Clusters Formation during Sedimentation of Dilute Suspensions

Abstract

Particle interactions in dilute monodispersed sedimenting suspensions of spherical particles are studied as a function of solid concentration. It is shown that in suspensions with solid concentrations below 0.83%, the interactions are too insignificant to effect the use of Stokes' law in sedimentation results. Beyond this concentration, however, a definite change in suspension behavior occurs, as particles come close enough to form clusters of varying sizes causing faster settling rates. Optimum clustering takes place around 4.5%-solid concentration, corresponding to mean interspacing of 2.2 particle diameter within suspension and giving settling rates 1.58 times faster than the Stokes' velocity for a mean particle. Clusters start breaking beyond this concentration as the sedimentation becomes more hindered and the return upward flow of liquid becomes increasingly tortuous. The probability of clusters formation and their stability as a function of particle size, concentration, and the Reynolds number of suspensions are also investigated. The studies are further extended to demonstrate the effect of “immobile” liquid within the clusters in interpreting the sedimentation results.     

Analysis of dilute solid–liquid suspensions in turbulent stirred tanks

In this work, dilute suspensions of solid particles in stirred tanks are investigated by Particle Image Velocimetry measurements, which were specifically designed to determine the effects of the dispersed phase on mean velocity and turbulence levels of the continuous phase and the local solid–liquid slip velocity. In order to determine the effect of particle size and concentration, glass particles of narrow size distribution were selected; the particle content was increased stepwise up the maximum of 0.2 vol.%. Overall, moderate dampening of liquid turbulent fluctuations was found with the smaller particles, while turbulence enhancement was observed with the bigger ones. Continuous phase turbulence was found to affect the local map of the particle settling velocity, which was also discussed on the basis of a force balance analysis. The reduction of particle settling velocity due to free stream turbulence under specific conditions is confirmed.     

Large-scale calculation of hydrodynamic transport properties for random suspensions of hard-sphere particles

A numerical method based on fast multipole summation scheme is used to calculate hydrodynamic interactions in random suspensions of non-colloidal hard-sphere particles. The calculation is carried out for suspensions of 1,024 particles randomly placed in periodic unit cell to determine hydrodynamic transport properties such as permeability of a viscous flow through porous medium, effective viscosity of suspension, and sedimentation velocity of the suspended particles. The particle volume fraction ø ranges from 0.01 to 0.25. Effect of particle number N on the transport properties was examined through the numerical calculations with N=64-1,024. It is shown that sedimentation velocity increases with N approaching an estimate for infinite N, and the finite N effect is negligible in effective viscosity and permeability problems. The present scheme is quite useful for obtaining a statistically-averaged quantity for random suspensions. As an example, ensemble-averaged velocity when position of one particle is fixed is numerically obtained in sedimentation problem. The numerical results are shown to be in excellent agreement with theoretical prediction.     

Sedimentation of coal particles in lower aliphatic alcohols and the stability of alcohol–coal suspensions

The sedimentation of coal particles in lower aliphatic alcohols from the methanol–pentanol series was studied. It was demonstrated that, in the metamorphism series, the alcohol–coal suspensions based on brown coal and anthracite are the most and least stable, respectively. It was found that the stability of the coal suspensions increases with the length of a hydrocarbon radical in the alcohol molecules. It was established that the sedimentation of coal particles in dilute alcohol–coal suspensions obeys Stokes’ law. The sedimentation of coal particles in concentrated alcohol–coal suspensions is of structural nature and strongly depends on interactions between the particles through a liquid layer. In this case, the most stable suspensions are those in which the surface tension of a dispersion medium approaches the surface tension of coal and a difference between the polarities of a dispersed phase and a dispersion medium decreases.     

Lateral migration of spherical particles in porous flow channels: application to membrane filtration

Lateral migration of spherical rigid neutrally buoyant particles moving in a laminar flow field in a porous channel is induced by an inertial lift force (tubular-pinch effect) and by a permeation drag force due to convection into the porous walls. The analysis of Cox and Brenner [7], for the particle motion in a nonporous duct is extended to include the effect of the wall porosity. Criteria are established under which the inertial and permeation drag force in the lateral direction can be vectorially added. Particle trajectories and concentrations profiles are calculated for a plane Poiseuille flow with one porous wall. For particles with radius of 1 μm, inertial and permeation drag forces are of comparable size under flow conditions often met in ultra- and hyperfiltration of dilute suspensions. For smaller particles the permeation drag force dominates.     

Particle‐laden liquid jet impingement on a moving substrate

The impingement of high speed jets on a moving surface was studied. The jet fluids were dilute suspensions of neutrally buoyant particles in water–glycerin solutions. At these low particle concentrations, the suspensions have Newtonian fluid viscosity. A variety of jet and surface velocities, solution properties, nozzle diameters, mean particle sizes, and volume fractions were studied. For each case the splash‐deposition threshold was quantified. It was observed that for jets with very small particles, addition of solids to the jet enhances deposition and postpones splash relative to a particle‐free water–glycerin solution with the same viscosity. In contrast, jets with larger particles in suspension were more prone to splash than single phase jets of the same viscosity. It is speculated that the change in character of the splash response for the jets with larger particles in suspension occurs when the particle diameter is comparable to the lamella thickness. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4673–4684, 2017     

Tracking of Particles in Froth Using Neutron Imaging

The movement of hydrophobic particles in a rising froth column is investigated. Gadolinium particles are hydrophobized and floated by means of small air bubbles. The generated froth is investigated by neutron imaging. Particles are identified by correlating the resulting radiographs with an artificial template of a typical particle and subsequent scanning for local maxima. The movement of the particles in the froth was analyzed for different froth stabilities, which resulted from various concentrations of the frother sodium oleate. Decreasing froth stability leads to lower superficial vertical particle velocity and to higher horizontal diffusion of particles due to bubble rupture.     

Fractionation of non-Brownian rod-like particle suspensions in a viscoplastic fluid

In this work we explore a fractionation technique for non-Brownian rod-like particle suspensions based upon the control of the threshold for motion in a yield stress fluid. The principle is demonstrated by observing the motion of particles under the influence of a centrifugal force in a weak gel. Here we develop calibration curves of the force required to initiate motion in a gel under numerous configurations of the particles. Demonstration separations of bidisperse suspensions are reported. Here we achieve complete separation of dilute suspensions based upon length, diameter, or density. The method is then applied to an industrially important suspension, that is a polydispersed papermaking fibre suspension, in which a length-based fractionation is reported.     

柱状颗粒沉降过程的CFD-DEM联合仿真和实验研究

针对柱状催化剂颗粒相对于球形颗粒的不同运动特性,选择不同长度直径为2 mm的5种柱状颗粒,采用CFD-DEM数值模拟仿真,研究柱状颗粒在管状容器中沉降的运动行为,并建立柱状颗粒沉降试验台,采用高速摄像拍摄的方法进行实验研究。结果表明,在不同位置释放相同直径和长度的柱状颗粒时,靠近壁面释放的颗粒会在沉降过程中向中心漂移,且比中心释放的颗粒沉降更慢,时间更长;改变柱状颗粒与水平面的夹角,在圆管中心释放颗粒,最终颗粒都会旋转至水平状态,与水平面夹角越大,底部所受阻力越大,转动持续时间随之增加;推导柱状颗粒沉降斯托克斯方程,并通过实验数据对方程中的阻力系数进行修正,将修正后的阻力系数导入用户自定义函数(UDF)计算颗粒沉降末速度,相对误差从原来使用球形颗粒阻力系数的50%下降到17%以内,模拟较为可靠。     

Simulation of sedimentation and fluidization of polydisperse suspensions via a Markov model

The particle-based approach to sedimentation is extended to include velocity fluctuations that result in hydrodynamic diffusion. The vector process describing the joint values of position and velocity is Markov. Thus, no integration of velocity is required. Height-velocity “skeletons” for each particle are generated from a bivariate-normal distribution with means, variances, and covariance that depend on three parameters. For each particle, there is a unique region in which the vector of species concentrations determines that particle's parameters and hence its Markov process, but the concentrations in that region depend on the Markov processes of neighboring particles. Though only discrete values of height and velocity are generated, the model ensures that sample paths and particle velocities are continuous. Furthermore, steady-state velocities are normally distributed and velocity autocorrelations decay exponentially. Published experimental results indicate that both are excellent approximations. For polydisperse suspensions, the Markov model is much simpler than the standard hydrodynamic-diffusion model and represents the actual process much better. We simulate the sedimentation and fluidization of polydisperse suspensions and study the effects of two additional parameters: variance and autocorrelation decay rate of particle velocities.     

ENHANCEMENT OF THE SEDIMENTATION RATES OF FIBROUS SUSPENSIONS

The settling of suspensions of slender rod-like particles with large aspect ratios was studied. The novel technique of enhancement of sedimentation rates by the addition of buoyant particle promoters was applied to such suspensions. The settling rates could be increased by many times by this simple technique. Sedimentation velocity increases of between 5 to 7 times have been observed for fibrous suspensions of concentrations of about 0.5%. A statistical analysis of the experimental data was performed to establish a correlation for the enhancement in settling velocities. The sediment volume was unaffected by the presence of buoyant particles. The buoyant parjticles were found to adsorb some surfactants onto their surfaces.     

ENHANCEMENT OF THE SEDIMENTATION RATES OF FIBROUS SUSPENSIONS

The settling of suspensions of slender rod-like particles with large aspect ratios was studied. The novel technique of enhancement of sedimentation rates by the addition of buoyant particle promoters was applied to such suspensions. The settling rates could be increased by many times by this simple technique. Sedimentation velocity increases of between 5 to 7 times have been observed for fibrous suspensions of concentrations of about 0.5%. A statistical analysis of the experimental data was performed to establish a correlation for the enhancement in settling velocities. The sediment volume was unaffected by the presence of buoyant particles. The buoyant parjticles were found to adsorb some surfactants onto their surfaces.     

Investigation on fine particle deposition from flowing suspensions onto planar surfaces

The method of the deposition kinetic measurements of very fine particles (size 0.1 – 5 μm) under well-defined hydrodynamic flow conditions has been presented. The proposed method, based on the rotating disc principle, enables direct and quantitative determination of the particle coating density by means of microscope counts. Our method is a modification of the method previously described by Marshall and Kitchener [12], Hull and Kitchener [10] and Clint et al. [5], used by them for measurements of colloid particle interaction with smooth surfaces.The experimental apparatus has been briefly described and the results of the particle deposition rate measurements from CaCO₃ and BaSO₄ suspensions (average particle diameters were 1.25 and 0.86 μm, respectively) onto glass and Cu₂S disc surfaces have been presented. The influence of such parameters as deposition time, suspension concentration, disc angular velocity, particle densities, and additions of dispersing agents on the particle deposition kinetics has been discussed.The experimental results have been compared with our previous theoretical predictions and a satisfactory conformability has been found, at least for dilute and stable suspensions.     

Influence of Acidity on the Stability and Rheological Properties of Ionically Stabilized Alumina Suspensions in Ethanol

The ionic stability of alumina particles in moderately concentrated ethanol suspensions is studied. Surface chemistry and interparticle forces are manipulated by controlling the acidity of the suspensions without dispersants. The acidity of ethanol solution is determined using ion transfer functions, wherein the relationships between acidity, alumina particle surface charge, zeta-potential, stability, and suspension rheological behavior are established. Positive isoelectric point (IEP) shift is observed for alumina in ethanol on increasing the solids concentration. However, dilute and concentrated aqueous suspensions of alumina give the same IEP. The viscosity and flow curves for alumina/ethanol suspensions are acidity dependent. The flow curves of the suspensions follow the Casson model, and the Casson yield value is used to evaluate suspension stability.     

Periodic motion of four spheres in a “kite” configuration

Cluster settling plays an important role in the sedimentation of dilute suspensions. Studies of isolated clusters indicate that they show considerable stability. In particular, spheres initially arranged in a horizontal isosceles triangle or rhombus exhibit simple periodic motion as they descend. Moving one sphere outward along the long diagonal of a rhombus produces a kite configuration that settles with a complicated periodic motion relative to its center of mass, which exhibits a back-and-forth movement as it descends. This makes the kite configuration the second member of a class between small clusters with simple periodic motions and isolated clusters that merely remain intact for a considerable time. If the displacement along the diagonal is too great, one sphere is left behind. Higher-order terms, which have little effect on widely separated spheres in a rhombus, are important in maintaining the periodicity of the kite configuration and in slowing its breakup.     

移动床除尘器捕集颗粒喷动再生的主要操作因素

通过对喷动再生操作前后的捕集颗粒进行采样,考察粉尘/捕集颗粒比、提升管气速、颗粒循环量等操作因素对再生效果的影响。结果表明,粉尘/捕集颗粒比、提升管气速、颗粒循环量为影响喷动再生效果的主要操作因素,随粉尘/捕集颗粒比增大、提升管气速增大、颗粒循环量减小,粒级效率增大;喷动再生器在提升管气速较高时,再生效率较高,但若提升管气速过高,捕集颗粒同样会随灰尘一起被带出;喷动再生过程不可避免地造成捕集颗粒的磨损,合适的提升管气速对整个喷动再生系统至关重要,一般为捕集颗粒带出速度的1.1?1.3倍。     

提升管内稀相中颗粒的运动行为

引　言很多研究已经发现[1～ 3] 提升管中存在稀相与密相颗粒团共存的微观两相 ,但以往的研究者多从固含率的角度分析提升管中的两相结构 ,而对于微观两相的运动行为尚缺乏足够的认识 .余皓[4 ] 及刘会娥[5] 的研究发现 ,提升管颗粒速度瞬时信号的概率密度分布呈现双峰形式 ,双     

Effects of dispersant concentration and pH on properties of lead zirconate titanate aqueous suspension

Lead zirconate titanate (PZT) aqueous suspensions were prepared at 60 wt.% solids loading using a commercial ammonium polyacrylate (APA) dispersant. Effects of the dispersant concentration on rheological behavior, dispersion and stability of PZT aqueous suspensions were investigated by means of zeta potential, viscosity and sedimentation height measurements. The results showed that, under suitable conditions, APA dispersant promoted particle dispersion and stabilization in PZT aqueous suspensions. For 60 wt.% solids loading suspensions, the dispersant concentration yielding the lowest viscosity was 0.5 wt.% based on PZT powder dried weight basis. Effects of pH on particle dispersion in the suspensions prepared with APA were studied by laser light scattering technique and scanning electron microscopy. The results showed an improvement in particle dispersion for the alkaline condition, which led to relatively low viscosity and highly stable suspension. Possible particle stabilization mechanisms at various pHs were discussed based on dissociation of the dispersant in water, polymer conformation and adsorption behavior of the dispersant on the particle surface.     

提升管内气固流动特性的离散元模拟

采用离散单元法模型对二维提升管内气固流动特性进行了数值模拟。利用标准k-ε模型模拟气相的湍流流动,考虑了颗粒间的van der Waals力和滚动摩擦的作用。通过对颗粒和气体流动行为的分析,得到了颗粒浓度、速度、温度及气体速度等的分布,研究了表观气速和颗粒循环速率对颗粒流动的影响。结果显示:颗粒在提升管内呈现边壁浓、中心稀的环核流动及上稀下浓的流动结构;气固两相都存在一定程度的返混现象;增加表观气速,使颗粒浓度降低、速度增大,颗粒分布更均匀;增加颗粒循环速率,使颗粒浓度增大,而颗粒速度对颗粒循环速率的变化不敏感,颗粒分布的不均匀性更强。模拟结果与文献中实验定性吻合。