Analysis of agglomerated packings

Results of computer simulation of the packing of particles in compacts from agglomerated powders are presented. The effect of the characteristics of agglomerated powders, such as the number of particles in the agglomerates, the size distribution of agglomerates, and the volume share of the fine fraction (individual particles) on the factors that determine the sinterability of compacts, i.e., the density, the mean number of contacts per particle, and the mean size and the mean coordination number of the pores, is investigated. It is established that compared to compacts from individual particles the presence of agglomerates sharply worsens the packing characteristics. The worst effect is due to agglomerates containing less that 30 – 40 particles. The packing characteristics can be improved by using powders with a wide size distribution of agglomerates or by adding unagglomerated particles. It is interesting that computer models of powder compacts can be used for predicting the strength properties of the materials sintered from these powders. Data on the influence of the packing characteristics on the mean strength and the Weibull modulus are presented.Translated from Ogneupory, No. 4, pp. 14–17, April, 1995.     

Cohesive strength of alumina powder compacts

In order to characterize the nature of the interparticle forces that causes particle agglomeration in submicron size alumina particles, eight commercial alumina powders were investigated. Since the strength of the agglomerates depends upon the interparticle forces and the packing density of the particles the Hartley model which relates the tensile strength, packing density of a powder compact, to the interparticle force has been applied. The present experimental results suggest that in the absence of any electrostatic forces (either force of attraction or repulsion between particles) van der Waals force is responsible for the agglomeration of alumina particles.     

A particle packing algorithm for pellet design with a predetermined size distribution

In this paper a particle packing algorithm is proposed which is to be used to predict the behaviour of pellets in the blast furnace on a first principal basis. Pellets consist of particles of various mineralogical composition and the structure in which they pack together to form a pellet is dependant on the size distribution of the particles and the pellet porosity. This packing structure can result in isolated volumes within the pellet where the local composition deviates from the overall average composition. This can result in, for example, melt formation at lower temperatures than expected, which will have a detrimental effect on the pellet strength. These local compositions result from the contacts between particles of different minerals and can thus be quantified by the coordination number of the particles. By using a validated coordination number model, which is unique for a particle packing algorithm, virtual pellets were created for a range of particle size distributions and porosities. The algorithm used the Monte Carlo method combined with the simulated annealing minimisation algorithm to solve the pellet simulations. The objective function is a combination of two functions, one describing the deviation from the target coordination number of the particles and the other the average fraction of overlapping volume of the particles per contact. In this way a realistic pellet structure was maintained while at the same time controlling the coordination number of the particles.     

Mechanical properties of talc-filled polypropylene. Influence of filler content,filler particle size and quality of dispersion

Mechanical properties of polypropylene-talc composites are measured as a function of talc concentration up to 40 wt.-%, Young's modulus of filled polypropylene shows linear increase with talc concentration up to double the value of unfilled polymer. Yield stress and Charpy notch toughness decrease with increasing talc content below matrix level at the highest filler content. Composite ultimate tensile elongation and tensile impact strength decrease sharply beginning at the lowest filler concentration. The influence of the talc particle size on the mechanical properties, especially composite toughness, mentioned above, is investigated. Four type of talc were used. Notch toughness decreases according to a linear dependence with mean size of talc particles. Evaluating impact strength possible content of agglomerates of filler and other additions is necessary to be included: tensile impact strength gives slow linear dependence with increasing content of filler particles and/or agglomerates above about 10 μm. The influence of talc particle size on the toughness of filled polypropylene becomes strong if the rubber particles are present.     

A theoretical model of the effect of distributed loading on the tensile strength of agglomerates as measured in the diametral compression test

The tensile strength of particle agglomerates is analyzed to indicate the effect of distributed loading through contact flattening during the diametral compression test. It is assumed that only the contact regions of the agglomerate are flattened and that the free boundary maintains its original position during loading. The increased packing density so produced is related to the total loading as a reaction force through an empirical relationship used to describe die compaction of powders. Agglomerate failure occurs when the maximum tensile stress caused by the platen loading exceeds the cohesive strength of the particle assemblage. Theoretical predictions of the effects of parameters such as bulk powder properties and the extent of load distribution on agglomerate strength are presented from the analysis.     

Note on notch and unnotch toughness of PP-CaCO3 composites: Influence of filler particle size and dispersion degree

The influence of the filler particle size and dispersion degree on the Charpy notch toughness (U notch) and tensile impact strength (without notch) in the polypropylene-microground calcium carbonate system was investigated. It was found that while the tensile impact strength was controlled by the content of particles and/or agglomerates coarser than about 10 µm (the strength decreased sharply with their increasing content), the Charpy notch toughness was not decreased even by large agglomerates (up to 100 µm), but dropped heavily with the increasing upper particle size of the filler measured before kneading into polymer. A model system polyethylene-glass beads revealed even an increase of the notch toughness with the increasing upper diameter of the glass beads (the upper diameter being in the 50–400 µm range).     

Settling of particles in liquids: Effects of material properties

This article presents a numerical study on the settling of uniform spheres in liquids by means of the discrete element method. The effects of particle and liquid properties, such as particle size, Hamaker constant, liquid density, and viscosity, on the formation of packed beds or cakes were studied in terms of packing fraction, radial distribution function (RDF), and coordination number (CN). The results showed that the packing fraction of a cake increases with increasing particle size but decreases with increasing the Hamaker constant, liquid density, and viscosity. RDF and CN also change correspondingly: packings with lower packing fraction generally have RDFs with fewer peaks and smaller mean CNs. A good correlation between packing fraction and other structural properties was identified. The analysis of the particle‐particle and liquid‐particle interactions showed that the packing properties are mainly affected by the ratio of the interparticle cohesion to the effective gravity of particles. The previously proposed equation linking packing fraction with the interparticle forces has been extended to incorporate the impact‐induced pressure force in a settling process. Based on the modified equation, the effects of key variables on the relationship between packing fraction and particle size were re‐examined for general application. © 2011 American Institute of Chemical Engineers AIChE J, 2012.     

Compressive mechanical properties of partially sintered porous alumina of bimodal particle size system

This paper examined theoretically and experimentally packing behavior, sintering behavior and compressive mechanical properties of sintered bodies of the bimodal particle size system of 80 vol% large particles (351 nm diameter)–20 vol% small particles (156 nm diameter). The increased packing density as compared with the mono size system was explained by the packing of small particles in 6-coordinated pore spaces among large particles owing to the similar size relation between 6-coordinated spherical pore and small particle. The sintering between adjacent large particles dominated the whole shrinkage of the powder compact of the bimodal particle size system. However, the bimodal particle size system has a high grain growth rate because of the different curvatures of adjacent small and large particles. The derived theoretical equations for the compressive strengths of both mono size system and bimodal particle size system suggest that the increase in the grain boundary area and relative density by sintering dominate the compressive strength of a sintered porous alumina. The experimental compressive strengths were well explained by the proposed theoretical models. The strength of the bimodal particle size system was high at low sintering temperatures but was low at high sintering temperatures as compared with that of mono size system of large particles. This was explained by mainly the change of grain boundary area with grain growth. The stress–strain relationship of the bimodal particle size system showed an unique pseudo-ductile property. This was well explained by the curved inside stress distribution along the sample height. The inside stress decreases toward the bottom layer. The fracture of one layer of sintered grains over the top surface proceeds continuously with compressive time along the sample height when an applied stress reaches the critical fracture strength.     

Investigation of Aerosol Surface Area Estimation from Number and Mass Concentration Measurements: Particle Density Effect

For nanoparticles with nonspherical morphologies, e.g., open agglomerates or fibrous particles, it is expected that the actual density of agglomerates may be significantly different from the bulk material density. It is further expected that using the material density may upset the relationship between surface area and mass when a method for estimating aerosol surface area from number and mass concentrations (referred to as “Maynard's estimation method”) is used. Therefore, it is necessary to quantitatively investigate how much the Maynard's estimation method depends on particle morphology and density. In this study, aerosol surface area estimated from number and mass concentration measurements was evaluated and compared with values from two reference methods: a method proposed by Lall and Friedlander for agglomerates and a mobility based method for compact nonspherical particles using well-defined polydisperse aerosols with known particle densities. Polydisperse silver aerosol particles were generated by an aerosol generation facility. Generated aerosols had a range of morphologies, count median diameters (CMD) between 25 and 50 nm, and geometric standard deviations (GSD) between 1.5 and 1.8. The surface area estimates from number and mass concentration measurements correlated well with the two reference values when gravimetric mass was used. The aerosol surface area estimates from the Maynard's estimation method were comparable to the reference method for all particle morphologies within the surface area ratios of 3.31 and 0.19 for assumed GSDs 1.5 and 1.8, respectively, when the bulk material density of silver was used. The difference between the Maynard's estimation method and surface area measured by the reference method for fractal-like agglomerates decreased from 79% to 23% when the measured effective particle density was used, while the difference for nearly spherical particles decreased from 30% to 24%. The results indicate that the use of particle density of agglomerates improves the accuracy of the Maynard's estimation method and that an effective density should be taken into account, when known, when estimating aerosol surface area of nonspherical aerosol such as open agglomerates and fibrous particles.     

Prediction for particle removal efficiency of a reverse jet scrubber

Numerical computation was conducted to predict the collection performance of a reverse jet scrubber for polydisperse particles. The particle size distribution of polydisperse particles was represented by a lognormal function, and the continuous evolution of the particle size distribution in a reverse jet scrubber is taken into account with the first three moment equations. Numerical results were compared with the analytic results using average relative velocity in all zones and experimental results.

In a reverse jet scrubber, the impaction is the main particle collection mechanism because of high relative velocity and short collection time. The particle collection by impaction increases with an increase in particle size, and geometric mean diameter and geometric standard deviation decrease as time goes on. High droplet velocity and gas velocity increase the particle collection efficiency, and the small droplet size also increases the collection efficiency because smaller droplet size provides broader surface area. The packing density is a factor affecting particle collection efficiency in a scrubbing process. The dense packing density also provides large surface area and leads to high collection efficiency.     

Highly filled thermoplastic composites. II: Effects of particle size distribution on some properties

The effect of irregularly shaped glass particle size and size distribution on the packing density and flexural mechanical properties of highly-filled composites with a rubbery thermoplastic matrix was studied. Increasing the particle's median size and size distribution width significantly increases the packing density of the composites. Compression molding causes the glass particles to fracture at a decreasing level with an increasing distribution width. Particle median size, rather than size distribution, affects the mechanical properties; The flexural modulus and strength increase and the ultimate deflection in flexure decreases with a decreasing median size. A “glass network” is formed in the compression molded composites because of the mechanical interlocking of particles. The nature of this continuous glass phase predominates the composites mechanical behavior. The particle's size and shape determine the nature of the glass network and, thus, have a dominating effect on the mechanical properties. The latter are significantly affected by the particle's surface properties. A specific silane treatment of the glass particles acts to reduce the particle/particle friction, resulting in a higher packing density. The treatment also acts as a cohesive liquid to increase the strength of the glass network, and to increase the particle/polymer adhesion, increasing the composites' strength and ductility.     

Effect of morphology and extent of infiltration on the cohesivity and dispersion mechanisms of particle agglomerates

A unified approach to predict the tendency for dispersion of particle agglomerates, inclusive of a wide range of particle and agglomerate properties, is presented. This framework is applied to analyze the behavior of three prototypical materials (fumed silica, calcium carbonate and titanium dioxide) across a range of agglomerate packing densities. Simulations of dispersion phenomena, which employ our previously developed solution for liquid-bridge interactions for wet interparticle contacts and the Rumpf model for the tensile strength of the dry and wet portions of the agglomerate, have been performed. Various mechanisms of dispersion are predicted for various conditions of agglomerate density and extent of fluid infiltration. These range from an adhesive mechanism at the wet-dry interface for sparse materials to a cohesive mechanism by erosion as agglomerate density increases. The results correspond well with the results of earlier experimental studies involving the same materials.     

Parametric study of fine particle fluidization under mechanical vibration

Investigations into the effects of vibration on fluidization of fine particles (4.8-216 μm average in size) show that the fluidization quality of fine particles can be enhanced under mechanical vibration, leading to larger bed pressure drops at low superficial gas velocities and lower values of u_mf. The effectiveness of vibration on improving fluidization is strongly dependent on the properties (Geldart particle type, size-distribution and shape) of the primary particles used and the vibration parameters (frequency, amplitude and angle) applied. The possible roles of mechanical vibration in fine particle fluidization have been studied with respect to bed voidage, pressure drop, agglomeration, and tensile strength of particle bed. Vibration is found to significantly reduce both the average size and the segregation of agglomerates in the bed, thus improving the fluidization quality of cohesive particles. Also, vibration can dramatically reduce the tensile strength of the particle bed. Obviously, vibration is an effective means to overcome the interparticle forces of fine powders in fluidization and enhance their fluidization quality.     

Sintering of Mullite-Containing Materials: II, Effect of Agglomeration

The sintering behavior of mullite powder compacts which contained soft and hard agglomerates was studied, The maximum density achieved depended on the size and packing of the agglomerates. Although the initial % total pore volume was kept constant, the presence of larger pores in the green compact, due to larger agglomerates, resulted in lower final densities after sintering. Densification rates were enhanced by the breakdown of agglomerates by grinding. The particle and agglomerate packing arrangements caused densification substages to occur. A schematic model is presented which agrees well with the observed experimental behavior.     

A Die Pressing Test for the Estimation of Agglomerate Strength

A die pressing test was developed for quick and inexpensive estimation of the agglomerate strength of ceramic powders. The critical nominal pressure ( p _c) at which contact areas between agglomerates start to increase rapidly was found from the relationship between change in sample height and applied pressure in uniaxial single-ended die pressing. A quantitative microscopic method was used for measuring the area fraction (Ψ) of agglomerates which transmits the force through the assembly. A die pressing agglomerate strength, σ_d, is defined as σ_d= 0.7 p _c/Ψ. This strength was compared with the agglomerate tensile strength obtained from single agglomerate diametral compression tests and found to be 50% higher than the latter because of multipoint loading. A suggested guideline is that the mean agglomerate tensile strength is approximately 52% of p _c determined in a die pressing test for spherical agglomerates. In addition to agglomerate tensile strength, the mean agglomerate size, the interior macropore structure of agglomerates, as well as the packing efficiencies between and inside agglomerates can be estimated by the procedure.     

Inhomogeneity of powder packing in compacts and strength of the ceramics obtained

Results of studying the effect of the packing inhomogeneity of the powder compact on the strength of sintered corundum ceramics are presented. In the powders used for molding powder compacts, agglomerates of various sizes were formed artificially. Under the same sintering conditions no substantial difference in the density or grain size of materials that initially differed in the inhomogeneity of particle packing were observed. Strength measurements revealed an inverse dependence of the strength on the degree of powder inhomogeneity in the starting compact. Translated from Ogneupory i Tekhnicheskaya Keramika, No. 5, pp. 14–19, May, 1997.     

Controlled Nucleation in Aerosol Reactors for Suppression of Agglomerate Formation: A Numerical Study

The formation of agglomerated particles can be a detriment to the production of highly sinterable materials. It has been seen experimentally that agglomerates are almost exclusively constructed from 10–30-nm primary particles. This paper develops criteria for the avoidance of these small primary particles through control of the nucleation rate. The relationship between particle size and number density can be used to obtain regions of stable and unstable particle growth. It is seen that the critical source rate for the prevention of runaway nucleation can be scaled without knowledge of the monomer number density.     

Numerical investigation of particle shape and particle friction on limiting bulk friction in direct shear tests and comparison with experiments

In this study, the discrete element method (DEM) was used to investigate the influence of particle shape and interparticle friction on the bulk friction in a Jenike direct shear test. Spherical particle and non-spherical particles using two overlapping sphere giving particle aspect ratio of up to 2 and a full range of interparticle contact friction coefficient were studied numerically. These were compared with physical Jenike shear tests conducted on single glass beads and paired glass beads. To separate the influence of sample packing density from interparticle contact friction on the bulk shearing response, the same initial packing was used for each particle shape in the simulations. The interplay between contact friction and particle interlocking arising from geometric interaction between particles to produce the bulk granular friction in a direct shear test is explored and several key observations are reported. The results also show that particle interlocking has a greater effect than packing density on the bulk friction and for each particle shape; DEM can produce a good quantitative match of the limiting bulk friction as long as similar initial packing density is achieved.     

Characterisation of inter-particle forces within agglomerated metallurgical powders

The strength of agglomerates of nickel flash furnace concentrate and dust was determined from experimental observations of agglomerates forming under controlled conditions, combined with mathematical equations from the literature. It was found that the agglomerates had a tensile strength ranging from 0.01 Pa to 38.7 Pa, while inter-particle forces ranged from 2.2 × 10^− 12 N to 1.5 × 10^− 10 N. These values were compared to the expected magnitude of van der Waals, electrostatic, magnetic and capillary forces within the agglomerates, and it was found that both electrostatic and van der Waals forces are likely to contribute to the cohesion of agglomerates, although sub-micron particles and the presence of sufficiently large asperities on the surface of particles limit the magnitude of van der Waals forces. Magnetic forces are large enough to contribute to the cohesion of dust agglomerates, which is in keeping with the high magnetite content of the recycle dust. It is postulated that electrostatic forces, acting over a longer range than van der Waals forces, may be responsible for initially bringing particles together. The methodology for determining inter-particle forces can be applied to the computer modelling of flash smelting systems, as well as other gas/particle systems such as fluidized beds.     

Flow mark defects reduction of injection-molded polypropylene by dynamically vulcanized polyolefin elastomer

Flow mark defects (FMs) worsen surface esthetics and mechanical properties of injection-molded polypropylene (PP). In this work, experiments and dissipative particle dynamic (DPD) simulations were used to investigate the effect of dynamically vulcanized polyolefin elastomer (POE) on FMs of injection-molded PP. Significant FMs reduction was achieved by dynamically vulcanized POE. DPD simulations indicated that POE molecules were randomly distributed in the PP, while dynamic vulcanization led to the formation of elastomeric quasi-clusters, and these quasi-clusters were able to reduce FMs. Both DPD simulations and scanning electron microscopy results showed that more agglomerates with longer and irregular shapes formed with longer vulcanization time and more initiators. The formation of too many agglomerates resulted in different pock surface defects. Dynamically vulcanized POE produced at optimal reaction conditions did not affect the tensile strength, tensile modulus, flexural strength, and flexural modulus, while breaking elongation and notched Izod impact strength of injection-molded PP decreased slightly. This work suggests that the addition of dynamically vulcanized POE may be a promising way to reduce FMs of injection-molded PP.