this class.     

Fragments spawning and interaction models for DEM breakage simulation

Particles breakage occurs in many industrial applications. During the last decade many works have been devoted for modelling and simulating such processes. A new and innovative procedure of empirical comminution functions for Discrete Element Method (DEM) simulations (Kalman et al. in Granul Matter 11(4):253–266, 2009) posed the question how to introduce the fragments of the broken particle back into the computational domain. Daughter particles (Fragments) spawning and interaction imposes several problems during DEM simulation. Some of the main problems are: seeding (allocating) daughter particles and their initial conditions i.e. fragments locations, velocities and physical properties. This work focuses on the daughter particles seeding and the interaction between “sibling” particles for spherical particles. Fragments spawning and interaction algorithm for particle breakage during DEM simulation was developed. The algorithm enables prediction of particle comminution/attrition processes using DEM applications. The new algorithm can utilize any breakage function allowing unlimited fragment size fractions. In the proposed model, sibling particles can overlap without increasing the energy of the system in the simulation. Particle-particle and particle-wall interactions are calculated using the standard DEM calculations. Daughter particles interactions were calculated using the developed temporary contact radius model. The model was utilized to predict particle comminution in jet milling and particle attrition during pneumatic conveying with great successes.     

Predicting porosity of binary mixtures made out of irregular nonspherical particles: Application to natural sediments

Predicting porosity or packing density of sediments made of coarse and fine components of arbitrary geometry is critical to many science and engineering applications. Well-established analytical models for packing of spheres express porosity of the binary mixture as a function of fine-to-coarse particle size ratio. Nevertheless, the applicability of such models to natural granular materials is limited given the nonspherical and irregular nature of the particles whose packing depends on both particle size and shape. The objective of this study is to develop a model that predicts the porosity of binary mixtures made up of irregular nonspherical particles. We modified a previously developed linear sphere-packing model so that it takes into account the effect of both the particle size and shape. As an input, the modified model uses the coarse-to-fine particles specific surface area ratio instead of using the particle size ratio required by the sphere-packing model. We tested the modified model by predicting the porosities of a binary mixture composed of coarse and fine calcite aggregates. We further validate the model by using published data on the porosity of binary mixtures made of synthesized, cubical and cylindrical particles. Our model predictions show good agreement with the measured porosity.     

Low frequency dielectric spectroscopy characterization of microcrystalline cellulose, tablets and paper

Cellulose fibres and particles in the form of powder, tablets and paper sheets have been investigated by very low frequency dielectric spectroscopy using a novel form of dielectric cell, in which two planar electrodes have been mounted in fixed positions at right angles. The broad pattern of response obtained from the samples is independent of the structural form of the cellulose sample, a loss peak in the 0.1–100 Hz range, and at lower frequencies a dispersion process which is dominated by an imperfect charge transport. Moisture has a significant influence on the rate of charge transport. In dry samples the dipolar loss peak was not evident but as the moisture content increased it appeared. Using a humidity normalizing technique the dielectric response for microcrystalline cellulose has been characterized over the equivalent of 14 decades in frequency. It has also been shown that there is a linear response between the capacitance and the density of microcrystalline cellulose samples. The consolidation of powder into tablets is discussed with respect of the observations of changes in capacitance, loss peak frequency and imperfect charge transport efficiency. Furthermore it was found possible to investigate differences between the dipolar relaxation rate “in” and “out” of the plane of paper in the stack. The relaxation time for dipoles “out” of the paper plane is 7 to 8 times longer than for dipoles “in” the paper plane. This revised version was published online in November 2006 with corrections to the Cover Date.     

CFD-DEM numerical study on air impacted packing densification of equiaxed cylindrical particles

A CFD-DEM model was developed to reproduce the packing densification process of mono-sized equiaxed cylindrical particles under air impact. The effects of operating parameters on packing density were firstly studied. Then various microscopic properties of packing structures such as coordination number (CN), contact types, particle orientations, pore features were characterized and compared. And corresponding densification mechanisms were analysed based on particle motion behaviour, local structure evolution, and forces. Results indicate that the air impact can realize the packing densification of cylindrical particles under appropriate conditions. The pore size distribution in the packing of cylindrical particles shows a tail at larger pore sizes compared with that in the packing of equal spheres. Both the size and the sphericity of the pores decrease in the final dense packing; also, more surface-surface and less surface-edge contacts between two particles therein can be formed. More cylindrical particles tend to be in parallel or perpendicular contact with each other to form more stable local structures during air impact. Most particles at higher position move down (direction of gravity/air impact) with about one particle length during the densification process and most particles exhibit translational motion to realize the local rearrangement for pore filling through air impact induced inter-particle forces.     

Note on Niederreiter-Xing's Propagation Rule for Linear Codes

We present a simple construction of long linear codes from shorter ones. Our approach is related to the product code construction; it generalizes and simplifies substantially the recent “Propagation Rule” by Niederreiter and Xing. Many optimal codes can be produced by our method. Received: June 23, 2000