Density segregation of dry and wet granular mixtures in gas fluidized beds

The Discrete Element Method combined with Computational Fluid Dynamics was coupled to a capillary liquid bridge force model for computational studies of mixing and segregation behaviors in gas fluidized beds containing dry or wet mixtures of granular materials with different densities. The tendency for density segregation decreased with increasing fluidizing velocity, coefficient of restitution, and amount of liquid present. Due to the presence of strong capillary forces between wet particles, there was a high tendency for particles to form agglomerates during the fluidization process, resulting in lower segregation efficiency in comparison with fluidization of dry particles. Particle‐particle collision forces were on average stronger than both fluid drag forces and capillary forces. The magnitudes of drag forces and particle‐particle collision forces increased with increasing fluidizing velocity and this led to higher mixing or segregation efficiencies observed in dry particles as well as in wet particles at higher fluidizing velocities. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4069–4086, 2015     

Prediction of fluidized bed behaviour in the presence of liquid bridges

The need to understand defluidization due to free surface liquid in gas–solid fluidized bed processes gave rise to a study of the effect of addition of non-volatile liquids with different viscosity and surface tension to a cold model gas–solid fluidized bed. The incremental addition of liquid to a fluidized bed of Geldart group B particles was observed, in general, to result in a transition to group A behaviour and eventually to group C behaviour. The BA and AC boundaries are shown to be associated with the balance between the interparticle liquid bridge forces and the fluid drag force. Using liquid bridge forces calculated from measurements of bridge geometry, the ratios of interparticle force to fluid drag force were found to vary between 0.6 and 1.07 for the AC boundary and between 0.02 and 0.06 for the BA transition boundary. Based on this approach, a practical diagram is developed enabling fluid bed behaviour to be predicted from a knowledge of particle, fluid and liquid properties and the quantity of liquid in the bed.     

Segregation of cohesive powders in a vibrated granular bed

The effects of small amounts of added liquid on the segregation behavior of a granular system under vertical vibration by DEM simulation are investigated in this study. The cohesive forces of grains are incorporated into DEM simulations via a simplified dynamic liquid bridge force model. The simulation results show that capillary forces in addition to viscous forces have an important effect on the segregation phenomenon. The segregation rate of larger intruder rises to the top of the bed is found to depend on the liquid content. The segregation rate is sharply increased when a small amount of liquid is added to granular system. A transition to the reduction of segregation rate occurs at a critical liquid content. It has shown that this transition can be interpreted as the increase of attractive force between grains due to viscous force. The viscous forces make the particles stick more tightly to each other and retard the movement of particles, thus reducing the segregation rate. The segregation rate is also related to the convection motion of the granular system. The presence of convection enhances the segregation rate of wet granular materials.     

Effect of blade angle and particle size on powder mixing performance in a rectangular box

This study focuses on the understanding of flow over a single blade and its impact on powder mixing. The Discrete or Distinct Element Method (DEM) is used and the flow of a single blade through a bed of a binary particle mixture is studied. Mixing performance with respect to a blade-rake angle and particle size is investigated using the Modified Generalized Mean Mixing Index (MGMMI) and the maximum mean instantaneous velocities. A wide range of angles and different loading scenarios of the binary particle mixture were studied. Velocity profiles for all these cases were computed, as well as the forces on particles and the blade. The results showed an inverse relation between the interparticle force and blade-rake angle. Systems with a higher number of larger particles experienced a higher interparticle force. Similar results were obtained for the blade force. The results for mixing efficiency showed that if the smaller particles are placed at the top this leads to a higher mixing performance. The mixing performance was highest for blade-rake angles that offered a maximal surface area or maximal resistance to the flow of particles, which occurred for blade-rake angles from 70° to 90°.     

On the relationship between porosity and interparticle forces

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

Modification of interparticle forces for nanoparticles using atomic layer deposition

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

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.     

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.     

EFFECTS OF INTERPARTICLE INTERACTIONS ON STABILITY, AGGREGATION AND SEDIMENTATION IN COLLOIDAL SUSPENSIONS

Relations between interparticle effective interactions, structure formation, stability and sedimentation for a colloidal system are presented in this paper. For a binary mixture of large and small particles, the potential of the mean forces between large particles is obtained from the Ornstein-Zernike equation. We incorporated the small particles in our numerical simulations by using this potential of the mean force as the interparticle effective interaction. Our numerical results reveal the phenomenon of strong particle aggregation due to the attractive depletion force exerted by small particles. In the absence of the effect of gravity, this aggregation can result in flocculation and the formation of particle clusters thereby forming “void” structures, while under the influence of gravity, the aggregation can greatly affect the sedimentation rates. An analytical expression relating the aggregation number to the sedimentation velocity is presented. Our sedimentation experiments with a bidisperse latex suspension as well as clay particle dispersions show both the destabilizing and stabilizing effects of small particles, which are in qualitative agreement with our theoretical predictions.     

Cohesive effects in powder mixing in a tumbling blender

Rotary drums are used as mixers, dryers, kilns and granulators. In all of these systems, powder cohesion deeply affects mixing and segregation, and it is critical in process scale up. In this paper, we focus on the effect of cohesion in mixing and size segregation of binary mixtures of uniform and non-uniform sizes in a partially filled rotating drum. The cohesive force between particle is simulated using a square-well potential and the numerical model is used to characterize flow and mixing properties. The model is validated by comparison to experimental images. Results show a time-dependent spatial distribution of cohesive powder that depends on the magnitude of cohesion and friction. In uniform binary systems, as cohesion increases, the rate of mixing first increases and then decreases, however for the case of non-uniform binary systems, we observe different mixing patterns depending on the relative magnitude of forces acting between particles of same/different sizes. Unlike free flowing material, for cohesive mixtures, a higher rotation speed is found to enhance mixing performance.     

Analysis of Capillary Forces in Liquid-Phase Sintering of Jagged Particles

It is predicted that contact geometries will markedly affect the kinds of interparticle forces and their dependence on liquid volume. The normal force between two spheres is maximum at infinitesimal liquid volumes, whereas for the corner-on-plane geometry it is zero and increases rapidly with volume. Sphere contacts have only normal forces, whereas contacts among jagged particles produce shears and torques which probably are important in particle rearrangement leading to densification.     

固液两相声共振混合数值模拟

声共振混合作为一种解决力/热敏感超细材料均匀分散混合问题的新方法,其技术特点是混合容器工作在共振状态下使用不超过200Hz的振动产生低频声场促进混合。本文采用气固液三相流模型对一种固体、一种液体在声共振混合容器中的混合过程进行建模。固体颗粒与液体之间相互作用系数采用Gidaspow公式。采用固体颗粒体积分数标准偏差作为标准对混合均匀性进行了评价。计算结果表明,在100g振动加速度下容器中出现了体流现象,并初步计算了不同高宽比、不同激振参数条件下的混合特性,对计算结果进行了分析。最后利用自搭建的声共振混合样机,分别在低固含量、高固含量条件下进行实验,记录混合过程中固体颗粒的运动轨迹。实验结果初步验证了仿真模拟的正确性以及声共振样机的混合能力。     

Mixing behaviors of wet granular materials in gas fluidized bed systems

The discrete element method combined with computational fluid dynamics was coupled with a capillary liquid bridge force model for computational studies of mixing behaviors in gas fluidized bed systems containing wet granular materials. Due to the presence of strong capillary liquid bridge forces between wet particles, relative motions between adjacent particles were hindered. There was a high tendency for wet particles to form large aggregates within which independent motions of individual particles were limited. This resulted in much lower mixing efficiencies in comparison with fluidization of dry particles. Capillary liquid bridge forces were on average stronger than both fluid drag forces and particle–particle collision forces and this accounted for the difficulty with which individual particles could be removed and transferred between aggregates. Such exchange of particles between aggregates was necessary for mixing to occur during fluidization of wet granular materials but required strong capillary liquid bridge forces to be overcome. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4058–4067, 2013     

DEM simulation on particle mixing in dry and wet particles spouted bed

In this paper, the mixing characteristics of the dry and wet particles in a rectangular spouted bed are simulated using a three-dimensional discrete element method (DEM). In particular, the influence of turbulence and liquid bridge force is investigated using the standard k-ε two-equation model and the Mikami model. The Ashton mixing index is adopted to evaluate the dynamic mixing process of the particle system. The geometry of the simulated bed is the same as that of the experimental bed by Liu et al. [G. Q. Liu, S. Q. Li, X. L. Zhao, Q. Yao. Chem. Eng. Sci. 63 (2008) 1131-1141]. The effect of the spouting gas velocity on the mixing process is discussed for the mixing of dry particles (without the liquid bridge force), while the effect of the moisture content is discussed for the mixing of wet particles (with the liquid bridge force).     

Calculation of the movement of polydisperse mixtures of solid particles in the flow of a Newtonian fluid in a horizontal pipe

The influence of pressure force; weight; the Archimedes, Magnus, and Safman forces; turbophoresis; and hydrodynamic resistance on solid particles, as well as impact interactions between particles and the lack of space of liquid flux in the interparticle region was taken into account during the motion of polymodal two-phase flow. The distribution of the volume concentration of solid particles was defined by their diffusion process and the motion velocity in transverse direction under the influence of the listed forces. The considered computation method showed satisfactory agreement with experimental data on the distribution of solid phase concentration and average velocity of suspension carrying flux.     

Hardness of moist agglomerates in relation to interparticle friction, capillary and viscous forces

Wet agglomerates deform plastically until they break through crack propagation. On the particulate level, liquid bridges are responsible for the strength of the wet agglomerate as they hold the particles together. Recent micro-scale studies have identified the role of liquid surface tension, bridge Laplace pressure and liquid viscosity, which, in combination, explain the axial strength of pendular liquid bridges. Different situations exist depending on the degree the liquid wets the particles and on the saturation of the agglomerate mass.On the wet agglomerate level, the hardness is related to three factors: the liquid binder surface tension and viscosity and the interparticle friction. A simple model is developed in this paper, based on the powder and liquid binder properties, which shows that the forces due to interparticle friction are generally predominant in wet agglomerates made from non-spherical particles. Although mechanical interlocking is not accounted for, the model yields accurate prediction of wet agglomerate hardness independently measured on wet masses of varying composition. This theoretical hardness could prove an interesting tool for wet granulation research and technology.     

Mixing of large particles in two-dimensional gas fluidized beds

The fluidization and solids mixing characteristics of very large particles were investigated in a two-dimensional gas fluidized bed. Bubble or slug induced drift and gross solids circulation appeared to be the predominant solids mixing mechanisms in this large particle bed. The contribution from wake mixing appeared to be negligible and radial mixing was more rapid than axial mixing. Apparently, segregation in the axial direction resulted from preferential transportation of the lighter particles upwards with rising bubbles and from interparticle competition to fill the voidage created by the rising bubbles. No appreciable segregation occurred in the radial direction. A nonstationary random walk model has been developed to characterize mixing and segregation of fluidized large particles.     

Effectiveness of mass transfer in a packed distillation column in relation to surface tension gradients

In packed columns large differences occur in the wetting of the particles and especially in the refreshing of the liquid on the wetted particles due to gradients in surface tension of the liquid/gas interface. Mass transfer rates may differ with a factor 2. In a column packed with Berl saddles distillation experiments were performed with a mixture n-heptane/cyclohexane. Ceramic Berl saddles of 4, 6 and 10 mm were used as well as aluminum Berl saddles of 4 mm. In some of the experiments the saddles were coated with PTFE (teflon). The driving force for mass transfer was varied over a wide range. Both negative and positive driving forces were realized. The influence of the surface tension driven refreshment of the interface is most pronounced for small particles; for larger liquid flow rates, that may be applied in beds with larger particles, the effect is obscured by the inertia of the downcoming liquid.     

Predicting the impact of adhesive forces on particle mixing and segregation

Processing of fine powders is a relevant operation in many industries, from pharmaceuticals to material synthesis. As the size of the particles decreases, van der Waals forces start to play an important role in the behavior of the granular material and can dramatically impact the degree of mixing. In this work, we study the mixing and segregation behavior of fine particle systems using models capable of solving both normal and tangential interactions of elastic-plastic particles in the presence of van der Waals forces. We use scaling arguments to analytically predict the asymptotic state of the system by comparing the relative magnitude of the adhesive force with the other relevant forces. These predictions are most easily summarized by phase-space diagrams which exhibit both mixed and segregated regions. We compare the result of our Particle Dynamics simulations for different particle systems with our predictions.

Graphical abstract

Here we develop a predictive model for assessing the impact of adhesive forces on the mixing and segregation of fine powders. Interestingly, these forces may both enhance mixing or cause segregation, depending on the properties of the differing particles.     

The permeability of quaternary particulate mixtures

The fall of small particles through a bed of large ones under the influence of gravity has been termed interparticle percolation and is a fundamental process that contributes to bulk segregation in free-flowing powders. For particles larger than the minimum interstices of the bed, percolation is induced only under shear.The bed of particles under shear is modelled as a series of layers in which the percolating particle moves from one layer to the next.A prediction for the Péclet number is made and is in good agreement with experiment. As the number of layers in the failure zone increases, the percolation behaviour becomes well described by a convective diffusion equation. Comparisons with a series of well-mixed reactors and axial mixing of a liquid flowing through a packed bed are made.