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.     

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.     

Effect of the Interparticle Pair Potential on the Rheological Behavior of Zirconia Powders: I, Electrostatic Double Layer Approach

Aqueous slurries containing 20 vol% ZrO₂ powder doped with 3 mol% Y₂O₃ were prepared by first dispersing the powder at pH 11, then adding 0.1 M to 1.0 M tetramethylammonium chloride (TMACl), or 1.0 M of TPACl, CsCl, and LiCl to produce different, weakly attractive particle networks. The particle pair potentials in the slurries were investigated by viscosity versus shear rate measurements. Slurries exhibited increasing viscosities (at a given shear rate) with increasing salt concentration and decreasing (unhydrated) counterion size. The viscosities for these weakly attractive networks were intermediate to dispersed (pH 11 without added salt) and flocced (isoelectric point, pH 7.5) slurries. Cylindrical bodies were consolidated from these slurries by pressure filtration at different applied pressures. The bodies consolidated from slurries formulated with TMACl had the highest packing densities relative to those consolidated from a flocculated slurry, but the relative densities were much lower than those achieved from bodies consolidated from a dispersed slurry. The plastic or brittle nature of these bodies was determined in uniaxial compression. Powder compacts consolidated from flocced slurries and slurries coagulated with 1 M TMACl, CsCl, and LiCl showed plastic behavior for filtration pressures ≤7.5 MPa. Results for ZrO₂ will be compared with those previously obtained for Al₂O₃, which produces plastic, consolidated bodies over a much broader range of slurry conditions.     

Rheology and Particle Packing of Chem- and Phys-Adsorbed, Alkylated Silicon Nitride Powders

Three alcohols with extended carbon chain lengths between ∼1 and 2 nm were chem-adsorbed on a Si₃N₄ powder by reacting with hydroxyl surface groups at temperatures 200°C. Slurry rheology, particle packing density, and body rheology were determined for toluene and dodecane slurries formed with these chem-adsorbed powders. These same properties were determined for slurries where the alcohol was simply added, but not reacted with the powder (phys-adsorbed powders). The viscosities of chem-adsorbed slurries are shear-thinning with longer chains producing lower viscosities at a given shear rate. The relative density of powder compacts produced by pressure filtration (10 MPa) was high (∼0.60) for octadecanol and dodecanol-reacted powders, and lower (∼0.50) for the octanol-reacted powder. When a sufficient amount > 10 times that required for chem-adsorption) of the same alcohol was simply added to the unreacted Si₃N₄ slurry system, the phys adsorbed slurries exhibited similar rheological behavior as the chem-dsorbed slurries, but, unlike chem-adsorbed slurries, their packing densty was lower, and their slurries were destabilized by water vapor. Stress relaxation experiments showed that bodies formed with the octadecanol chem-adsorbed powders were plastic after consolidation, whereas phys-dsorbed bodies were brittle (fractured before flow). All evidence suggests that the short-chained alkyl groups are steric "stabilizers" at small interparticle distances and thus prevent the particles from making surface-surface contact in common organic liquids; i.e., they produce a short-range interparticle, repulsive potential. Chem-adsorbed molecules, but not phys-adsorbed molecules, persist during particle packing and in moist environments.     

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.     

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.     

Effects of pH and Particle Size on the Processing of and the Development of Microstructure in Alumina–Zirconia Composites

The aqueous processing of binary suspensions that contain 0.50-μm alumina and either 0.20- or 0.71-μm zirconia was studied from pH 3 to 11, emphasizing colloidally stable systems. Differences in particle size and density can induce differential sedimentation and lead to a nonuniform oxide distribution in pellets prepared by pressure filtration. Uniformity improves when the zeta potentials of the unlike particles are of the same sign but differ greatly in magnitude, i.e., in the pH range 5 to 6, where the oxides experience a weak, mutual association. However, when they are more similar electrostatically, they do not mutually associate and uniformity suffers. This nonuniformity occurs with the adjustment of pH to ≪5 (pos ive particles) and the adsorption of soluble species that strongly alter the zeta potential, e.g., after the preexposure of zirconia to aluminum chloride (positive particles) and the addition of polyacrylic acid (negative particles). In these cases, either high viscosity or rapid consolidation are required to ensure a uniform distribution. The disparity in the particle number fraction, derived from the size differences, and the thermodynamic interparticle energies control the prefired microstructure and are central to the prediction of the proper processing conditions.     

Concentrated suspension-based additive manufacturing – viscosity,packing density,and segregation

This paper describes the influence of particle size distribution (PSD) of refractory silica on the suspension viscosity, packing density, and segregation in layers solidified by ceramic stereolithography (CerSLA). Using bimodal PSD displays most significant decrease of suspension viscosity than suspension made of mono-modal PSD. Given the Krieger-Dougherty model and packing density experiment, the lower viscosity results from the higher maximum volume fraction, φ_m, reached through the closely packed particles. Furthermore, from the differential sedimentation of coarser or denser particles in suspensions, particle size segregation in layers is detected. To determine the distribution of particle size within each layer, a linear intercept method is used, which demonstrates the vertical changes in PSD. Mono–modal PSD case show severe segregations in solidified layers in which the population of larger or denser particles is greater near the bottom. However, much less segregation occurs with bimodal PSD due to suppressed segregation.     

水力旋流器内非牛顿流体多相流场的数值模拟

利用一种非牛顿流体黏度修正模型描述水力旋流器内高浓度矿浆的非牛顿流动特性,并结合雷诺应力模型(RSM)、混合多相流模型(Mixture)以及拉格朗日颗粒追踪模型(LPT)建立了一种适用于模拟水力旋流器内非牛顿流体多相流场的数学模型。模拟结果与报道的实验值的相对误差均在10%以内,表明了该模型的可靠性。结果表明,非牛顿流体黏度的空间分布与矿浆密度的空间分布类似。沿零轴速包络面(LZVV)的轮廓存在一个高密度环,其原因为某粒径范围内的颗粒受到的径向合力为零,颗粒群沿LZVV做高速旋转运动。分散相的空间分布取决于不同粒径的颗粒受力。对于不同粒径的单位质量颗粒,向外离心力的数值大约为向内压力梯度力的两倍左右,使得大颗粒进入下行流并在底流口收集。随着颗粒粒径的减小,总体向内且具有波动性的流体曳力呈指数增长。向内的流体曳力将部分颗粒推向轴心,经上行流逃逸,同时也增强了颗粒运动的随机性。当颗粒粒径小于一定值后,流体曳力远远大于离心力和压力梯度力,颗粒运动的随机性非常强,宏观表现为均匀分布。     

中国卫生陶瓷行业的发展与努力方向

经过30多年的迅猛发展,中国卫生陶瓷产量已多年位居世界第一,成为名符其实的世界卫生陶瓷生产大国。笔者介绍了中国卫生陶瓷行业由最初引进国外先进技术和设备到消化吸收,科技创新,逐步形成完整的工业体系的发展历程;指出了中国卫生陶瓷目前尚存在的不足;提出了中国卫生陶瓷行业会今后努力的方向。     

Yodel: A Yield Stress Model for Suspensions

A model for the yield stress of particulate suspensions is presented that incorporates microstructural parameters taking into account volume fraction of solids, particle size, particle size distribution, maximum packing, percolation threshold, and interparticle forces. The model relates the interparticle forces between particles of dissimilar size and the statistical distribution of particle pairs expected for measured or log-normal size distributions. The model is tested on published data of sub-micron ceramic suspensions and represents the measured data very well, over a wide range of volume fractions of solids. The model shows the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter. Not all the parameters in the model could be directly evaluated; thus, two were used as adjustable variables: the maximum packing fraction and the minimum interparticle separation distance. The values for these two adjustable variables provided by the model are in good agreement with separate determinations of these parameters. This indicates that the model and the approximations used in its derivation capture the main parameters that influence the yield stress of particulate suspensions and should help us to better predict changes in the rheological properties of complex suspensions. The model predicts the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter, but the experimental results do not show a clear dependence on diameter. This result is consistent with previous evaluations, which have shown significant variations in this dependence, and the reasons behind the yield stress dependence on particle size are discussed in the context of the radius of curvature of particles at contact.     

High voidage fluidization — the prediction of particle and fluid velocities

A fluidized system in which there is a combination of small particle size, low density difference between solids and fluid, and high fluid viscosity is characterized by high voidage and a low value of interparticle fluid velocity. In a ‘flow-through’ reactor in which these conditions prevail it is possible to define the net upward velocities of the solids and fluid in a way which takes account of the size distribution of the solids, so that there is a unique upward velocity for each particle size. From this, the equilibrium particle size distribution in the reactor can be predicted.     

VibraForming and In Situ Flocculation of Consolidated, Coagulated, Alumina Slurries

Aqueous, alumina slurries dispersed at low pH form weakly attractive networks when excess counterions are added. These slurries can be consolidated to a high relative packing density via either pressure filtration or centrifugation without mass segregation or density gradients. These saturated, consolidated bodies can be reshaped by vibrating them into a complex-shaped die cavity, a process termed VibraForm-ing. The yield stress of these bodies can be increased by adding urea to the slurry before consolidation and then heating the VibraFormed body to change the pH of the water within the body to the isoelectric point for the alumina powder. The increased yield stress, characterized by stress relaxation experiments, allows the body to be removed from the die cavity without shape distortion.     

Effects of the Homogeneity of Particle Coordination on Solid-State Sintering of Transparent Alumina

A quantitative assessment of the homogeneity of particle coordination in green bodies is achieved by addressing pore structures. Avoiding a coarser tail of the pore size distribution is important but insufficient for optimum sintering. Instead, the steepest slope of the main body of the distribution is responsible for a maximum density at lowest temperature, and further progress is enabled by minimizing interparticle spacing (the average pore size). Ranking different technologies with different associated pore size distributions, the same correlation holds for the impact of homogeneity on (i) sintering densification as (ii) for the onset of intense grain growth during the final sintering stage. For all of the investigated processing approaches the pore size distributions are observed to remain constant through the initial and intermediate states of sintering.     

Controlling attractive interparticle forces via small anionic and cationic additives in kaolin clay slurries

Interparticle forces govern slurry behavior in flow, mixing, sedimentation and thickening. This study evaluates the use of small anionic and cationic additives with pH to control the interparticle forces in kaolin slurry via the yield stress parameter. Both phosphate and citrate additives were found to reduce the interparticle attractive force or yield stress in the moderate pH region of 4–12. These relatively low charged additives were unable to impart a sufficiently strong repulsive interparticle force to completely disperse the slurry. Three linear relationships between yield stress and the square of zeta potential were observed in slurry with and without these additives, indicating that the yield stress–DLVO force model is obeyed in each linear region. The mid-range zeta potential region yielded a positive slope which was attributed to heterogeneous charge attraction between clay particles. It is this heterogeneous charge attraction that was weakened by the adsorbed additives. In contrast, cationic Polyethylenimine (PEI) of Mw 70,000 increases the yield stress at all pH level via bridging. Charge reversal was also observed at high PEI concentrations. In two cases, the pH of maximum yield stress and zero zeta potential coincided. A single linear yield stress–zeta potential squared relationship was observed despite particle bridging interaction being the dominant interparticle force.     

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.     

粒度级配对神华煤成浆特性影响的试验研究

为了研究粒度级配对神华煤成浆特性的影响,通过筛分和干法调浆,探讨了不同粒度分布煤粉的成浆性,结果表明:在添加剂用量为0.3%(干基/干煤)时,具有连续级配特征的原始煤粉可制备出质量分数为61%的煤浆;利用筛分法,分别去除原始煤粉中0.045 mm以下、0.045 mm^0.15 mm、0.15 mm^0.3 mm和0.045 mm^0.3 mm部分,得到4种具有不连续级配特征的样品,其所制煤浆流变性发生了较大变化,其中去除0.045 mm^0.3 mm部分的样品的成浆质量分数提高了3个百分点,在黏度符合要求的前提下流动性大幅提高;连续级配和非连续级配的煤浆均存在黏度与流动性不统一的现象,当级配中粗细颗粒粒径差较大且细颗粒含量达到一定值时,这种现象更加明显。采用粒度级配技术制浆,其细颗粒含量存在一个合理的区间。     

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.     

Modeling and rheology of HTPB based composite solid propellants

The propellant with the minimum viscosity required for a defect-free casting can be obtained by proper selection of the size and fractions of solid components leading to maximum packing density. Furnas' model was used to predict the particulate composition for the maximum packing density. Components with certain size dispersions were combined to yield a size distribution that is closest to the optimum one given by Furnas for maximum packing. The closeness of the calculated size distribution to the optimum one was tested by using the least square technique. The results obtained were experimentally confirmed by viscosity measurement of uncured propellants having HTPB binder and trimodal solid part accordingly prepared by using aluminum (volumetric mean particle diameter of 10.4 μm) and ammonium perchlorate with four different sizes (volumetric mean particle diameters: 9.22, 31.4, 171, and 323 μm). The experimental measurements showed that the compositions for the minimum viscosity are in good agreement with those predicted by using the model for maximum packing. The propellant consisting of particles with mean diameters of 10.4, 31.4, and 323 μm was found to yield the minimum viscosity. This minimum viscosity was observed when the fraction of the sizes with respect to total solids was 0.141, 0.300, and 0.559, respectively.