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.     

Effect of vibration condition and inter-particle frictions on the packing of uniform spheres

We present a numerical study of the packing of uniform spheres under three-dimensional vibration using the discrete element method (DEM), focusing on the effects of vibration condition (amplitude and frequency) and inter-particle frictions (sliding and rolling frictions). The results are analysed in terms of packing density, coordination number (CN), radial distribution function (RDF) and pore structure. It is shown that increasing either the vibration amplitude or frequency causes packing density to increase initially to a maximum and then decrease. Both vibration frequency and amplitude should be considered to characterize the effect of vibration process on packing structure. The sliding and rolling frictions between particles can decrease packing density since they dissipate energy, although the effect of rolling friction is less significant. In line with the change of packing density, microstructural properties such as CN, RDF and pore distribution also change: a looser packing often corresponds to smaller CN, less peaked RDF and larger but more widely distributed pores.     

Melt‐rheological behavior of high‐solid cement‐in‐polymer dispersions

The rheological behavior of a series of poly(ethylene oxide) melts containing nonhydrated cement is investigated using stress‐sweep measurements. The influence of the polymer end‐group—diol, monomethyl ether, and dimethyl ether—, molecular weight, and the particle volume fraction is examined. The data suggests that monomethyl ethers adsorb with their single OH group head‐on on the cement surface, which reduces the interparticle friction and the viscosity, but mixtures based on monomethyl ethers exhibit shear‐thickening behavior. The diols cause the formation of hydrogen‐bonded particle networks leading to high viscosities, but these mixtures exhibit shear‐thinning behavior due to the collapse of the network upon shearing. On increasing the particle volume fraction, the samples feature a nonlinear increase in viscosity. Fitting these data indicated that the maximum particle volume fraction is close to the random packing density of spheres and decreases with decreasing shear stress. As coating for glass rovings, the mixtures match the reinforcing performance of solvent‐based systems despite lower cement content. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

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.     

Interparticle Potentials in Nonaqueous Silicon Nitride Suspensions

The rheological properties of nonaqueous silicon nitride suspensions are studied. Suspensions were prepared to volume fractions of solids of 0.21, 0.25, 0.29, and 0.33, and dispersed with phosphate ester in a mixture of solvents (methyl ethyl ketone, methyl isobutyl ketone, and cyclohexanone). Expanded viscosity curves were obtained by measuring under controlled rate and stress conditions, and the experimental data were fitted to the Cross model that provides the high shear limiting viscosity (η_∞). The evolution of viscosity with volume fraction of solids was fitted to the Krieger-Dougherty equation, to predict the maximum packing fraction (φ_m). The electrostatic pair potential was calculated based on the DLVO theory by evaluating the dielectric constant of the three-component solvent and the Hamaker constant of the Si₃N₄–solvent system. The surface potential was calculated by measuring the elastic modulus through dynamic rheological measurements. The steric potential was also evaluated from the available models. It has been observed that phosphate ester provides a purely steric stabilization at short separation distances (up to 9 nm), while electrostatic forces dominate at larger separation distances.     

Modeling of sedimentation of polydisperse spherical beads with a broad size distribution

This article deals with experimental and theoretical studies of the sedimentation of polydisperse agarose beads with broad particle size distributions. A light-extinction principle was used to measure the variation of solid concentration in the suspension with time and settling distance. Different experimental conditions have been used to show the influence of solid concentration and liquid density and viscosity on the settling behavior of the beads. The sedimentation process was described mathematically by a system of conservation law using Masliyah's hindered settling function. The physical properties of the beads and the optical properties of the suspension were carefully examined to enable a reliable comparison between experimental and simulation results. The model gives good predictions under all the conditions studied, showing its soundness in formulating the hindered settling process of polydisperse particles in a suspension.     

Improved Equation of the Continuous Particle Size Distribution for Dense Packing

The Furnas model describes the discrete particle size distribution for densest packing. Using a model that considers a continuous particle size distribution for the densest packing to be a mixture of infinite Furnas discrete particle size groups, an equation for the cumulative particle size distribution providing the densest packing was derived. Monosize particles with different shapes have a different packing pore fraction. One parameter in the equation is the pore fraction of packed monosize particles; the particle size distribution for achieving densest packing is a function of this pore fraction. A reduced form of this equation is also presented as a working equation. The equation derived here is compared to the modified Andreasen equation for dense packing. An equation and the correlated graph for calculating theoretically the geometric mean particle size and an equation for calculating the specific surface area of the particle size distribution of the improved equation are also derived.     

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.     

Mass Transfer In Trickle‐Bed Reactors With Structured Packing

An experimental investigation was carried out to examine the fluid dynamic and mass transfer behavior of structured packing, with the liquid and gas phase flowing co‐currently downwards in the column. Liquid to packing mass transfer coefficients for three positions within the pack were measured by an electrochemical method, varying both the liquid and gas loads as well as the physical properties of the liquid phase. Due to the high void fraction of structured packing, much higher liquid flow rates can be used than in traditional particle trickle‐beds. It was found that in the range studied, the gas superficial velocity has no effect on the mass transfer rate and thus, a general mass transfer correlation in terms of liquid Reynolds number only, was developed. Wetted areas and the radial distribution of liquid through the packing element were determined by a colorimetric method. Within the range of liquid flow rates investigated, complete wetting is not achieved, even with the low viscosity solutions. The measured ratios of hydraulic to geometric area, agree reasonably well with values predicted by existing relationships.     

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.     

Effects on the melt rheology of systems of Nd‐Fe‐B particles suspended in a poly(phenylene sulfide) and liquid crystalline polymer blend

The melt rheology of blends of a liquid crystalline polymer (LCP) and poly(phenylene sulfide) (PPS) and their composites with ferromagnetic Nd‐Fe‐B particles (MQP) was studied. We investigated the effects of LCP concentration, Nd‐Fe‐B particle volume fraction and size, distribution, and shear rate on the rheological properties of these composites. Enthalpy of fusion changes that were observed resulted from the addition of the LCP and Nd‐Fe‐B particles to the polymer blends/composites. The shear rate and frequency dependencies of the materials revealed a viscosity reduction at low (1–3 wt%) and moderate (10–15 wt%) LCP concentrations, and strong effects on the shear‐thinning characteristics of the melt. The suspensions of polydispersed Nd‐Fe‐B particle configurations in PPS that were of lower size ratios gave better processability, which is contradictory to previously reported behavior of suspensions containing spherical particles. Specifically, the compositions with unimodal and a bimodal distribution of Nd‐Fe‐B particles gave the lowest viscosities. The experimental data were correlated with semi‐empirical viscosity model equations of Maron‐Pierce, Krieger‐Dougherty, Eilers, and Thomas and were found to be consistent with the data. The maximum packing fraction, ϕ_m, of the MQP particles was estimated to be within the range of 0.78 ϕ ≤_m ≤ 1.0 through graphical and parametric evaluation methods.     

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.     

淘洗六水氯化铝过程中晶体沉降速度与纯化规律分析

针对粉煤灰酸法制氧化铝工艺中六水氯化铝结晶纯度难以控制、需进一步纯化的问题建立液固淘洗过程模拟实验,考察了液相密度、黏度、颗粒粒度及体积分数对颗粒沉降速度的影响,并用液体对颗粒的抵抗阻力对其修正,建立了关于沉降速度的计算模型,相对误差小于10%,能够较好地预测该体系下颗粒的沉降速度。按照淘洗过程模拟实验条件及对应的颗粒沉降速度设计静态实验,考察了钠、钙、镁和钾4种杂质离子随淘洗时间的变化规律,得到较优淘洗时间为60s。实验结果表明,杂质离子脱除率依次为Na⁺>Ca²⁺>Mg²⁺>K⁺,且最高脱除率均可达80%以上,杂质离子脱除率随着液固比的增大而提高,与沉降速度计算模型趋势一致,研究结果可为淘洗工艺的设计计算和优化提供参考。     

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.     

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.     

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.     

Modulus evaluation of particulate composites using generalized viscosity model for solutions with suspended particles

The theoretical relationship between the shear modulus of a particulate reinforced composite and the viscosity of a solution with suspended particles was first proposed by Goodier. Since that time several partially successful attempts have been made in the literature to derive equations to describe the available relative shear modulus–particulate concentration data. Recently a new generalized suspension viscosity equation appeared in the literature which for the first time addresses the detailed effects of particle size, particle size distribution, and packing fraction. This new viscosity equation was applied to available modulus literature on particulate composites in this study. Four significant particulate composite modulus derivations in the literature were all shown in this study to yield the same theoretical “intrinsic modulus” of a particulate composite. The generalized viscosity–modulus equation yielded an excellent fit of the shear modulus–particulate concentration data of both Smallwood and Nielsen using a variable intrinsic modulus. Some fillers predicted the Einstein limiting value of the intrinsic modulus while other fillers yielded intrinsic modulus values that were either larger or smaller than this value. The intrinsic modulus for carbon black in rubber was much larger than Einstein's predicted value. However, intrinsic modulus values smaller than Einstein's prediction were obtained at temperatures below the glass transition temperature of the matrix. Unfortunately, the previously obtained direct relationship between the particle interaction coefficient and particulate size for suspension viscosities with a constant intrinsic viscosity was not obtaind for shear modulus—particulate concentration data using a variable intrinsic modulus. © 1994 John Wiley & Sons, Inc.     

Characteristics of anthraquinone hydrogenation catalysts in a liquid‐solid fluidized bed

The fluidization characteristics of anthraquinone hydrogenation catalysts were investigated in a liquid–solid fluidized bed. The effects of the initial bed conditions such as particle size, bed depth‐to‐column diameter ratio and liquid density and viscosity on the fluidization behaviour, bed expansion and applicability of the Richardson–Zaki equation were studied. The results reveal a strong particle size effect on the Richardson–Zaki (R‐Z) expansion index which in general decreased as the particle diameter increased. One type of particles exhibited two distinct bed expansion behaviours, depending mainly on the bed depth‐to‐column diameter ratio, with an experimentally established boundary at . This behaviour could be attributed to increasing wall friction and a tendency to exhibit slugging. The dependence of the Richardson–Zaki exponent on the liquid dynamic viscosity confirms the classic result .     

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.     

Effect of volume fraction and particle size on wall slip in flow of polymeric suspensions

For especially highly concentrated suspensions, slip at the wall is the controlling phenomenon of their rheological behavior. Upon correction for slip at the wall, concentrated suspensions were observed to have non‐Newtonian behavior. In this study, to determine the true rheological behavior of model concentrated suspensions, “multiple gap separation method” was applied using a parallel‐disk rheometer. The model suspensions studied were polymethyl methacrylate particles having average particle sizes, in the range of 37–231 μm, in hydroxyl terminated polybutadiene. The effects of particle size and solid particle volume fraction on the wall slip and the true viscosity of model concentrated suspensions were investigated. It is observed that, as the volume fraction of particles increased, the wall slip velocity and the viscosity corrected for slip effects also increased. In addition, for model suspensions in which the solid volume fraction was ≥81% of the maximum packing fraction, non‐Newtonian behavior was observed upon wall slip correction. On the other hand, as the particle size increased, the wall slip velocity was observed to increase and the true viscosity was observed to decrease. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 439–448, 2005