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.     

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.     

Rheology of Glaze Suspensions

Rheological properties of suspensions and ceramic glaze slurries under steady flow conditions have been considered. Colloidal forces play an important role in the rheology of such ceramic slurries. Since the potential function characterizes the rheology of colloidal systems, a new dimensionless group, viz. potential number, is introduced within a dimensional analysis representing the relative significance of the potential to the Brownian energy. In order to relate the relative viscosity to other dimensionless groups, a new model is proposed by the inclusion of an extra term in addition to that of the hard‐sphere theory owing to the fact that the presence of colloidal forces always increases the fluid viscosity with respect to that predicted by the hard‐sphere. Steady viscosity measurements have been carried out on ceramic glaze suspensions at different volume fractions, particle diameters, and shear rates. Experimental results have been used to modify the model relating the relative viscosity to the Péclet number, potential number, volume fraction, and maximum packing fraction.     

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.     

Factors Controlling the Sintering of Ceramic Particulate Composites: I, Conventional Processing

The effect of processing and material parameters on the sintering and coarsening of model composites consisting of a fine-grained ZnO matrix and coarse, rigid, inert particulate inclusions of ZrO₂ was investigated. The green composites were formed by two methods: (i) mixing the matrix and inclusion powders in a ball-mill followed by die-pressing and (ii) slip casting. For both forming methods, the inclusions caused a significant reduction in the density and the grain size of the composite matrix but had almost no effect on the grain size vs density relationship. The effects of inclusion volume fraction and sintering temperature were somewhat independent of the forming method. However, for the slip-cast composites, the effect of inclusion size was less severe and the packing of the matrix phase immediately surrounding the inclusion showed some improvement. The sintering kinetics and microstructural observations indicated that two main factors controlled the sintering of these composites: (i) interactions between the randomly distributed inclusion particles that created a constraint on the matrix and (ii) the packing of the matrix, especially in regions immediately surrounding the inclusion particles.     

Studies of the Effects of Particle Size Distribution on the Packing Efficiency of Particles

In the studies of pigment volume effects in paint films, particle packing has been shown to be very important. The effects of particle size distribution on this packing has been known but has received little quantitative consideration. In this paper we consider the packing of real and model continuous distributions of particle sizes. An extension of an algorithm for the calculation of random densest packing is given which applies to continuous distributions. Using a log-normal distribution as a model, the effect of the width of a single distribution on packing is considered. Mixtures of distributions are also considered with the calculation of packing efficiency as a function of mean size ratio and distribution widths. Maxima are shown to occur in the packing efficiency of mixtures of distributions as a function of the volume fractions of the individual distributions. The implications of these packing variations in real systems are then discussed.     

基于紧密堆积理论优化超高性能混凝土钢纤维参数

基于改良的Andreasen & Andersen 颗粒堆积模型优化设计了超高性能混凝土(UHPC)的基础配合比,研究了钢纤维的形状、含量及混杂钢纤维对UHPC湿堆积密实度的影响。然后采用D-最优设计(DOD)方法,预测和评估混杂钢纤维对UHPC湿堆积密实度的影响,并基于DOD模型优化设计了UHPC的最佳钢纤维掺量。结果表明,长直纤维、短直纤维、端钩纤维的掺入会对UHPC堆积体系、密实度带来不同程度的影响,其中端钩纤维对UHPC密实度的降低程度最大。此外,钢纤维掺量与UHPC堆积体系也有一定关系,当纤维掺量超过2.0%(体积分数,下同)时,UHPC的密实度急剧下降,造成UHPC堆积体系的显著破坏;基于建立的DOD优化模型分析得出,0.9%的长直纤维与1.1%端钩纤维为最佳纤维混杂方式,可使得钢纤维对UHPC堆积体系的扰乱作用最小化。     

Three-dimensional phase-field study of grain coarsening and grain shape accommodation in the final stage of liquid-phase sintering

A 3-dimensional phase-field model is implemented to simulate the grain evolution in the final stage of liquid-phase sintering. The model considers a liquid phase and a polycrystalline solid phase. Results for varying ratios of the solid–solid interface energy to solid–liquid interface energy and varying solid volume fractions are presented. A variety of microstructures, from fully connected grain structures with liquid pockets at the grain junctions to individual grains fully wetted by the liquid matrix, is seen. The 3 main mechanisms for particle shape accommodation, namely, contact flattening, Ostwald ripening and particle bonding, are reproduced in the simulations. The solid volume fraction, particle size distribution, contiguity, connectivity, particle–particle contact areas and the number of particle contacts per particle are measured as a function of time. The exponent in the power growth law varies between 2.4, for the fully connected grain structures, and 3, for the completely wetted grains.     

Bimodal dispersions in coating applications

This paper describes a study of several model bimodal particle size distribution latex systems produced by blending large and small particle size anionically stabilised latices over a wide range of blend ratios. Minimum film forming temperature (MFT), drying rate, tensile and water uptake measurements were carried out. At a 80/20 weight ratio large/small particles a minimum was observed in the MFT and also in the extent of water absorption of latex films with short drying times, although for films dried for longer periods no such minimum in water absorption was observed. Drying profiles fit well with existing models, except for the 80/201/s blend which exhibits more complex drying behaviour. Low shear rate viscosity of selected blends was measured over a range of latex solids contents. The Theological data were fitted by the Krieger-Dougherty equation which was used to calculate the maximum volume packing fraction. An 80/20 blend (large/small) was found to exhibit a higher maximum volume fraction than that of either pure component of the blend, demonstrating the better packing achievable in blending. A theoretical treatment of the coalescence of bimodal particles is presented in an appendix to the paper.     

The effect of air on the packing structure of fine particles

A numerical study of the effect of air on the packing structure of fine particles has been performed by a combined continuum and discrete numerical model. The forces considered are gravity, contact force, drag force, and van der Waals forces. The results are analyzed in terms of particle rearrangement, local porosity, coordination number, radial distribution function, and the distribution of contact forces. The results indicate the degree to which drag and van der Waals forces promote mean porosity increases and mean coordination number decreases. Drag forces allow contacts of particles reaching a state of rest in a packing to be closer to the Coulomb failure criterion for shear displacement when van der Waals forces are small. Increasing van der Waals forces imposes contact conditions that are far away from the Coulomb failure criterion. Increased drag and van der Waals forces tends to lead to more heterogeneous structure. It is demonstrated that average normal contact force is related to the ratio of van der Waals forces to particle weight.     

Modelling the zero shear viscosity of bimodal high solid content latex: Calculation of the maximum packing fraction

Different rheological tests were performed on monodisperse polystyrene latices and mixtures of two different latices with different particle sizes. A critical volume fraction φ_c was defined for each of the latices. Subsequently, a method based on the estimation of the porosity of a bed of randomly placed spherical particles was adapted to allow us to define the maximum packing fraction for any bimodal system. This method can be used for any ratio of particle diameter and volume fraction for the two populations provided one has knowledge of the critical volume fractions of related monodisperse latices (see Pishvaei et al., 2005. Polymer 46, 1235-1244). The model was tested experimentally, and rheological tests allowed us to validate the values of the critical volume fraction (φ_c) of different bimodal latices. A master curve of viscosity vs. polymer concentration was obtained using the concept of reduced volume fraction. The results prove that we can predict the viscosity of multimodal systems from the knowledge of monomodal packing fraction.     

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.     

The effect of particle size distribution on packing density

The packing density of a multi-particle system is found to increase if the particle size distribution is extended. Results are reported for Gaussian and log-normal size distributions using dense random packing of two sands with particle sizes of front <0.07 to 8.0 mm. Packing density is shown to be a function only of size distribution represented by a dimensionless standard deviation, and of particle shape. It is independent of particle size. Packing densities of binary mixtures of continuously distributed systems are found to depend upon the composition of the mixture, the mean-size ratio of the components of the binary, and upon the packing density of the individual components. Maxima occur at compositions of 55 to 75% larger component, and increasing mean-size ratios result in greater packing densities. The “increase in packing density” factor is a useful function for comparing, and setting limits to, packing densities of binary mixtures. The results should allow improved prediction and control of packing densities of many commonly encountered particle systems.     

Scale and structure dependent drag in gas–solid flows

Drag plays a crucial role in hydrodynamic modeling and simulations of gas–solid flows, which is significantly affected by particle Reynolds number, solid volume fraction, heterogeneity, granular temperature, particle-fluid density ratio, and so on. To clarify and quantify the multiscale effects of these factors, large-scale particle-resolved direct numerical simulations of gas–solid flows with up to 115,200 freely moving particles are conducted. Both domain-averaged kinetic properties and local averaged dimensionless drag are sampled and analyzed. It is revealed that the complex scale-dependence of drag is attributed to the multiscale effects of heterogeneous structures and particle fluctuating velocity. The granular temperature and the scalar variance of solid volume fraction are also found to be scale-dependent. On account of these, a new drag correlation as the function of Froude number is proposed with consideration of scale-dependence.     

Viscosity of Electrostatically Stabilized Dispersions of Monodispersed, Bimodal, and Trimodal Silica Particles

Effect of particle size and polydispersity on the viscosity and maximum packing fraction of aqueous colloidal dispersions has been studied. For dispersions of mono-sized particles, the results indicate that there is a linear relationship between the log(η) (viscosity) and particle size at a fixed shear rate and volume fraction of solids. However, there is a particle diameter at which there is a decrease in the dependency of viscosity on particle size as the slope of the linear plots of log(η) versus particle diameter changes to a smaller value. Preliminary calculations indicate that this particle size may correspond to a separation distance at which electrostatic energy as compared with the thermal energy of the particles can be ignored. In the case of bimodal dispersions, the viscosity is affected by both absolute size and the ratio of the two sizes. The effect of particle size ratio on the viscosity was investigated using bimodal dispersions of the same size coarse particles, but fines of different sizes. There is a critical volume ratio below which bimodal dispersions of larger size ratios show lower viscosities than systems of smaller size ratios. Above this volume ratio of the two sizes, the trend becomes reversed and the fines will have a dominant effect on the viscosity behavior of the bimodal system. Statistically designed experiments were carried out using trimodal mixtures of monodispersed silica particles and it was shown that tridispersed suspensions demonstrate similar behavior as bidispersed suspensions, with a minimum in viscosity observed as a function of particle volume ratio.     

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.     

基于可压缩堆积模型的透水混凝土配合比设计

基于可压缩堆积模型,以全孔隙率为设计指标,提出了一种考虑成型过程和集料级配影响的透水混凝土配合比设计方法.该方法首先根据可压缩堆积模型挑选出干堆积密实度较高的级配集料,引入反映成型过程影响的比例因子λ建立了集料在透水混凝土中的堆积密实度与其干堆积密实度之间的关系,进而确定出单位体积透水混凝土的集料用量;然后根据集料用量和水灰比,计算得到透水混凝土的水泥浆体体积和水泥用量.对依据该方法设计的透水混凝土性能验证试验表明,实测全孔隙率与设计全孔隙率非常吻合,达到预设目标;透水混凝土强度随小粒径集料体积分数的变化趋势与集料干堆积密实度的相近,但是并非干堆积密实越高则强度越高,强度还受到集料粒径的影响.     

Factors Controlling the Sintering of Ceramic Particulate Composites: II, Coated Inclusion Particles

Composite powders were synthesized by coating coarse ZrO₂ inclusion particles with a cladding of fine-grained, crystalline ZnO powder using a chemical precipitation technique. Three different inclusion sizes (1, 3, and 14 μm) were used by selecting the size of the starting ZrO₂ powder, and the volume fraction of the inclusions was controlled by the amount of ZnO precipitated. The powders were compacted by uniaxial pressing in a die and then sintered at a constant heating rate of 4°C/min to 1500°C. The sintering kinetics were almost independent of the inclusion volume fraction, and of the inclusion size, for inclusion contents up to ∼40 vol%. Furthermore, composites containing up to ∼40 vol% inclusions were sintered to almost full density under the same conditions used for the unreinforced matrix. This is considerably better than the densities obtained for conventionally mixed powders, where a modest inclusion content (< ∼ 10 vol%) has been observed to cause a severe reduction in the sintered density of the composite matrix. The kinetic data and microstructural observations are a further indication that the main factors which oppose the free sintering of ceramic particulate composites are processing-related; these factors are (i) inclusion-inclusion interactions which constrain the matrix and (ii) the packing of the matrix phase in regions immediately surrounding the inclusions.     

Optimization of the microstructure of porous composite cathodes in solid oxide fuel cells

A comprehensive micromodel to predict the electrochemical performance of porous composite LSM‐YSZ cathodes in solid oxide fuel cells (SOFCs) is developed. The random packing sphere model is used to estimate the cathode microstructural properties required for the micromodel. The micromodel developed takes into account the complex interdependency among the mass transport, electron and ion transports, and the electrochemical reaction, and can be used for optimization of the microstructure of porous LSM‐YSZ composite cathodes. It is shown that the electrochemical performance of these cathodes depends on the microstructural variables of the cathode porosity, thickness, particle size ratio, and size and volume fraction of LSM particles. The effect of these microstructural variables on the cathode total resistance, as the objective function to achieve the optimum microstructure for the cathode, is studied through computer simulation. The results indicated that for a LSM‐YSZ cathode operated at the average temperature of 1073.15 K, bulk oxygen partial pressure of 0.21 atm, and total current density of 5000 Am^?2, and constrained to the minimum value of 1 μm for the size of LSM particles and 0.25 for the cathode porosity, the optimum microstructure is obtained at the particle size ratio of unity, LSM particle size of 1 μm and volume fraction of 0.413, porosity of 0.25, and thickness of 60 μm. The cathode total resistance corresponding to the cathode optimized is estimated to be 0.291 Ω cm². © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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.