Spheroidal particle stability in semisolid processing

A model for diffusion-controlled spherical particle growth is presented and solved numerically, showing how, on cooling at a sufficient rate from a given fraction solid, growth velocity first increases and then decreases rapidly when solute fields of adjacent particles overlap. An approximate analytical solution for the spherical particle growth velocity is then developed and shown to be valid until the solute fields begin to overlap. A particle stability model is next presented, building on the preceding analytic solution. This model permits prediction of the maximum cooling rate at which a semisolid slurry or reheated semisolid billet can be cooled while still retaining the spherical growth morphology. The model shows that particle stability is favored by high particle density, high fraction solid, and low cooling rate. The predictions of the stability model are found to be in good quantitative agreement with experimental data collected for Al-4.5 wt pct Cu alloy. Engineering applications of the results obtained are discussed.     

Diffusion fields associated with size and shape coarsening of oblate spheroids

The diffusion field or solute concentration distributed around an oblate spheroidal particle simulating a disc-shaped precipitate has been solved for varying particle aspect ratios and varying concentrations along the precipitate surface because of the curvature effect. With oblate spheroidal coordinates, the principal curvatures of the oblate spheroidal surface are derived as functions of the angular variable, and the Laplace field equation is separated into two Legendre equations on the angular variable and on the radial variable. The analytical solution to the Laplace equation, fitting the present boundary conditions, is secured as the sum of a Legendre function and a Legendre series composed of Legendre functions of the second kind with imaginary arguments. The Legendre function gives the concentration distribution with an ignored curvature effect, whereas the series shows the contribution from the curvature effect. Numerical results of normalized concentrations are presented as functions of the radial and angular variables for selected aspect ratios. The concentration distributions around both oblate and prolate spheroidal particles are shown to reduce to the concentration distributed around a spherical particle when the aspect ratio of the spheroids approaches unity.     

Investigation of the Density Characteristics of Three-Dimensional Stochastic Packs of Spherical Particles Using a Computer Model

A series of computer experiments were performed to model the random packing of spherical particles. Known algorithms for dense packing were modified to optimize density characteristics. The distribution of local density in random packs of spherical particles was investigated. The effect of boundary conditions on the density characteristics was determined, and the dimensions of the boundary distorted zone evaluated. Methods for controlling the integral density and local density distribution in packs of spherical particles were determined. These are based on the concept of density characteristics as functions of the ratio of particle sizes and numbers in a fraction, and in a mixture.     

SBA-15脱除超细颗粒的机制研究

利用扫描电迁移率颗粒物粒径谱仪（SMPS),针对不同孔径的介孔材料SBA-15,探索对UFPs（2.5～25 nm）的去除效率及脱除机理,以期为介孔材料过滤脱除UFPs在钢铁工业颗粒物超低排放控制的应用提供理论基础。基于实验结果及表征分析得知:UFPs入孔效应使大孔径介孔过滤介质效率更佳;介孔材料孔径端部内外表面存在大量UFPs亲和位点,提高端部复杂程度有利于提升材料过滤性能;氮气的有无对UFPs去除结果基本没有影响;介孔的存在使UFPs扩散效应更强,颗粒入孔使扩散系数增加,故UFPs在介孔材料实际扩散结果与传统扩散模式理论值（m=?2/3）不同。      

Densification of Powders by Particle Deformation

Abstract

Based on a previous experimental study of particle deformation during powder compaction, a model is developed for describing the densification behaviour of an irregular packing of spherical particles. Using the radial density function of a ‘random dense packing’, the increase in both the average size and the number of contact faces are calculated. A simple criterion for local yielding allows the compaction pressure to be determined for relative densities up to 90%. In the final stage of compaction, particle deformation, now constrained by neighbouring contacts, is modelled by extrusion into the remaining pore space. A compaction equation encompassing both stages is presented; its application to non-spherical powders elucidates the role of particle shape during powder densification. PM/0150     

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.     

Preliminary study to determine the sintering stress from microstructural analysis of green parts

Solid-state sintering theory predicts shrinkage kinetics assuming the two-sphere model. Spheres are of equal diameter, undeformed and smooth. The actual condition of powder particles in cold compacted green parts deviates very much from this model: particles have a broad size distribution and an irregular surface profile, they are not spherical and plastically deformed. Therefore the sintering stress cannot be directly correlated to the particle radius, as made in the two-sphere model. The actual neck curvature radius should be therefore determined. In this work, a first attempt to determine sintering stress experimentally is presented. Iron green parts produced by cold isostatic pressing were pre-sintered in order to provide a minimum consolidation avoiding densification. By means of image analysis, the microstructure was investigated to characterise the particle and the pore morphology, and in particular their profiles. A geometrical model of the pore morphology was proposed, from which the radii of curvature in correspondence of the neck regions may be calculated.     

Manufacturing of Open-Cell Zn-22Al-2Cu Alloy Foams by a Centrifugal-Replication Process

Centrifugal force was used to produce open-cell Zn-22Al-2Cu alloy foams by the replication method. Three different sizes (0.50, 0.69, and 0.95 mm) of NaCl spherical particles were used as space holders. A relatively low infiltration pressure was required to infiltrate completely the liquid metal into the three pore sizes, and it was determined based on the centrifugation system parameters. The infiltration pressure required was decreased when the diameter of the particle was increased. The porosity of the foam was increased from 58 to 63 pct, when the pore size was increased from 0.50 to 0.95 mm, while the relative density was decreased from 0.42 to 0.36. The NaCl preform was preheated to avoid the freezing and to keep the rheological properties of the melt. The centrifugal-replication method is a suitable technique for the fabrication of open-cell Zn-Al-Cu alloy foams with small pore size. The compressive mechanical properties of the open-cell Zn-22Al-2Cu foams increased when the pore size decreased.

     

Effects of Ionic Strength on Fine Particle Clogging of Soil Filters

The effects of ionic strength of the permeating fluid on the clogging of soil filters and drainage layers are addressed using both experimental and modeling investigations. In the experimental phase, a sandy soil representative of soil filters was permeated with pore fluids containing kaolinite particles. The ionic strength of the solutions was changed using different concentrations of NaOH and KCl. The permeability reductions of the soil filter were determined by varying pore fluid and particle suspension parameters. Higher ionic strength caused more flocculation of the kaolinite particles and resulted in more rapid reduction of permeability. In the modeling phase, a physical clogging model developed previously by the authors, was used to account for the ionic strength effects. A lumped parameter θ0 was used in the model to account for the ionic strength of the pore fluid and the several interparticle forces, for example gravitational, inertial, hydrodynamic, electric double layer, and van der Waals forces. The effect of the lumped parameter θ0 on the permeability reduction was found to be greater than the effect of the sizes of the influent particles. For the same ionic strengths, NaOH resulted in larger flocs of kaolinite particles than KCl, and caused more rapid reduction in permeability.     

Rheological Behavior of Fine and Large Particle Suspensions

A new rheometric system, the ball measuring system, is used to determine the rheological behavior of fluids with large particles. To assess the applicability of the new system for debris flow material, artificial fine particle suspensions are investigated with the ball measuring system and a conventional concentric cylinder system. The agreement between the flow curves obtained by both systems is good. In a second step, defined amounts of coarser grains are added stepwise to the fine particle suspension to obtain different large particle suspensions. There is an increase in data scattering with an increase in large particle concentration. Thus, the question is raised for which grain size distribution, sediment concentration, and which process the traditional rheological approach is still appropriate when describing the flow process of debris flow mixtures. The curve fitting for the different fine and large particle suspensions is described using the Herschel–Bulkley model. Finally, the range of application for the ball measuring system is discussed. Today it is a suitable new rheometric system for fluids with particle sizes up to 10 mm and for measurements in the laminar flow field. The application for this system could potentially be expanded, for example, to measure fluids with particles sizes up to 200 mm with a large scale device.     

Reaction Kinetics of Immobilized-Cell Denitrification. I: Background and Model Development

A simplified, quasi-steady-state model has been formulated for groundwater denitrification using immobilized cells. The model takes into account the diffusion-limited penetration of nitrate and nitrite into the immobilized-cell biocatalyst particle, uniform intraparticle cell density, equivalent slab geometry for the spherical particle, zero-order intrinsic reaction kinetics of the immobilized cells, sequential reduction of nitrate to nitrite and nitrite to dinitrogen within the particle, no inhibition of the sequential reactions by either nitrate or nitrite, and ideal plug flow conditions in the bioreactor. As a result, the reaction in the bulk fluid of the plug-flow bioreactor can be described by a half-order kinetics, and the process is characterized by the half-order reaction rate constants for nitrate and nitrite reduction. These constants incorporate the intrinsic reaction kinetics of the immobilized cells, the size and packing density of biocatalyst particles in the reactor, and the effective diffusion coefficients of nitrate and nitrite in the particle matrix.     

Stress-Controlled Filtration with Compressible Particles

This paper documents a novel filtration technology that incorporates low-stiffness filter matrix particles. The application of isotropic stresses leads to the compression of particles and ensuing pore throat size reductions in the filter matrix. The filtration capacity of the matrix is improved with increasing confinement because the retention of filtrate particles increases due to particulate plugging and bridging on the reduced pore throats. Conversely, relaxing the applied stresses renders system expansion, increased pore throat sizes, and enhanced flushing of entrapped particles from the filter. Experimental results indicate that this technology is most efficient in cases where particle retention occurs due to geometrical constraints (i.e., bridging); however, the system can also render filtration by surface deposition due to the net electrical attraction between the filtrate and filter. Experimental results are analyzed by considering particle-scale filtration mechanisms.     

Time-Dependent Particle Transport through Granular Filters

This paper describes an analytical model of filtration for granular media, based on the mechanics of particle migration under hydraulic loads. A new equation to predict the probability of particle movement through a 3D network model of the filter voids has been developed. Void constriction sizes are determined based on the particle-size distribution and relative density of the filter. An important new development is the differentiation between particles that form part of the filter structure and fine particles that are loose within the filter voids, or coarse particles that are enmeshed in a matrix of fines. The rate of particle erosion and transport is governed by the consideration of mass and momentum conservation. The model describes the time-dependent change of flow rate and base and filter particle-size distribution, porosity, and permeability. The model has application in the design of granular filters for noncohesive uniform, well-, and broadly graded base and filter materials.     

Nucleation on ceramic particles in cast metal-matrix composites

In order to understand the nucleation on ceramic particles in the melts of metal-matrix composites (MMCs), the effect of segregation of solute on the surface of reinforcement particles in the melt has been analyzed as a function of particle temperature and the surface energy of the particle/liquid melt. The temperature of the particle in the melt, calculated analytically, was found to become close to the melt temperature within a very short time of contact between the particle and the melt. The solute concentration near the particle surface will, therefore, primarily be influenced by the surface energy of the particle and the melt. Based on this, the undercooling due to solute segregation around the particle and the chemical free-energy change due to the formation of the new solid phase on the particle were calculated in selected hypo- and hypereutectic Al-Si alloy melts containing (1) SiC particles or (2) graphite particles. The chemical free-energy change (driving force for nucleation) due to the formation of the new phase on the particle is lower for hypoeutectic compositions than for hypereutectic compositions in the aluminum-silicon alloy systems; this is due to the higher undercooling in the hypereutectic alloys due to solute segregation on the surface of the particle. This suggests that the formation of the primary phase on the surfaces of particles in the melt should be more favorable in the hypereutectic compositions than for hypoeutectic compositions. This also indicates that even when the particle temperature is not significantly lower than the liquidus temperature, nucleation on the particles can take place due to the segregation of the solute on the particles. Experimental observations of the microstructure of several cast metal-matrix composites, including Al-Si-SiC and Al-Si-graphite, show (1) the presence of silicon in contact with the reinforcement particles in hypereutectic alloys, suggesting that nucleation and growth of primary silicon under certain conditions occurs on silicon carbide and graphite particles, possibly due to solute segregation on the surface of the particles, and (2) the presence of reinforcement particles in the last-freezing interdendritic regions of the primary phases in hypoeutectic alloys, suggesting the absence of nucleation of primary phases on the reinforcement surface, as predicted by the analysis.     

Pinning of grain boundaries by deformable particles

Interaction between a grain boundary and deformable particles has been modeled. It is shown that deformable particles pin the grain boundaries more effectively than rigid spherical particles. The required driving force to unpin a grain boundary increases with decreasing the interphase energy of the deformable particle. Deformable particles also reduce the rate of grain-boundary migration more effectively than rigid spherical particles. The rate of grain boundary migration decreases with the interphase energy of the deformable particle. The model allows the shape of a deformable particle to be determined as the particle is dragged by a grain boundary. The particle shape allows prediction of the force acting on the particle.     

Kinetics of neck growth during loose stack sintering

The kinetics of loose stack sintering of spherical iron powder were monitored by measuring some global microstructural attributes associated with the interparticle contact necks. The neck size and the number of interparticle contacts per unit volume were calculated from these data. A direct comparison of the experimental and theoretically predicted neck sizes has been carried out. The neck sizes predicted by the model for surface diffusion controlled sintering are muchhigher than the corre-sponding experimental values. The number of interparticle contacts per particle does not change with isothermal sintering time or temperature, and it is predominantly determined by the initial stacking of particles in the powder mass. The change of atmosphere from dry hydrogen to argon does not affect the neck growth kinetics significantly.     

Damage due to fracture of brittle reinforcements in a ductile matrix

A micromechanical model is developed for brittle particle reinforced metal matrix composites sustaining damage. A composite with uniformly distributed damage is modelled by a three-phase damage cell consisting of a cracked particle in a cylindrical matrix cell embedded in an undamaged composite cylinder. The fraction of broken particles to all particles is taken as the ratio of the broken-particle/matrix cell volume to the whole damage cell volume. Systematic analysis is carried out for aligned spherical and cylindrical particles in an elastic-perfectly plastic matrix subject to tensile loading normal to the plane of particle cracks. The influence of damage evolution paths on the composite stress-strain behavior is investigated. Results are given for the effects of damaged particle percentage, total particle volume fraction and particle shape on the overall composite limit flow behavior. Significant reduction in composite limit flow stress may occur if most of the particles are broken. For composite with spherical reinforcement, the reduction is found to be linearly dependent on the percentage of damaged particles.     

铁矿烧结过程微细颗粒物排放行为

 采用ELPI+设备(荷电低压撞击器)对铁矿烧结过程微细颗粒物进行在线检测与采样，利用场发射扫描电子显微镜(FESEM EDS)对采集的颗粒物形貌特征进行分析，研究铁矿烧结过程中微细颗粒物的排放行为。研究结果表明，PM10大量释放集中在烧结升温段，且颗粒物质量浓度与数目浓度在粒径分布上有较大差异，其中质量浓度峰值区间为5.37～10.00 μm，数目浓度峰值区间为0.10～0.16 μm；形貌特征上，微细颗粒物呈规则的球形、方块形和片状；不同粒径物质组成差异明显，其中颗粒物中的K、Na主要以KCl和NaCl的形式存在，含量随颗粒物粒级的增大而略有降低。     

Spatial distribution of Fe3C-particles in steel during coarsening

The particles’ arrangement of disperse phases can be described by the space distribution of particle centers as well as by relations between center positions and particle sizes. By means of the sphere models of known stochastic properties one can obtain some information on the particle arrangement by stereology. The models make it possible to determine (by calculation or simulation) functions which characterise the distribution of the centers of two-dimensional particles In planar sections, i.e., the pair-coorrelation function and the nearest neighbour distance distribution, and compare them with respective empirical functions. The steorological analysis of the two disperse systems of Fe₃C-particles in steel observed during the different stages of the coarsening process indicate that these dispersions follow the Stienen model (a model for non-overlapping spheres), i.e., the particle centers form a Poisson point field while the particle sizes are dependent on and determined by the nearest neighbours distance of the particle centers.     

Equilibrium solute concentration surrounding elastically interacting precipitates

Elastically induced equilibrium solute concentration profiles surrounding a single isolated precipitate and two elastically interacting precipitates are determined under the conditions of an applied shear and tensile stress, as well as an isotropic stress-free transformation strain. The self consistent open-system elastic constants approach is employed to account explicitly for the coupling between the stress and concentration fields. Substantial concentration changes are predicted near the surfaces of the particles which can sometimes exceed 50 pct. With self consistency to first-order in the concentration change, no net solute enhancement is observed surrounding isolated particles while net solute segregation is observed for elastically interacting particles.