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.     

Investigation of the dispersion of carbon black agglomerates of various sizes in simple-shear flows

The dispersion of spherical carbon black agglomerates suspended in polydimethyl siloxane liquid and subjected to simple shear flows has been studied in a cone-and-plate shearing device. Sets of dispersion experiments were carried out for agglomerates of various size and packing density. For agglomerates of equal density and under conditions of equivalent cone rotation rates, the dispersion rates of small agglomerates were smaller than those observed for larger agglomerates. Since the agglomerates occupy a significant fraction of the flow domain, the magnitude and distribution of shear stress acting on the agglomerate at a fixed cone rotation rate depends on the ratio of agglomerate size relative to the size of the gap between the cone and plate. To investigate whether this effect could cause the observed variation in dispersion behavior, we performed three-dimensional simulations of the flow fields within the cone-and-plate device and calculated the resulting stress fields acting on spherical agglomerates. These results helped guide additional experiments in which the peak stress acting on agglomerates of various sizes was matched. However, even under matched stress conditions, the dispersion kinetics was found to vary according to the agglomerate size. In addition, the dispersion kinetics for identical sized agglomerates was found to depend on their processing history. Both of these results lead to the conclusion that some other effect, likely the infiltration of the processing fluid within the agglomerate structure, also influences the dispersion behavior.     

Dispersion and aspect ratio of carbon nanotubes in aqueous suspension and their relationship with electrical resistivity of carbon nanotube filled polymer composites

Multiwalled carbon nanotube (MWCNT)/acrylonitrile butadiene styrene (ABS) composites were prepared by a processing method using solvent–nonsolvent precipitation. Size distributions of MWCNT agglomerates in aqueous suspension were investigated in order to predict aspect ratio of nanotubes by evaluating the effects of sonication time, MWCNT content, and surfactant. Aspect ratios of MWCNTs were predicted on the basis of the size distribution measurements for MWCNT agglomerates. Sonication time or applied sonic energy has a strong effect on the size distribution of MWCNT agglomerates. Compared with simple shear mixing method, it was shown that this processing method is more suitable for the MWCNT/ABS composites. An electrical percolation threshold was observed for the weight fraction of MWCNTs in the range of about 0.5–1.0 wt.%. Shorter MWCNTs are more suitable to induce fine dispersion, but lead to higher percolation threshold weight fraction. It was illustrated that fine dispersion can overcome the handicap of short length or low aspect ratio of MWCNTs.     

Agglomeration of fine particles subjected to centripetal compaction

Agglomeration is a common phenomenon in many processes. The mechanical properties of agglomerates strongly depend on their structures. This paper presents a numerical study of the agglomeration of fine particles down to 1 μm in size based on the discrete element method. The agglomerates were formed with particles initially generated randomly in a spherical space and then packed under an assumed centripetal force. Agglomerate structure, packing density, coordination number and tensile strength were analysed with particular reference to the effect of particle size associated with the van der Waals attraction. The results showed that both the packing density and coordination number of the agglomerates decay exponentially to their limits as agglomerate size increases. The tensile strength of the agglomerates was calculated from the simulations and shown to decrease with the increase of particle size. The strength was also estimated from the Rumpf model supported by the empirical equations formulated based on the present simulation results. The good agreement between the results from the simulations and the estimation indicates that the equations are useful to facilitate engineering applications.     

The behaviour of the dispersed phase in liquid-liquid cocurrent flow through a packed bed

The drop size distributions produced by the cocurrent flow of kerosene dispersed in water through a vertical column packed with spheres have been measured at different levels of flow rate, volume fraction dispersed phase, packing diameter and height of packed bed. The drop size measurements were made by isolating and photographing a portion of the dispersion as it emerged from the packing. The Sauter mean diameter is predicted by: where C is a constant, f(?) is the phase fraction effect, ∈ is the power input per unit volume, τ is the residence time and d_p is the packing diameter.     

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 Stochastic Pocket Model for Aluminum Agglomeration in Solid Propellants

A new model is derived to estimate the size and fraction of aluminum agglomerates at the surface of a burning propellant. The basic idea relies on well‐known pocket models in which aluminum is supposed to aggregate and melt within pocket volumes imposed by largest oxidizer particles. The proposed model essentially relaxes simple assumptions of previous pocket models on propellant structure by accounting for an actual microstructure obtained by packing. The use of statistical tools from stochastic geometry enables to determine a statistical pocket size volume and hence agglomerate diameter and agglomeration fraction. Application to several AP/Al propellants gives encouraging results that are shown to be superior to former pocket models.     

Macrokinetics of Combustion of Monodisperse Agglomerates in the Flame of a Model Solid Propellant

The paper describes a procedure for studying the macrokinetics of combustion of agglomerates in a solid propellant flame using special samples of a model propellant generating monodisperse agglomerates. Empirical dependences of the incompleteness of aluminum combustion in the combustion products of a propellant based on ammonium perchlorate and HMX on time and pressure were established. The mass fraction of oxide accumulated on a burning agglomerate versus the degree of aluminum conversion was determined. For fine agglomerates (310–350 m), this fraction decreases with increase in the degree of conversion. For large agglomerates (400–540 mum), it increases, and, hence, the mass of large agglomerates increases as aluminum burns out. Because of accumulation of oxide, the agglomerate size does not change markedly in the examined range of parameters.     

Effect of lubrication on the distribution of force between spherical agglomerates during compression

We employ the carbon paper technique to aid the understanding of in die force and spatial distributions, upon compression of approximately 1 mm sized spherical agglomerates (pellets) of microcrystalline cellulose (MCC). The aim in this study was to test for the effect of lubricant film on force and spatial distributions. Pellets of MCC were formed via granulation and extrusion/spheronisation. Investigation of pellet bed compression was performed on a materials tester. Prior to compression studies the pellets were characterised for bulk density, size and deformability. Two pellet types were investigated; MCC and MCC lubricated with magnesium stearate. The carbon paper technique relies upon carbon paper as the medium for transferring imprints from compressed pellets onto photo quality paper. The digitised images of these imprints form the basis of analysis through the use of image processing software. Using the carbon paper technique within the range of 10-30 MPa indicates that lubrication does not have a significant effect on the distribution of forces between spherical agglomerates during uniaxial compression. Spatial analysis of the imprints revealed that the lubricated pellets exhibited a higher packing order than the unlubricated ones at low applied pressures (10 and 20 MPa), a difference that could not be observed at 30 MPa. Hence interparticle friction and/or cohesion appear to influence the initial particle rearrangement, whereas confinement is suggested to dominate at higher pressures.     

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.     

Processing and Sintering of Ultrafine MgO-ZrO2 and (MgO, Y2O3)-ZrO2 Powders

Chemical coprecipitation was used to produce ultrafine and easily sinterable MgO-stabilized and (MgO, Y₂O₃) stabilized ZrO₂ powders. The sintering behavior is very sensitive to post-precipitation washing because "hard" agglomerates form when the precipitated gels are washed with water, whereas "soft" agglomerates form when they are washed with ethanol. The soft agglomerates pack uniformly, resulting in homogeneous shrinkage of powder compacts to near-theoretical density. The hard agglomerates result in compacts which have regions of localized densification and a signifiint fraction of residual porosity.     

Yield Stress of Multimodal Powder Suspensions: An Extension of the YODEL (Yield Stress mODEL)

The prediction of the rheological properties of concentrated suspensions is of great importance both in industrial processes (ceramics, cements, and pharmaceutics) and natural phenomena (debris flow, soil erosion). In a previous paper, we presented a new model (YODEL) that can predict the yield stress of concentrated particulate suspensions. The model is based on first principles and takes into account particle size distribution, interparticle forces, and microstructural features. It was validated using data from the literature on four different alumina powder suspensions. The current paper extends the application field of the YODEL, successfully, to multimodal distributions of much interest in the cement and concrete field. The key parameter governing the predictive capacity of the YODEL for multimodal distributions was shown to be the maximum packing fraction of the powder mixtures. The de Larrad compressive packing model was used to provide a maximum packing fraction for mixtures from their particle size distributions. The YODEL can predict yield stresses of multimodal suspensions within 10% of the experimental results. Further improvement of the maximum packing fraction prediction should help in our goal of yield stress prediction from basic powder and suspension characteristics.     

Dispersion of high-viscosity liquid-liquid systems by flow through SMX static mixer elements

The pressure drop and the dispersed phase drop size distribution have been measured for flow through SMX static mixer elements, in columns of diameter 41.18 and 15.75 mm, for a continuous phase of aqueous corn syrup and a dispersed phase of silicone oil. For single-phase flow the pressure drops were consistent with known literature correlations. In the presence of the dispersed phase the pressure drops were increased about 20% above the expected single-phase values, showing more short-term fluctuations but with no significant effect of the flow fraction of the dispersed phase. Droplet size distributions were measured by the computer-aided analysis of images from a digital camera. For shorter lengths of packing the distributions showed a significant “tail” at the large-diameter end, but as the packing length was increased the tail decreased or became non-existent. The mean drop sizes have been compared with a new model based on drop formation at equivalent point sources within the packing.     

Numerical simulation of flow behavior of agglomerates in gas–cohesive particles fluidized beds using agglomerates-based approach

Flow behavior of gas and agglomerates is numerically investigated in fluidized beds using a transient two-fluid model. It is assumed that the particles move as agglomerates rather than single particles in the gas–cohesive particles fluidized beds. The present model is coupled a modified kinetic theory model proposed by Arastoopour (2001) with an agglomerate-based approach (ABA). The interaction between gas and agglomerates is considered. The agglomerates properties are estimated from the ABA. Predictions are compared with experimental data measured by Jiradilok (2005) in a bubbling fluidized bed and Li and Tong (2004) in a circulating fluidized bed. The distributions of velocity, concentration and diameter of agglomerates, and pressure drop are numerically obtained. The influences of the contact bonding energy on the distributions of velocity and concentration of agglomerates are analyzed.     

Condensed Combustion Products of Aluminized Propellants. III. Effect of an Inert Gaseous Combustion Environment

The effect of gaseous combustion environment on particle size distribution and chemical compositions of condensed combustion products of a model propellant containing ammonium perchlorate, binder, and 23.4% aluminum was studied. Experiments were conducted at pressures of 0.6, 4.0, and 7.5MPa. Oxide particles with sizes of 1.2–60 m and agglomerates with sizes from 60 m to maximum were investigated. In experiments with nitrogen and helium, the difference in the mean sizes of the sampled agglomerates does not exceed the experimental error. The difference in the amount of unreacted (metallic) aluminum in the agglomerates sampled in nitrogen and helium is also negligible. Replacement of nitrogen by helium affects the size distribution of the oxide particles by increasing the mass fraction of particles with sizes of 1.2–10 m, and this effect is enhanced with pressure.     

超细粉流化机理和团聚现象的探讨

在直径60mm的流化床中，以SiO2和TiO2超细粉为原料，考察了粉体物性、粉体填充状态和空气湿度等因素对超细粉流化行为和聚团性质的影响，结果表明：超细粉的流态化经历了活塞流、过渡区和聚团流化3个阶段；聚团的流化行为与大颗粒相似；初始填充状态对超细粉流化行为和聚团大小有重要影响，松填充有利于减小聚团尺寸和减少颗粒夹带，提高流化质量；并结合粉体层受力分析，对超细粉的流化机理和团聚现象进行了探讨。     

A One-Dimensional Model for Coagulation,Sintering, and Surface Growth of Aerosol Agglomerates

The size of the primary particles in aerosol agglomerates is determined in part by the interplay of surface growth, coagulation, and sintering. These processes are modelled by a one-dimensional (1-D) discrete-sectional model, DISGLOM2, which predicts the evolution of agglomerate and primary particle size distributions. DISGLOM2 is an extended version of DISGLOM (Rogak 1997), in which particles smaller than the "melting diameter" were assumed to sinter instantly while bigger particles did not sinter at all. Gradual sintering, "condensational obliteration" (whereby primary particles are lost during heavy surface growth), and diffusional wall deposition have been incorporated into DISGLOM2. Results from DISGLOM2 were comparable with those from 2-D sectional models, but DISGLOM2 was much faster. In addition, DISGLOM2 includes the effects of "condensation" of small spherical particles on large agglomerates, which were not modelled previously. The effect of condensation was shown to be significant at low temperature. DISGLOM2 was used to predict the primary particle diameter of titania particles generated by precursor reaction. By adding gradual sintering, the growth rate of agglomerate particles by coagulation was slightly decreased and the primary particle size considerably increased compared with the results given by DISGLOM. Although DISGLOM2 is an efficient model of the relevant physical processes, the predictions are sensitive to the kinetics of precursor reactions and particle sintering, which can be difficult to characterize in real experimental systems.     

Bipolar diffusion charging of spheres and agglomerate aerosol particles

The effect of particle shape on the diffusion charging of aerosols was investigated. The charging-equivalent sphere diameter d_QE, found previously to be much larger than the mobility diameter d_m, may be related to the uncharged fraction of particles leaving a bipolar diffusion charger. This fraction was measured for three types of particles classified by electrical mobility: polystyrene latex (PSL) spheres, ammonium sulfate spheres and TiO₂ agglomerates of 10–20 nm primary particles. The uncharged fraction was 5% lower for the agglomerates than for spheres with the same mobility, for size range 100 < d_m < 800 nm. This implies that d_QE 1.1 d_m for the agglomerates, which is a smaller difference between d_QE and d_m than reported by previous studies, but is consistent with the theoretical predictions (Laframboise and Chang, 1977, J. Aerosol Sci. 8, 331–338).     

Size Distribution Change of Titania Nano-Particle Agglomerates Generated by Gas Phase Reaction,Agglomeration, and Sintering

In the manufacturing of nanometer-sized material particlulates by aerosol gas-to-particle conversion processes, it is important to analyze how the gas-phase chemical reaction, nucleation, agglomeration, and sintering rates control the size distribution and morphology of particles. In this study, titania particles were produced experimentally by the thermal decomposition of titanium tetraisopropoxide (TTIP) and oxidation of titanium tetrachloride (TiCl 4 ) using a laminar flow aerosol reactor. The effect of reaction temperature on the size and morphology of the generated particles was investigated under various conditions. The size distributions of agglomerates were measured using a DMA/CNC system. The size distributions of primary particles were measured using TEM pictures of the agglomerates sampled by a thermophoretic aerosol sampler. In order to model the growth of both agglomerates and primary particles simultaneously, a two-dimensional discrete-sectional representation of the size distribution was employed, solving the aerosol general dynamic equation for chemical reaction, agglomeration, and sintering. Qualitative agreement between the experimentally observed results and the simulation are satisfactory for the large variations in reactor temperature explored.     

Packing of Quaternary Mixtures of Fibrous Particles

This paper presents an experimental investigation of packing of quaternary mixtures of fibrous particles of the same diameter but different lengths. The results indicate that the packing density is heavily dependent on the fractional solid volumes and hence the size and shape distributions involved. The packing of fibrous particles appears to be dominated by the shape effect rather than the size effect, and can be satisfactorily predicted by the modified linear packing model.