Microstructural Shape Factors: Relation of Random Planar Sections to Three-Dimensional Microstructures

The relation of random planar sections of anisometric microstructures to the actual three-dimensional anisometry is considered for oblate and prolate spheroids and cylinders. Simple formulae are obtained relating the two-dimensional (2-D) to three-dimensional (3-D) aspect ratios; for oblate systems with large aspect ratios, the area-weighted average 2-D aspect ratio varies linearly with the actual aspect ratio, whereas for prolate systems of large aspect ratio, the 2-D aspect ratio varies logarithmically with actual aspect ratio. Extension to polydisperse systems yields a shape factor, R , which gives greatest weight to grains (or particles) having the highest volume fraction. This not only preserves the linear and logarithmic functionalities found in monodisperse systems, but favorably affects the sensitivity of R to visually apparent differences among microstructures.     

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.     

Investigation of flow properties of metal powders from narrow particle size distribution to polydisperse mixtures through an improved Hall-flowmeter

Initially, we critically examined the results provided by the improved Hall-flowmeter, based on bulk volume flow rate, with narrow particle size distribution metal powders (iron, aluminium and copper) of different sizes (fine to coarse) and shapes (nearly spherical to non-spherical). Binary and ternary mixtures of various combinations of fine (< 100 μm) and coarse (> 100 μm) metal powders at different size ratios and weight fractions were allowed to discharge from a mass flow hopper. The results show that the mass flow rate of polydisperse mixtures of metal powders is affected by four factors: the size ratio, the volume fraction of the smallest sieved fraction, the initial mass flow rate and the shape of metal powders.     

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.     

Particle shape and suspension rheology of short-fiber systems

The effective viscosity of short-fiber suspensions is studied from a theoretical and experimental point of view. The theory of dilute suspensions with elongated particles is briefly summarized and explicit formulae for the dependence of the intrinsic viscosity on the particle shape (aspect ratio) are given in a form that should be useful for practical purposes. Concentration regimes, the influence of Brownian motion and sedimentation kinetics are mentioned. The effective viscosity of suspensions of two polydisperse wollastonites with significantly different average aspect ratios (approximately 5 and 16, respectively) is measured in dependence of the solids volume fraction and fitted with power-law models (Krieger and Maron–Pierce relations). It is shown that the intrinsic viscosity determined is higher than theoretically predicted via the Brenner formula, while the critical volume fraction is lower than predicted by the empirical Kitano relation. Possible reasons for these discrepancies, common to most real polydisperse systems, are discussed.     

Effects of particle shape and size on devolatilization of biomass particle

Experimental and theoretical investigations indicate particle shape and size influence biomass particle dynamics, including drying, heating rate, and reaction rate. Experimental samples include disc/flake-like, cylindrical/cylinder-like, and equant (nearly spherical) shapes of wood particles with similar particle masses and volumes but different surface areas. Small samples (320 μm) passed through a laboratory entrained-flow reactor in a nitrogen atmosphere and a maximum reactor wall temperature of 1600 K. Large samples were suspended in the center of a single-particle reactor. Experimental data indicate that equant particles react more slowly than the other shapes, with the difference becoming more significant as particle mass or aspect ratio increases and reaching a factor of two or more for particles with sizes over 10 mm. A one-dimensional, time-dependent particle model simulates the rapid pyrolysis process of particles with different shapes. The model characterizes particles in three basic shapes (sphere, cylinder, and flat plate). With the particle geometric information (particle aspect ratio, volume, and surface area) included, this model simulates the devolatilization process of biomass particles of any shape. Model simulations of the three shapes show satisfactory agreement with the experimental data. Model predictions show that both particle shape and size affect the product yield distribution. Near-spherical particles exhibit lower volatile and higher tar yields relative to aspherical particles with the same mass under similar conditions. Volatile yields decrease with increasing particle size for particles of all shapes. Assuming spherical or isothermal conditions for biomass particles leads to large errors at most biomass particle sizes of practical interest.     

Impact of material property and operating conditions on mass flux profiles of monodisperse and polydisperse Group B particles in a CFB riser

Experiments directed at understanding local mass flux behavior of Geldart Group B materials in the riser of a gas-solids circulating fluidized bed (CFB) have been carried out. Three monodisperse materials (with differences in particle size and/or material density), two binary mixtures (one with only a particle size difference between the species and the other with only a material density difference), and one continuous particle size distribution (PSD) have been investigated at four operating conditions. Results show that the riser axial position has the greatest influence on mass flux behavior, especially near the top of the riser, where profile shapes consistently have an inverted U-shape or V-shape. The material type (i.e., monodisperse materials of different particle sizes and/or particle densities or different types of polydispersity) and operating conditions effects are secondary but more apparent at the riser bottom. An interesting observation involving binary mixtures is that while the mass flux profiles of the density-difference binary mixture mimics that of one of its (monodisperse) constituent components, the size-difference binary mimics neither of its two monodisperse components.     

A coupled DEM/CFD analysis of the effect of air on powder flow during die filling

Die filling from a stationary shoe in a vacuum and in the presence of air was numerically analyzed using an Eulerian‐Lagrangian model, which employs a discrete element method (DEM) for the particles and computational fluid dynamics (CFD) for the air with a two‐way air‐particle interaction coupling term. Monodisperse and polydisperse powder systems have been simulated to explore the effect of the presence of air on the die filling process. For die filling with monodisperse powders, the influences of particle size and density on the flow behavior were explored. The numerical simulations revealed that the presence of air has a significant impact on the powder flow behavior, especially for systems with smaller and/or lighter particles. Flow has been characterized in terms of a dimensionless mass flow rate, and it has been shown that for die filling in a vacuum this is constant. The flow characteristics for die filling in air can be classified into two regimes. There is an air‐inert regime in which the particle size and density are sufficiently large that the effect of air flow becomes negligible, and the dimensionless mass flow rate is essentially identical to that obtained for die filling in a vacuum. There is also an air‐sensitive regime, for smaller particle sizes and lower particle densities, in which the dimensionless mass flow rate increases as the particle size and density increase. The effects of particle‐size distribution and adhesion on the flow behavior have also been investigated. It was found that, in a vacuum, the dimensionless mass flow rate for polydisperse systems is nearly identical to that for monodisperse systems. In the presence of air, a lower dimensionless mass flow rate is obtained for polydisperse systems compared to monodisperse systems, demonstrating that air effects become more significant. Furthermore, it has been shown that, as expected, the dimensionless mass flow rate decreases as the surface energy increases (i.e., for more cohesive powders). © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Characterization of Mixing and Size Segregation in a Rotating Drum by a Particle Tracking Method

The mechanisms of segregation in solids mixing, even in simple rotating drums, are not clearly understood. Although most past studies have focused on binary mixtures, this work investigates the effect of polydispersity on granular flow, mixing, and segregation in a rotating drum operated in rolling regime through particle trajectories obtained from the radioactive particle tracking technique. Velocity profiles, radial segregation, and axial dispersion coefficients for monodisperse and polydisperse systems of glass beads are analyzed with respect to rotational speed and particle size. A model is introduced to predict the residence times along streamlines and evaluate the rate at which the material renews at the free surface and within the inner layers of the bed. Our results reveal similar velocity profiles and residence times for monodisperse and polydisperse systems. They also indicate that the particles distribute along the radial direction of the drum, although not necessarily in a core/shell configuration. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1894–1905, 2013     

The effect of particle shape on simple shear flows

Simple shear flows, (without gravity force and implemented using periodic boundary conditions or in Couette flow configurations with gravity) have been the subject of study using DEM simulation for more than two decades. Earlier studies explored the effect of attributes such as shear rate, particle size and domain scale on the distribution of the particles in the flow, velocity profiles and the stress distributions. These studies were conducted using simple shapes for the particles such as spheres. In recent years, the importance of particle shape on flow has been recognized in a range of industrial application including mixing, comminution, hopper discharge and chute flows. In this paper, we return to the simple shear flows and quantitatively explore the effect of particle shape on velocity, volume fraction, granular temperature and stress distributions across the channel. Particle shape is found to sharply increase the strength of the material making it stronger and harder to shear. The generation of particle spin throughout the flow of non-circular particles leads to high granular temperatures, dilative pressures and lower solid fractions in the core of the flow. For aspect ratios between 0.6 and 0.5, a transition in the effective behaviour of the wall boundary conditions is identified. The connections of shape to spin, to granular temperature, to bulk flow changes are elaborated.     

Spouting behaviors of binary mixtures of cylindroid and spherical particles

Spouting behaviors of cylindroid and spherical particles in a spouted bed are experimentally investigated. The characteristics of flow pattern and pressure drop of the binary mixtures are figured out and three kinds of cylindroid particles with different sizes and shapes are involved in experiments to discuss effects of particle size and shape on the spouting behaviors in beds. The emphasis is laid on the influence of the volume fraction of cylindroid particles, X_c, on the spouting phenomena, including the total pressure drop, the minimum spouting velocity, and fountain height. Results show that, the shapes and sizes of cylindroid particles, mainly including equivolume diameter and aspect ratio, significantly affect the spouting behaviors. There is a maximum volume fraction, X_c,max, for each kind of cylinders to maintain the stable fountain at a certain gas velocity. With the same gas velocity, X_c,max is lower for the cylinders with higher aspect ratio. © 2014 American Institute of Chemical Engineers AIChE J, 61: 58–67, 2015     

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.     

Using the discrete element method to develop collisional dissipation rate models that incorporate particle shape

Discrete Element Method simulations of Homogeneous Cooling Systems (HCS) are used to develop a collisional dissipation rate model for non‐spherical particle systems that can be incorporated in a two‐fluid multiphase flow framework. Two types of frictionless, elongated particle models are compared in the HCS simulations: glued‐sphere and true cylinder. Simulation results show that the ratio of translational to rotational granular temperatures is equal to one for the true cylindrical particles with particle aspect ratios (AR) greater than one and glued‐sphere particles with AR >1.5, while the temperature ratio is less than one for glued‐sphere particles with 1 < AR <1.5. The total collisional dissipation rate, which is associated with both translational and rotational granular temperature change rates, increases linearly with the particle aspect ratio. Thus, a collisional dissipation rate model for the elongated cylinders is developed by a simple modification of the existing spherical particle model. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5384–5395, 2017     

Discrete particle simulation of gas fluidization of ellipsoidal particles

Fluidization is widely used in industries and has been extensively studied, either experimentally or theoretically, in the past decades. In recent years, a coupled simulation approach of discrete element method (DEM) and computational fluid dynamics (CFD) has been successfully developed to study the gas–solid flow and heat transfer in fluidization at a particle scale. However, to date, such studies mainly deal with spherical particles. The effect of particle shape on fluidization is recognized but not properly quantified. In this paper, the CFD–DEM approach is extended to consider the fluidization of ellipsoidal particles. In the simulation, particles used are either oblate or prolate, with aspect ratios varying from very flat (aspect ratio=0.25) to elongated (aspect ratio=3.5), representing cylinder-type and disk-type shaped particles, respectively. The commonly used correlations to determine the fluid drag force acting on a non-spherical particle are compared first. Then the model is verified in terms of solid flow patterns. The effect of aspect ratio on the flow pattern, the relationship between pressure drop and gas superficial velocity, and microscopic parameters such as coordination number, particle orientation and force structure are investigated. It is shown that particle shape affects bed permeability and the minimum fluidization velocity significantly. The coordination number generally increases with aspect ratio deviating from 1.0. The analysis of particle orientations shows that the bed structures for ellipsoids are not random as that for spheres. Oblate particles prefer facing upward or downward while prolate particles prefer horizontal orientation. Spheres have the largest particle–particle contact force and fluid drag force under the comparable conditions. With aspect ratio deviating from 1.0, particle–particle interaction and fluid drag become relatively weak. The proposed model shows a promising method in examining the effect of particle shape on different flow behaviour in gas fluidization.     

Extending the EMMS/bubbling model to fluidization of binary particle mixture: Formulation and steady-state validation

The EMMS/bubbling model originally proposed for fluidization of monodisperse particles is extended to fluidization of binary particle mixture in this study. The dense and dilute phases are considered to comprise of two types of particles differing in size and/or density. Governing equations and the stability condition are then formulated and solved by using an optimization numerical scheme. The effects of bubble diameter are first investigated and a suitable bubble diameter correlation is chosen. Preliminary validation for steady state behavior shows the extended model can fairly capture the overall hydrodynamic behaviors in terms of volume fraction of bubbles and average bed voidage for both monodisperse and binary particle systems. This encourages us to integrate this model with CFD for more validations in the future.     

Effect of particle morphological parameters on sand grains packing properties and rheology of model mortars

In this paper, we study the rheological behavior of mixtures of various sand particles suspended in model laboratory yield stress fluids. Using image analysis, we assess the morphology of the studied sand particles. We then measure the packing properties of these particles and show that, as a first approximation, the overall shape of the particles (i.e. the aspect ratio) is the dominant morphological parameter conditioning packing. We finally use magnetic resonance imaging (MRI) to assess the rheological behavior of suspensions of these sands in a water-in-oil emulsion and show that both the yield stress and consistency diverge for the same critical volume fraction, which seems to be fully correlated to both the random dense packing fraction and loose packing fraction of the grains. We finally suggest that there exists a correlation between a variation in yield stress and a variation in viscosity due to a change in the particle morphology.     

Calculation of the hindered settling velocity of a bimodal mixture of solid particles of arbitrary shape in a Newtonian fluid

A method for calculating the settling velocity of a bimodal mixture of particles of arbitrary shape is proposed. The method uses the concept of effective particle diameter, which characterizes the particle shape, volume, and midsection area. The method takes into account the contact interaction between particles of different sizes due to their collisions. The calculation results are compared with experimental data on settling of bimodal mixtures of limestone particles of arbitrary shape.     

Two‐step continuous production of monodisperse colloidal ellipsoids at rates of one gram per day

We report a two‐step process for the continuous production of monodisperse polystyrene colloidal ellipsoids of aspect ratios up to 6.8 at rates that exceed 1.0 g per day, an improvement on previously reported synthetic batch processing rates of nearly a factor of 20. This scale up is accomplished by continuous evaporative processing of a polymer solution into an elastomeric film embedded with colloidal spheres. Subsequently, the film is continuously elongated at a temperature that stretches the embedded spheres into ellipsoids. The method is used to deform initially 1.0 μm diameter spheres into ellipsoids of aspect ratio 1.27 ± 0.15, 3.31 ± 0.44, 3.91 ± 0.72, 4.14 ± 0.47, and 6.77 ± 1.01. The particle production rate reported here opens new possibilities for applications of monodisperse ellipsoids, such as self‐assembly and optical characterization of complex crystalline unit cells, as well as rheological characterization of dilute gels and dense suspensions. © 2017 American Institute of Chemical Engineers AIChE J, 64: 697–707, 2018     

Optical inline analysis and monitoring of particle size and shape distributions for multiple applications: Scientific and industrial relevance

Particles occur in almost all processes in chemical and life sciences. The particle size and shape influence the process performance and product quality, and in turn they are influenced by the flow behavior of the particles during production. Monitoring and controlling such characteristics in multiphase systems to obtain sufficient qualities will greatly facilitate the achievement of reproducible and defined distributions. So far, obtaining this information inline has been challenging, because existing instruments lack measurement precision, being unable to process overlapping signals from different particle phases in highly concentrated multiphase systems. However, recent advances in photo-optics made it possible to monitor such features (particle size distribution (PSD), aspect ratio and particle concentration) with advanced image analysis (IA) in real-time. New analysis workflows as well as single feature extractions from the images using multiple image analysis algorithms allowed the precise real-time measurements of size, shape and concentration of particle collectives even separated from each other in three phase systems. The performances, advantages and drawbacks with other non-photo-optical methods for assessing the particle size distribution are compared and discussed.     

Preparation of Colloidal Boehmite Needles by Hydrothermal Treatment of Aluminum Alkoxide Precursors

Fairly monodisperse colloidal boehmite fibrils with a high aspect ratio were synthesized by hydrothermal treatment at 150°C of an acidified aqueous alkoxide solution, prepared by adding an aqueous HCl solution to an aluminum alkoxide precursor. The average particle length could be controlled between about 100 and 500 nm by varying the initial amounts of alkoxide and acid. Using two different alkoxides in a 1:1 molar ratio yielded the most needlelike product, having a particle length standard deviation of 40%. The boehmite particles were polycrystalline and contained 0.14 mol of excess H₂O per mol of AlOOH, bound to the particle surface.