Effect of Interparticle Potentials and Sedimentation on Particle Packing Density of Bimodal Particle Distributions During Pressure Filtration

Effect of interparticle forces, bimodal particle size distribution, and slurry viscosity on particle packing in alumina bodies consolidated by pressure filtration is presented. The requirements for packing colloidal particles to their highest density are strong repulsive interparticle forces and optimum particle size distribution. Even though these conditions are met, the high packing density in consolidated bodies may be adversely affected by particle segregation resulting from sedimentation. Therefore, the slurry during consolidation must have a sufficiently high viscosity to prevent sedimentation.     

On the relationship between porosity and interparticle forces

This paper presents an attempt to quantify the relationship between porosity and interparticle forces for mono-sized spheres. Two systems are considered: the packing of wet coarse spheres where the dominant interparticle force is the capillary force, and the packing of dry fine spheres where the dominant force is the van der Waals force. The interrelationships between porosity, capillary force and liquid content are first discussed based on the well-established theories and experimental observations. The resultant relationship between porosity and capillary force is then applied to the packing of fine particles to quantify the van der Waals force in a packing. A generalised relationship between porosity and interparticle forces results as an extension of this analysis. The usefulness of this relationship is finally demonstrated in depicting the fundamentals governing the relationship between porosity and particle size.     

Modification of interparticle forces for nanoparticles using atomic layer deposition

Silica and titania nanoparticles were individually coated with ultrathin alumina films using atomic layer deposition (ALD) in a fluidized bed reactor. The effect of the coating on interparticle forces was studied. Coated particles showed increased interactions which impacted their flowability. This behavior was attributed to modifications of the Hamaker coefficient and the size of nanoparticles. Stronger interparticle forces translated into a larger mean aggregate size during fluidization, which increased the minimum fluidization velocity. A lower bed expansion was observed for coated particles due to enhanced interparticle forces that increased the cohesive strength of the bed. Increased cohesiveness of coated powders was also determined through angle of repose and Hausner index measurements. The dispersability of nanopowders was studied through sedimentation and z-potential analysis. The optimum dispersion conditions and isoelectric point of nanoparticle suspensions changed due to the surface modification. A novel atomic force microscope (AFM) technique was used to directly measure interactions between nanoparticles dispersed on a flat substrate and the tip of an AFM cantilever. Both Van der Waals and electrostatic interactions were detected during these measurements. Long and short range interactions were modified by the surface coating.     

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.     

粘性糊料颗粒间的作用力及其机理分析

在阴极炭块组装过程中，粘性糊料颗粒间的相互作用导致颗粒的成团和破碎，由此影响糊料的微观和宏观行为。本文对两颗粒间的毛细力、范德华力、粘性力、接触力、静电力和重力六种相互作用力的计算进行了阐述。通过对这些相互作用力的量级分析，得到了导致糊料中颗粒成团和破碎行为的主要作用力，并分析了颗粒尺寸对相互作用力的影响。最后对碰撞变形过程中主要作用力随碰撞时间的变化规律进行了研究，通过对比这些力在碰撞过程中的相对大小对颗粒成团的机理进行力学解释。     

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.     

Development of Short-Range Repulsive Potentials in Aqueous, Silicon Nitride Slurries

The properties of aqueous, dispersed, silicon nitride slurries, with an isoelectric point of pH 5.5, can be changed with additions of NH₄CI. At pH 10 the effect of adding NH₄Cl is similar to that suggested by DLVO theory; namely, for concentrations .0.5 M , the viscosity vs shear rate behavior, the elastic modulus, and the relative packing density are identical to those for slurries prepared at the isoelectric point. On the other hand, the effect of salt on dispersed slurries prepared at pH 2 differs from the behavior implied by classic DLVO theory; i.e., measurement of the same properties showed that the attractive interparticle potential was much weaker relative to that produced at the isoelectric point. As previously reported for alumina slurries, the results suggest that a short-range, repulsive interparticle potential is developed in salt-added slurries prepared at pH 2 which prevents attractive particles in the slurry from touching and aids particle packing. The same short-range potential apparently is not developed with salt additions at pH 10. The difference between silicon nitride and alumina slurries is apparent when the slurries are consolidated. Bodies consolidated from any silicon nitride slurry are elastic (i.e., they fracture before they flow) unlike salt-added alumina slur-ries, which are plastic.     

Particle Crowding Analysis of Slip Casting

The particle crowding index and interparticle spacing terms were calculated for seven alumina suspensions. The particle crowding index was used to interpret the casting rate for the tested alumina suspensions; the index was successfully correlated with the casting rate for cakes that produced the same modes of porosity. Unfortunately, this index could not be correlated with the casting rate for the particle system that produced varied porosity as a function of composition. The interparticle spacing term was correlated with viscosity for particle size distributions between 31 and 0.1 μm. For particle size distributions extended to 44 μm, the viscosity could not be correlated with interparticle spacing, because the quantity of fine particles, rather than the particle packing, controlled the viscosity.     

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.     

Influence of Interparticle Forces on the Rheological Behavior of Pressure-Consolidated Alumina Particle Slurries

The stress relaxation behavior of alumina powder compacts, consolidated from aqueous slurries by pressure filtration, is reported. The interparticle forces were controlled prior to consolidation by changing the pH from 3 to 9 and by adding different amounts of salt (0.1 to 2.0 M NH₄Cl) to slurries maintained at pH 4. Disk-shaped bodies were rapidly compiessed to an axial strain of 2%, and the resulting stress relaxation data were monitored as a function of time. For bodies formed from dispersed slurries (pH ≤ 4 without added salt), the stress relaxation behavior consisted of an irreproducible mixture of plastic and elastic response. The initial stress and the stress retained afterlong relaxation periods were highest for bodies formed with flocced slurries (pH 9). For bodies formed with coagulated slurries (pH 4 with added salt), the initial stress increased with the addition of 0.1 to 0.5M salt, but the bodies behaved plastically, with more than 90% of the initial stress relaxing within a short period. These results are consistent with a shortrange, repulsive interparticle force that lowers the attractive force between particles. They also suggest that interparticle forces in consolidated bodies can be controlled in a way that should prove useful in preventing damage that occurs during processing and reshaping Operations.     

Better Sintering through Green-State Deformation Processing

Aqueous colloidal suspensions of alumina were processed in the dispersed state and the flocculated state by controlling the double-layer interactions between the particles. Repulsive particle forces led to high packing densities but the green bodies were mechanically so weak that they were unable to retain their shape (the dispersed case). Attractive forces led to good green strength but the packing density was low and the particles were agglomerated (the flocculated case). The agglomerated structure of the flocced specimens could be fragmented by mechanical deformation of the green compact; the deformation was carried out under a superimposed hydrostatic pressure of less than 1 MPa. The flow stess of the flocculated structures depended on the deformation rate, and on the magnitude of the superimposed hydrostatic pressure. The flow stress was 2.5 kPa at a strain rate of 0.1 s⁻¹. Deformation processing of the flocced structures increased the green (relative) density from 0.51 to 0.62. The sintering behavior of underformed and deformation-processed flocced structures was studied. Deformation-processed green bodies sintered more rapidly and yielded a final grain size that was smaller and more uniform than that obtained from the undeformed specimens. The ability to homogenize and densify the packing of flocculated structures by deformation processing suggests new opportunities in green-state processing, for example (i) uniform mixing of more than one kind of particle or particles and fibers, and (ii) net shape forming by injection molding or extrusion, without the use of organic binders.     

Segregation in granular materials and the direct measurement of surface forces using atomic force microscopy

It is known that one of the dominant forces controlling the macroscopic motion of particles is the cohesive force due to the presence of liquid bridges between particles. In a mixing process, this force directly impacts the degree of homogeneity achievable by the system. The work presented here provides a quantitative analysis of this relationship through concurrent direct measurements of surface forces due to moisture and blending/segregation experiments. Atomic force microscopy (AFM) was employed to measure the force required to remove the AFM's cantilever from the surface of a glass bead with varying degrees of surface moisture. Corresponding blending/segregation experiments were performed using the same materials and conditions to develop a correlation between the interparticle forces due to the liquid layer and the final state of a mixing process. The extent to which greater moisture content increased the interparticle surface forces was quantified, and it was observed that segregation decreases proportionately to increases in surface forces.     

天然气水合物颗粒微观受力及聚集特性研究进展

水合物颗粒微观受力和聚集是影响水合物浆稳定流动的关键,本文调研了国内外研究水合物颗粒受力和聚集常用的测量装置,主要有聚焦光束反射测量仪、颗粒图像显微镜、高压差示扫描量热仪、微机械测力装置;受力测量和理论研究证明了毛细液桥力是导致水合物颗粒聚集的主要黏附力;介绍了常用于水合物聚集特性研究的受力平衡模型,通过该模型可以计算得到水合物颗粒最大临界聚集粒径;总结了众学者提出的水合物颗粒聚集机理,并阐述了基于群体平衡模型建立的接触诱导-剪切限制聚集机理的物理模型,该模型能够很好地描述水合物颗粒的动态聚集过程;水合物颗粒微观受力和聚集机理的深入研究和明确将对石油天然气的输送具有非常重大的意义,确定防聚集对水合物聚集的影响是未来研究的重点。     

影响粉末流化的本征作用力及其调节

本文归纳了人们对粒间力的分析和计算，指出了影响颗粒间作用进而影响其流化质量的各种因素，并从改善微细物料流化质量的角度，综述了近年来国内外流化微细物料的诸多措施，将其归结为两大类型：外力场方法与本征途径，以作为进一步探求微细物料流态化的研究基础．     

Assembly of alumina particles in aqueous suspensions induced by high-frequency AC electric field

The role of high-frequency alternating current (AC) electric field in the assembly of alumina particles in aqueous media was investigated. Field–particle interactions were in situ investigated for coarse and fine powder particles in very dilute suspensions. For both coarse and fine particles, AC field-induced assembly led to the formation of chains of particles within a minute, which were aligned in the field direction. However, a much finer network of particle chains evolved in fine particle suspensions. Threshold field strength for chain formation was also lower for fine particles (28 V/mm) than for coarse particles (50 V/mm), suggesting stronger interactions for finer particles. Chain length increased with both field strength and field duration. Chain formation was attributed to mutual dielectrophoretic (DEP) interaction forces. Increase in DEP forces with field strength resulted in enhanced interactions. For finer particles, decreasing interparticle distance might have favored stronger interactions. Suspension microstructure was disrupted as soon as the field was removed. However, higher field duration was associated with an improved pattern stability and retention following the field removal. Finally, particle motion was studied in deliberately applied spatially nonuniform AC field, which revealed different mechanisms of chain formation for coarse (negative-DEP) and fine (positive-DEP) particles.     

Nanocrystalline γ-Alumina Synthesized by Sonohydrolysis of Alkoxide Precursor in the Presence of Organic Acids: Structure and Morphological Properties

γ-Al₂O₃ nanoparticles with an average size of 5 nm were synthesized by the hydrolysis of aluminum triisopropoxide under the influence of power ultrasound (100 W/cm²) and in the presence of formic or oxalic acids as peptizers, followed by calcination. The structural and morphological properties of the as-prepared precursor hydroxides and calcined nanocrystalline powders were characterized by XRD, SEM, TEM, TGA, IR, and BET. The ultrasound-driven cavitation process has been shown to affect the agglomeration of the precursor nanoparticles by condensation of interparticle hydroxyls. The oxalate anions were strongly adsorbed on the surface of the precursor nanoparticles and thus retarded the ultrasound-driven condensation of interparticle hydroxyls. Formic acid showed a lesser degree of adsorption on the surface of the precursor particles. The ultrasound-driven agglomeration of the primary particles as well as the role of organic modifiers on the microstructural properties of the precursor and the target alumina phases have been discussed.     

The role of the van der Waals force in the agglomeration of powders containing submicron particles

A model has been developed which relates the tensile strength and packing density of powder compacts containing submicron particles to the interparticle force. Hamaker's expression for the van der Waals force and the law of corresponding states are used to develop an expression for the reduced inter-particle force R which is used to evaluate an energy parameter ?_o for a given powder on an absolute scale. The tensile strength of several carbon black and titanium dioxide powders was measured using a split-cell apparatus. Analysis of plots of R against separation distance for the carbon blacks gives an average value of ?_o = 2.1 × 10^?19 J which compares favorably with the literature value of 1.09 × 10^?19 J for the Hamaker constant. This is taken as confirmation that the van der Waals force is dominant in agglomerates of submicron carbon black particles. Similar plots for titanium dioxide powders give values of ?_o that are much higher than that attributed to the van der Waals force alone; the extra force may be due to water on the particle surfaces in the form of adsorbed layers or liquid bridges.     

Effect of Zwitterionic Surfactants on Interparticle Forces, Rheology, and Particle Packing of Silicon Nitride Slurries

Phosphocholine (PC) zwitterionic surfactants, with different hydrocarbon chain lengths (C₆C₆PC to C₉C₉PC), were absorbed on the surface of silicon nitride near the isoelectric point (pH 6). Adsorption of the surfactants changed the lateral and normal surface forces, the rheology, and the consolidation behavior of the particles. The normal force between two silicon nitride surfaces as a function of separation and the lateral (friction) forces were measured using an atomic force microscope (AFM). These measurements indicated that surfactant adsorption reduced the magnitude of the long-range attractive van der Waals force and produced a repulsive short-range force. Although the adsorbed layers provided a barrier to particle contact, they could be ejected with a critical force that increased with the hydrocarbon chain length. The effect of an adsorbed layer on the viscosity and consolidation of slurries was also measured. The viscosity of all slurries decreased with increasing shear rate, indicative of attractive particle networks. The highest viscosity was observed for slurries formulated at the isoelectric point without added surfactant. Much lower viscosities were observed when the surfactant concentration was greater than the critical micelle concentration (cmc). A relative density of 0.46 was obtained via pressure filtration at 4 MPa without a surfactant, and between 0.46 to 0.59 (C₆C₆PC to C₉C₉PC, respectively) for surfactant concentrations greater than the cmc. Comparing force measurements with rheology and packing density provides a basis for discussing the role of interparticle forces in ceramic powder processing via colloidal routes.     

Agglomeration modeling of small and large particles by a diffusion theory approach

The interaction particle‐binder during the wet granulation process plays a major role in the agglomeration of particles. This interaction has been modeled by a force balance acting on the particle where the binder's viscous force increases the strength of liquid bridge and facilitates the particle agglomeration. In this work, agglomeration kernels based on Brownian movement approach of small particles in the binder layer, the size ratio between particles (monodispersed and polydispersed), and binder's viscous forces were considered to model the wet granulation process of pharmaceutical powders in a laboratory‐scale high shear mixer. The assumptions of no‐stationary and pseudostationary behavior were suitable to describe the growth kinetics of the two stages (fast and slow) observed. A volume ratio of 150 between large and small particles produces the most effective granulation growth. The developed kernels were tested simulating experimental data obtained from a high shear mixer. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

ADHESION FORCES OF SPHERICAL ALUMINA PARTICLES ON CERAMIC SUBSTRATES

Adhesion forces of spherical alumina particles on ceramic substrates were studied. Results of direct force measurements using an atomic force microscope (AFM) were compared with theoretical results of a new rod model and with molecular dynamic computer simulation. Spherical alumina particles were produced by a flame process. The particles were glued to cantilevers, and interaction forces were measured by the AFM. A significant reduction of adhesion forces due to adsorbed layers was observed. The interaction volumes were determined by AFM scanning using a soft cantilever. The measured interaction forces were compared with calculated forces using the Hamaker concept including an adsorbed surface layer and the determined interaction volume (rod model). It turned out that calculated adhesion forces, neglecting deformation, are smaller than measured ones. This problem can be overcome if deformation according to Hertz is included in the rod model. Even for such a hard material as alumina, deformation occurs in the contact zone, which was also observed in a molecular dynamic computer simulation.