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.     

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.     

Analysis of the Coagulation of Small-Sized Particles during Convection

The effect of the velocity of small-sized particles in a flow on their aggregation is considered. For the simplest type of coagulation kernel, an exact solution is found for the problem of the evolution of the particle-size distribution in a powder during particle sedimentation under gravity and in a centrifugal force field.     

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.     

Coalescence model of particles in coaxial impinging streams

Coalescence is mainly affected by particle-to-particle collisions. A new model based on an equation expressing the condition for interparticle collision rate as well as the equation of motion of a single particle, has been developed for coaxial impinging streams. The model assumes that coalescence takes place only between small and large particles. In addition to the drag force usually influencing the behavior in impinging streams, the force acting on a large particle due to its collisions with small particles, has also been accounted for in the equation of motion. The effect of the change of the mass of the large particles on the acceleration due to coalescence with small particles, has also been included in the model. The model enables one to predict the composition of the product after coalescence from the composition of the feed and the operating conditions of the coalescentor.     

Aerosol Deposition in the Vicinity of a Stagnation Point

A method is presented to compute the trajectories of aerosol particles in the vicinity of a stagnation point and thus to obtain their rates of deposition. According to this method a particle starts its motion on the initial streamline, moves from one streamline to another under the influence of inertia, and touches the collector surface while on the interceptional streamline. The method takes advantage of the fact that in stagnation flow close to the splitting streamline most of the changes take place in a small region of high streamline curvature. The method of singular perturbation analysis is applied to calculate the particle trajectory in this region. This paper considers small Stokes numbers for which the particles are shown to have a stopping distance equal to their Stokes number. The computation of the particle trajectories depends on the ratio of these stopping distances s to the radii of curvature of the fluid streamline r. For large and medium s/r ratios the trajectories exhibit boundary layer type behavior, while for small ratios no such behavior is seen. Two examples demonstrate the use of the present theory. The first is that of particle sedimentation in a fibrous filler. The second is the sedimentation of small particles in potential plane-stagnation flow. The results compare very favorably with available numerical or exact solutions.     

Material ductility and toughening mechanism of polypropylene blended with bimodal distributed particle size of styrene–ethylene–butadiene–styrene triblock copolymer at high strain rate

The material ductility and toughening mechanisms under high strain rate are characterized in the polypropylene (PP) blended with two different styrene–ethylene–butadiene–styrene triblock copolymer (SEBS) by the tensile tests at the nominal strain rates from 0.3 to 100 s^?1, fracture surface observations, interparticle distances, and the morphological finite element (FE) analyses. It is found that the bimodal‐distributed SEBS particle morphology enhances the impact material ductility by craze bands formation, which is caused by the stress interaction between large rubber particles with the highly elongated small rubber particles inside the fibrils of the craze. It is found that there are three conditions for craze bands formation. The first condition is that the total SEBS content is larger than 15 wt %. Second condition is that the weight ratio of small SEBS particles against total SEBS particles should be larger than 0.06. Third condition is that the interparticle distance of large SEBS particles should be larger than 100 nm. In the numerical aspects, the present constitutive law with the craze nucleation and growth can successfully predict the craze bands in the microstructural FE models, leading to the useful procedure for identifying the ductile brittle transition based on the microstructure. The synergistic effect of these rubber particles gives rise to a strong increase in the ductility of these bimodal rubber particle distributed PP systems. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

燃煤可吸入颗粒物在磁场中聚并脱除机理

提出了燃煤可吸入颗粒物在均匀磁场中的二元碰撞聚并模型,应用该模型计算了大同烟煤飞灰粒子的聚并系数,在此基础上通过求解聚并动力学方程计算了粒子的聚并脱除效率,并与实验结果进行了对比。数值模拟结果表明,燃煤可吸入颗粒物聚并系数随粒径的增大而增大,粒径差异越大,重力对聚并的加强作用越大;粒径越大,布朗力对聚并的影响越弱;同聚并系数对外磁场强度的变化规律一样,粒子的聚并脱除效率随外磁场的增强而增大,在粒子饱和磁化后,聚并脱除效率达到最大值;延长粒子在磁场中的停留时间以及增大其质量浓度,都可以提高粒子的聚并脱除效率,在质量浓度和停留时间分别为40 g·m-3和1. 2 s时,粒子聚并脱除效率可达44%;数值模拟结果与实验结果相一致。     

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.     

Particle dispersion in a turbulent natural convection channel flow

Direct numerical simulations of particle dispersion in the turbulent natural convection flow between two vertical walls kept at constant but different temperatures are reported. It is assumed that the particles do not affect the flow (i.e. the dilute phase approximation is adopted). Particles with different levels of inertia, or Stokes numbers (0.843≤St≤17.45), are tracked according to the drag force imposed by the fluid. The gravity force is included for two cases, St=0.843 and St=17.45. The different levels of turbulence near the wall and near the center of the channel produce, as in isothermal turbulent channel or pipe flow, a larger concentration of particles near the wall. This effect becomes more important, and the deposition velocity of particles on the wall increases, as the particle inertia is increased. The simulations at St=8.38 and St=17.45 predict similar concentration profiles and deposition velocities according to the large inertia of these particles. The deposition velocities, obtained when the gravity force is ignored in the particle equations, follow the trend observed and measured for isothermal turbulent channel flows in the diffusion impaction regime. For the conditions considered, the gravity vector imposes a strong descending motion on the particles and this produces the increase of the particle concentration near the wall and a reduction of the deposition velocities in comparison with the results without the gravity force.     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

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°.     

基于微分代数积分矩量法的聚并器超细颗粒聚团研究

研究聚并器内布朗聚团和湍流聚团引起超细颗粒聚团,特别考虑颗粒之间近程力（范德华引力、静电斥力）和颗粒与气体之间的流体力学作用力对颗粒聚团的影响。基于FLUENT软件UDF功能自定义聚团核,考虑颗粒之间近程力和流体力学作用力对聚并率的影响,引入碰撞效率α对聚团核进行修正,得到修正湍流聚并模型并将该模型与理想湍流聚并模型进行比较。应用群体平衡模型（population balance model,PBM）耦合CFD对颗粒聚团过程进行数值模拟,并采用微分代数积分矩量法（DAE-QMOM）求解群体平衡方程。结果表明：理想湍流聚并模型与实验结果误差为8.92%,而修正改进的湍流聚团模型与实验结果误差仅为3.35%,更加符合实际情况;微分代数积分矩量法具有较高的效率,而且误差较小,相比PD积分矩量法有明显的优势,稳定性也比较突出。     

Dynamics of self-organizing single-line particle trains in the channel flow of a power-law fluid

The formation of self-organizing single-line particle train in a channel flow of a power-law fluid is studied using the lattice Boltzmann method with power-law index 0.6 ≤ n ≤ 1.2,particle volume concentration 0.8% ≤Φ≤ 6.4%,Reynolds number 10 ≤ Re ≤ 100,and blockage ratio 0.2 ≤ k ≤ 0.4. The numerical method is validated by comparing the present results with the previous ones.The effect n,Φ,Re and k on the interparticle spacing and parallelism of particle train is discussed.The results showed that the randomly distributed particles would migrate towards the vicinity of the equilibrium position and form the ordered particle train in the power-law fluid.The equilibrium position of particles is closer to the channel centerline in the shear-thickening fluid than that in the Newtonian fluid and shear-thinning fluid.The particles are not perfectly parallel in the equilibrium position,hence IH is used to describe the inclination of the line linking the equilibrium position of each particle.When self-organizing single-line particle train is formed,the particle train has a better parallelism and hence benefit for particle focusing in the shearthickening fluid at high Φ,low Re and small k.Meanwhile,the interparticle spacing is the largest and hence benefit for particle separation in the shear-thinning fluid at low Φ,low Re and small k.     

生物分离工程课程中的疑点讨论

本文在非惯性参照系的研究基础上,对离心场中运动的粒子进行受力和运动分析.并将离心场与重力场中沉降的粒子进行对比,把沉降速度公式移植到离心场中.并用上述理论对常见离心法中的离心粒子进行运动状态的分析.     

THE STOKES HYDRODYNAMIC RESISTANCE OF NONSPHERICAL PARTICLES

A review is presented of the motion of an isolated, nonspherical particle of general shape settling at small Reynolds numbers through an unbounded quiescent fluid—with a view towards establishing whether or not all particles ultimately attain a unique, time-independent terminal state, independently of their initial orientation and state of motion. Effects of inhomogeneities in internal mass distribution are incorporated into the analysis. Differences are pointed out between gravity and centrifugal settling rates for nonspherical particles. These arise from the tendency of such particles to adopt preferential orientations in a centrifugal field of force owing to variations in field strength over the length of the particle, ft is pointed out that Coriolis forces acting on both the fluid and particle in a centrifuge cause the particles to settle more slowly. Moreover, in the case of spherical particles, the particle path deviates from a purely radial trajectory. Effects of both translational and rotational Brownian motions on the mean settling velocities of submicron particles is discussed, again for generally-shaped particle. A detailed summary of the contents of this paper is provided at its conclusion.     

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.     

A new method for the control of dilute suspension sedimentation by horizontal movement

This research addresses some factors that control the stability of dilute suspensions in sedimentation processes under a dynamic environment. Experimental and numerical studies were conducted about the sedimentation velocity control of dilute suspensions by horizontal movement for particle concentrations up to 8 wt.%. Nearly monodispersed particles were used as test particles. The effects of horizontal movement speed and amplitude on particle sedimentation process were investigated. Under stationary conditions, particles settle in only one vertical direction because of gravitational force. However, complicated particle motions arise under moving conditions due to circulation flow in horizontal moving conditions. The results show that horizontal movement can reduce the particle settling velocity or maintain the stability of the suspension.     

Preparation,Particle Characterizations and Application of Nano-Pigment Suspension

In this work, we focus on preparation of nano-suspension of organic pigment for different milling method to discuss optimum formula, milling effect, particle characterizations (particle size, sedimentation velocity and stability) by analytical centrifugation system. Due to the variation of centrifugal force, time scales and space variations occur in the suspension such that during the migration of particles, the light transmission, and the vanishing coordinates are plotted on a profile. Therefore, objective of the article was evaluated to predict the particle characterizations between the particle distribution state and long-term stability as accelerated test during centrifugation. Besides, we were also used to observe nano-suspension of organic pigment the mean size, aggregation phenomena and dispersibility of the pigment particles by SEM and TEM. Additionally, we applied to manufacture the LCD-based blue filter and discussed performance of the blue filer by transmission of UV light, color evolution and adhesion ability assessments in this study.