Constriction-Based Retention Criterion for Granular Filter Design

The filter design criteria in practice are currently based on laboratory tests that were carried out on uniform base soil and filter materials. These criteria mostly involve specific particle size ratios, where the system of base soil and filter is represented by some characteristic particle sizes. Consequently, these criteria have limitations when applied to nonuniform materials. In filters, it is the constriction size rather than the particle size that affects filtration. In this paper, a mathematical procedure to determine the controlling constriction size is introduced, and subsequently, a constriction-based retention criterion for granular filters is presented. The model also incorporates the effect of nonuniformity of base soil in terms of its particle size distribution, considering the surface area of the particles. The proposed retention criterion is verified based on experimental data taken from past studies plus large-scale filtration tests carried out by the authors. The model successfully and distinctly demarcates the boundary between effective and ineffective filters in the case of cohensionless base soils.     

Effect of Particle Grading on the Response of an Idealized Granular Assemblage

The effects of particle-size distribution on a granular assemblage’s mechanical response were studied through a series of numerical triaxial tests using the three-dimensional (3D) discrete-element method. An assemblage was formed by spherical particles of various sizes. A simple linear contact model was adopted with the crucial consideration of varying contact stiffness with particle diameter. Numerical triaxial tests were mimicked by imposing axial compression under constant lateral pressure and constant volume condition, respectively. It was found that an assemblage with a wider particle grading gives more contractive response and behaves toward strain hardening upon shearing. Its critical state locates at a lower position in a void ratio versus mean normal stress plot. Nevertheless, no obvious difference in the critical stress ratio was shown. Model constants in a simple but efficient phenomenologically based granular material model within the framework of critical-state soil mechanics were calibrated from the numerical test results. Results show that some model constants exhibit linear variation with the coefficient of uniformity whereas others are almost independent of particle grading. This investigation provides an opportunity to better understand the implications and meanings of model constants in a phenomenologically based model from the microscale perspective.     

FACTORS AFFECTING THE COMPACTION OF TUNGSTEN POWDERS

Abstract

It is difficult to form tungsten powders into compacts by pressure-forming methods. The brittleness of the powder particles causes them to fracture under pressure instead of producing the typical “point welds” exhibited by more ductile particles. Because of this, the powder characteristics such as particle size, size distribution, and particle shape play a most important role in the compacting of tungsten powders.

Both regular- and irregular-shaped particles of tungsten powder are discussed as regards the formation of strong and dense compacts from these powders. Powders composed of irregular-shaped particles gave stronger, but less dense compacts. The effects of particle size and particle-size distribution are also considered. Each of these factors has individual as well as combined effects. It was found that certain critical particle-size distributions produced the densest compacts.

It is concluded that interlocking of particles, which is brought about by surface irregularities, and interfit, which is determined by correct particle-size distribution, are the determining factors in the compaction of tungsten powders.     

Image-Based System for Particle Counting and Sizing

A procedure is developed to provide measurements of particle size by adapting parts of a commercially available particle image velocimetry system to obtain in situ digital images of the particles. The procedure is nonintrusive and is able to capture images of the particles as they are mixed, thus avoiding the need for disturbing the flow or withdrawing samples for later analysis. Measured size distributions are shown to compare closely with manufacturer's values for standard polystyrene spherical particles, and particles with diameters as small as 6 μm are resolved. The system also is shown to track changes in particle-size distribution during an aggregation test. In addition, information on particle geometry is obtained, which should be useful for improving the ability to model aggregation processes. A simple modeling framework based on the Smoluchowski equation is presented to demonstrate the use of data obtained with this procedure in particle aggregation modeling.     

Enhanced Criterion for Base Soil Retention in Embankment Dam Filters

In effective filters, potentially erodible base particles are transported to the filter and retained to form a stable self-filtration layer. At any given time, the mass proportion of the filter and the base materials in this layer depends on the initial porosity of the filter and the subsequent porosity of the self-filtration layer. In this paper, an analytical procedure is given to obtain the particle size distribution (PSD) of the self-filtration layer by combining the PSDs of the filter and the base soil modified by Dc95, where 95% of filter constrictions are finer than the size denoted by Dc95. The assessment of internal stability of the PSD of the self-filtration layer forms a rational model to successfully identify the effective filters from their ineffective counterparts. The proposed model is verified by large-scale laboratory tests carried out by the writers in addition to other published data. The model performance is acceptable in relation to various base and filter materials, and provides an alternative and rigorous design approach by eliminating most limitations of the conventional particle based criteria (e.g., D15/d85 ratio).     

高纯三氧化钼激光粒度分布的测定与分析

用扫描电镜观察了高纯三氧化钼的形貌，高纯三氧化钼是长条状的单颗粒聚集成的团聚体。用激光粒度仪的干法测定了高纯三氧化钼团聚体的激光粒度分布，用水作分散剂测定了高纯三氧化钼分散体的激光粒度分布，结果表明高纯三氧化钼的激光粒度分布值与电镜测量的颗粒及颗粒团尺寸一致，这样的测试方法能全面正确地反映高纯三氧化钼粒度的特征。讨论了高纯三氧化钼激光粒度分布对后续的还原过程及钼粉质量的影响。     

基于分形方法的煤炭研磨颗粒粒度分布模型

为了预测并控制煤炭在研磨过程中任意时刻的颗粒粒度分布,利用分形方法建立了表征煤炭研磨颗粒粒度分布动态变化的颗粒数分布模型、颗粒表面积分布模型和颗粒质量分布模型.颗粒数分布模型直观地描述了颗粒粒径主要存在的范围;颗粒表面积分布模型可以用来研究研磨过程中能耗的变化;颗粒质量分布模型可以用来计算研磨颗粒的堆密度和成浆浓度.通过分形粒度分布与实际粒度分布的比较,验证了模型的正确性.     

The rotary kiln: An investigation of bed heat transfer in the transverse plane

Rotary kilns are commonly employed to thermally process granular materials. While kiln rotation promotes particle mixing and heat transfer, it also leads to de-mixing through segregation of finer or denser particles, creating a “kidney” within the bed. Experience and experimental evidence indicate that rotation-induced mixing is insufficient to eliminate radial thermal gradients within the bed, but it is unclear as to whether particle segregation plays a significant role in the development of these gradients. This article presents experimental data obtained by heating sand of varying particle-size distributions within a 0.4-m ID batch rotary kiln to bed temperatures up to 775 °C. The results suggest that segregation has little influence on heat transfer within the bed and that radial thermal gradients are primarily the result of inadequate particle mixing. In order to scale up the experimental results, a mathematical model for heat transfer within the transverse plane was developed. A key variable for the model is the mixing-induced conductivity applied to the active layer, for which an empirical value is derived by fitting model predictions to the experimental data. Based on several assumptions for scaling of mixing conductivity with kiln size, model predictions for radial thermal gradients are presented for industrial-scale kilns in the 2- to 4-m ID range.     

Capturing Nonspherical Shape of Granular Media with Disk Clusters

In discrete numerical modeling of granular materials, idealization of individual particles is required, as it is not practical to model a large number of particles, each with its actual shape and size. To minimize computation times, researchers often use two-dimensional, circular elements. However, biaxial and direct shear tests on such specimens result in low strengths compared to granular materials, due, in part, to excessive rolling of the perfectly circular particles. In this paper, a new particle type, disk clusters, is presented. A disk cluster is a group of circular disks permanently connected to form an irregularly shaped particle that more closely represents the shape of granular materials and has less tendency to rotate. Development and implementation of disk cluster particles into a discontinuous deformation analysis program is presented. Validations of the mechanics of a single disk cluster, biaxial shear, and anchor pullout simulations illustrate the usefulness of this new particle type.     

Effect of Media Grain Shape on Particle Straining during Filtration

This paper investigates how straining mechanisms of angular media (crushed limestone) provide improved filtration performance compared to rounded media (river stone). Columns of granular media were set in resin, sectioned, photographed, and digitized to produce a three-dimensional model of pore space geometry. This process was repeated for four filter media, each representing different grain shapes or packing densities. From measured pore throat distributions, a stepwise particle movement model was used to estimate the maximum volume of particles that could be stored in the bulk of the filter media. The results showed that the more angular the media, the wider the range of particle sizes that could be strained in the bulk of the filter. The stepwise model was applied only to individual particles; trapping of colloidal particles was not considered. However, when individual particles are too small to be strained, the same pore throat trapping contributes to the physical capture of avalanches and flocculates. Thus the findings of this work are relevant to deep bed filtration applications where headloss results from straining, such as storm-water best management practices or soil filters.     

Simplified Relationships for Particle-Size Distribution and Permeation Groutability Limits for Soils

The particle-size distribution of soil with mean particle size and fines content are used not only in soil classifications but also in a number of other soil property relationships. In this study, two simple relationships (hyperbolic [tan?h(x)] and S-curve) were investigated to represent the particle size distribution of soils. The parameters of the hyperbolic model were correlated to various soil parameters such as the mean particle size, particle size range, and fines content. There was no direct correlation between Fredlund (four-parameter model) and S-curve model parameters and the soil parameters. The predictions of the two (hyperbolic) and three (S-curve) parameter models were compared to the four-parameter model (unimodal) using limited soil data from the literature and the agreements were good. The hyperbolic model was used to map the Unified Soil Classification System. A recent study had quantified the relationship between the grouting pressure and the fines content in nonplastic soils. Also in the current practice, upper and lower particle-size distribution limits are used in determining the groutability of soils. In this study, the relationship between grouting pressure and fines contents of the soil was generalized using the hyperbolic particle-size distribution model and verified with a groutability study using an acrylamide grout. Based on limited data in the literature, the groutability of soils was defined using a new set of parameters, grouting pressure, fines content, and mean particle size diameter of the soil.     

Measurement of Particle Dynamics in Rapid Granular Shear Flows

Micromechanics of rapid granular flows is studied in a two-dimensional planar granular Couette flow apparatus. The device is capable of generating particulate flows at different shearing rates and solid fractions. Monosize plastic disks are sheared across an annular test section for several shear rates. The motion of particles is recorded through a high speed digital camera and analyzed by image processing techniques. The average and fluctuation velocity profiles are obtained and granular temperature relations with shear rate are investigated. Average streaming velocity across the shear cell decays slightly faster than exponential, and is rather Gaussian when not too close to the wall. Fluctuation velocities and granular temperature across the shear cell are related to effective shear rate. Interparticle collisions are estimated from the particle trajectories and probability distribution of collision angles obtained from particle collision data. In dense flows, three peaks of collision angles are observed, which signal the onset of triangular structure formulation and cause crystallization. It is found that the distribution of collision angles is anisotropic.     

Fabric Study of Granular Materials after Compaction

Numerous micromechanical models have been developed based on assemblies of spherical particles with certain fabric distributions. Most of these distributions are hypothetical, and only very few of them can be determined experimentally. This paper presents a study to provide some useful fabric information for granular material. The discrete element method is used to study the microscopic information for granular materials after compaction. Specimens with 520 identical ellipsoidal elements are generated and compressed under different conditions. Up to six different aspect ratios are used to study their effect on the compression process. Two different compression methods and five different microfrictions between particles are used. The fabric of the specimens after compaction, including the total number of contacts, the distribution of particle orientations, the distribution of branch vectors, the distribution of the length of branch vectors, and the spatial distribution of a similar length of branch vector, is presented. The relations between these fabrics and particle shape, microfriction, and the compression process are also developed.     

Elastic Model for Partially Saturated Granular Materials

This paper presents the development of an elastic model for partially saturated granular materials based on micromechanical factor consideration. A granular material is considered as an assembly of particles. The stress-strain relationship for an assembly can be determined by integrating the behavior at all interparticle contacts and by using a static hypothesis, which relates the average stress of the granular assembly to a mean field of particle contact forces. As for the nonsaturated state, capillary forces at grain contacts are added to the contact forces created by an external load. These are then calculated as a function of the degree of saturation, depending on the grain size distribution and on the void ratio of the granular assembly. Hypothesizing a Hertz-Mindlin law for the grain contacts leads to an elastic nonlinear behavior of the particulate material. The prediction of the stress-strain model is compared to experimental results obtained from several different granular materials in dry, partially saturated and fully saturated states. The numerical predictions demonstrate that the model is capable of taking into account the influence of key parameters, such as degree of saturation, void ratio, and mean stress.     

Effects of agitation on size distribution of particulate matter in large-volume parenterals

The particle-size distributions of six types of large-volume parenterals subjected to different degrees of agitation were determined using an automatic particle counter. Data acquired from each solution, which had been maintained in a stored condition, subjected to agitation by inverting 20 times, and then mechanically shaken for 30 min, produced a linear relationship between log N greater than D and log D. Both the slope (K) and the number of particles per milliliter exceeding 1 micrometer in diameter (N greater than 1) exhibited a dependence on the degree of agitation. Their combined effect indicates that agitation by 20 hand inversions removed particulate matter from the surface of the container, which increased the total number of particles in solution (greater than 1 micrometer) but did not significantly alter the relative size distribution. Agitation for 30 min, however, disintegrated agglomerates and produced a particle-size distribution with a greatly increased number of particles whose diameters were less than 1 micrometer and a corresponding decrease in the number of particles exceeding 1 micrometer in diameter. The particle-size distribution of a parenteral solution determined by this in situ instrumental method was, therefore, dependent upon the degree of agitation to which the parenteral was subjected prior to examination.     

Quantification and Simulation of Particle Kinematics and Local Strains in Granular Materials Using X-Ray Tomography Imaging and Discrete-Element Method

Microfeatures of granular materials have significant effects on their macrobehaviors. Unfortunately, three-dimensional (3D) quantitative measurements of microfeatures are rare in literature because of the limitations of conventional techniques in obtaining microquantities such as microdisplacements and local strains. This paper presents a new method for quantifying the particle kinematics and local strains for a soft confined compression test using X-ray computed tomography and compares the experimental measurements with the simulated results using the discrete-element method (DEM). The experimental method can identify and recognize 3D individual particles automatically, which is essential for quantifying particle kinematics and local strains. 3D DEM simulations of the soft confined compression test were performed by using spherical particles and irregular particles. The simulated global deformations and particle translations that were based on irregular particles showed better agreement with the experimental measurements than those that were based on spherical particles. The simulated movements of spherical particles were more erratic, and the material composed of spherical particles showed larger vertical contraction and radial dilation.     

基于三维离散元法的无钟高炉装料行为

利用三维离散元法建立了无钟高炉布料模型,分析了料罐、旋转溜槽中的颗粒流动行为以及颗粒离开溜槽后的下落轨迹和料堆形成,可视化再现了装料过程.结果发现:炉料在流动过程中始终存在粒度偏析,料罐排料流为漏斗流,小颗粒由于偏析而倾向于后期排出;溜槽倾角对颗粒流动行为和料堆形成影响较大;溜槽内颗粒流由于溜槽旋转而向侧上部偏离和翻动,小颗粒因靠近壁面而位于料流内侧,大颗粒因聚集在溜槽上部而处在料流外侧,炉料颗粒偏析、偏转翻动和速度分布影响下落轨迹;在炉料下落到料面的堆积过程中,大颗粒易于向炉喉中心和边缘偏析,小颗粒因位于料流内侧和渗透作用而分布在堆尖下方且偏向中心侧.结合激光网格炉内测量技术料流轨迹测量结果,验证了模型的适用性.     

Dynamic Modeling of Bentazon Removal by Pseudo-Moving-Bed Granular Activated Carbon Filtration Applied to Full-Scale Water Treatment

A model for the removal of pesticides by granular activated carbon (GAC) filtration in full-scale water treatment is presented. The model describes GAC filtration in a pseudo-moving-bed configuration, where two filters are operated in series and after breakthrough the first filter is regenerated and becomes the second filter. The influent of the second filter is changing due to gradual breakthrough of the first filter. Therefore, a dynamic model is developed based on kinetics, equilibrium, and mass balance equations. The model is calibrated and validated on data of full-scale and pilot plants. Operational strategies are evaluated of two different cases. From this study it can be concluded that a dynamic mathematical model can be successfully used to evaluate the performance and operation of full-scale GAC filters for pesticide removal and can be used for operational decision support. Data obtained from practice can be used for calibration without additional laboratory work.     

Assessing the Potential of Internal Erosion and Suffusion of Granular Soils

This study presents a new empirical criterion for assessing the potential of internal erosion and suffusion of granular soils. This method considers the bimodal structure of a soil having a primary coarse fabric and loose finer particles based on the porosities influenced by the particle size distribution and the degree of compaction. By comparing the representative particle size of a loose finer fraction with the controlling constriction size of a primary coarse fabric, a distinct boundary between internally stable and unstable soils with respect to internal erosion may be found.     

Anisotropic Nonlinear Elastic Model for Particulate Materials

This paper presents the development of an elastic model for particulate materials based on micromechanics considerations. A particulate material is considered as an assembly of particles. The stress–strain relationship for an assembly can be determined by integrating the behavior of the interparticle contacts in all orientations and using a static hypothesis which relates the average stress of the granular assembly to a mean field of particle contact forces. Hypothesizing a Hertz–Mindlin law for the particle contacts leads to an elastic nonlinear behavior of the particulate material, we were able to determine the elastic constants of the granular assembly based on the properties of the particle contacts. The numerical predictions, compared to the results obtained during experimental studies on different granular materials, show that the model is capable of taking into account both the influence of the inherent anisotropy and the influence of the stress-induced anisotropy for different stress conditions.