A Numerical Simulation of the Boycott Effect

The lattice Boltzmann method has been used to simulate the velocity field induced and the motion of an ensemble of particles during the sedimentation process in inclined tubes. The simulations show the trajectories and flow behavior of individual particles and particle-particle and particle-wall interactions as well as the formation of particle clusters. The global convection motion that was experimentally observed during such processes and tends to enhance the sedimentation process is also reproduced numerically. In addition we have found that smaller intermittent vortices, formed from the wakes of groups of settling particles, also play an important role in the sedimentation process and the final distribution of particles.     

Stochastic sedimentation and hydrodynamic diffusion

Molecular collisions with very small particles induce Brownian motion. Consequently, such particles exhibit classical diffusion during their sedimentation. However, identical particles too large to be affected by Brownian motion also change their relative positions. This phenomenon is called hydrodynamic diffusion. Long before this term was coined, the variability of individual particle trajectories had been recognized and a stochastic model had been formulated. In general, stochastic and diffusion approaches are formally equivalent. The convective and diffusive terms in a diffusion equation correspond formally to the drift and diffusion terms of a Fokker–Planck equation (FPE). This FPE can be cast in the form of a stochastic differential equation (SDE) that is much easier to solve numerically. The solution of the associated SDE, via a large number of stochastic paths, yields the solution of the original equation. The three-parameter Markov model, formulated a decade before hydrodynamic diffusion became fashionable, describes one-dimensional sedimentation as a simple SDE for the velocity process {V(t)}. It predicts correctly that the steady-state distribution of particle velocities is Gaussian and that the autocorrelation of velocities decays exponentially. The corresponding position process {X(t)} is not Markov, but the bivariate process {X(t), V(t)} is both Gaussian and Markov. The SDE pair yields continuous velocities and sample paths. The other approach does not use the diffusion process corresponding to the FPE for the three-parameter model; rather, it uses an analogy to Fickian diffusion of molecules. By focusing on velocity rather than position, the stochastic model has several advantages. It subsumes Kynch’s theory as a first approximation, but corresponds to the reality that particle velocities are, in fact, continuous. It also profits from powerful theorems about stochastic processes in general and Markov processes in particular. It allows transient phenomena to be modeled by using parameters determined from the steady-state. It is very simple and efficient to simulate, but the three parameters must be determined experimentally or computationally. Relevant data are still sparse, but recent experimental and computational work is beginning to determine values of the three parameters and even the additional two parameters needed to simulate three-dimensional motion. If the dependence of the parameters on solids concentration is known, this model can simulate the sedimentation of the entire slurry, including the packed bed and the slurry–supernate interface. Simulations using half a million particles are already feasible with a desktop computer.     

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 Hindered Sedimentation of the Coarse Fraction of a Bidisperse Suspension in the Presence of Interfractional Coagulation

The peculiarities of the sedimentation of aggregates in a bidisperse (or two-fraction) suspension have been studied. A complete set of equations for the dynamics of an aggregate and suspension in the presence of the interfractional coagulation process and the hindering effect has been given. For the marginal Stokes and Newtonian regimes (corresponding to small and large Reynolds numbers), formulas have been obtained for the stationary sedimentation rate of aggregates, and their analysis has been performed. Some results of the numerical integration of the equations of motion of large particles in a suspension are have been. It has been established that the coagulation leads to an increase in the sedimentation rate of an aggregate and, on the contrary, the hindrance contributes to a decrease in the sedimentation rate. The nonmonotonic behavior of the sedimentation rate of aggregates as a function of the volume fraction of the dispersed phase is found.     

计算颗粒粒度分布的递推算法

针对光透过离心沉降法的数据处理,综合应用Stokes公式和Lambert–Beer定律,考虑了颗粒消光系数的影响和离心沉降中的径向稀释效应, 提出计算颗粒粒度分布的递推算法. 实验结果表明, 该算法计算过程简单,结果准确, 也可用于重力沉降.     

Dynamics of a suspension in the presence of liquid filtration,disperse phase sedimentation,and precipitate formation processes

The problem of suspension filtration has been considered with allowance for the formation of a precipitate by sedimenting disperse particles in one-dimensional formulation. The behavior of a suspension is described with a set of equations for the one-dimensional inertialess motion of a two-phase mixture, and the motion of a liquid through a porous precipitate layer has been described with a filtration equation based on the Darcy law. The particular (limit) cases of an equidense suspension (when the densities of both solid and liquid phases are equal) and an equilibrium suspension (when the sizes of particles are small enough to neglect their sedimentation) and the asymptotic case when the density of disperse particles is much greater than the density of a liquid phase have been studied. Some formulas for the characteristic times of disperse phase sedimentation and liquid filtration have been derived. The limit regimes of slow filtration and slow sedimentation are analyzed. In the general case, the problem has been solved in implicit form.     

SEDIMENTATION OF PARTICLES IN NON-NEWTONIAN FLUIDS

The influence of non-Newtonian flow behavior on sedimentation velocity of particles is investigated using an approximate solution for the motion of an assemblage of solid spheres presented previously by the authors. It is theoretically predicted that the pseudoplaslicity decreases the sedimentation velocity and its reduction is pronounced at large voidage. The present theory is discussed using the available empirical correlations.     

SEDIMENTATION OF PARTICLES IN NON-NEWTONIAN FLUIDS

The influence of non-Newtonian flow behavior on sedimentation velocity of particles is investigated using an approximate solution for the motion of an assemblage of solid spheres presented previously by the authors. It is theoretically predicted that the pseudoplaslicity decreases the sedimentation velocity and its reduction is pronounced at large voidage. The present theory is discussed using the available empirical correlations.     

Thermophoresis of Liquid Airborne Particles in Gravity at Continuum Regime

An analytical study is presented for the thermophoretic motion of an aerosol droplet in a prescribed temperature gradient under the influence of gravity. The Peclet and Reynolds numbers are assumed small, so that the temperature distributions are governed by the Laplace equation and the flow fields are governed by the Stokes equation. The temperature discontinuity, thermal creep, and hydrodynamic slip features that occurred at the droplet surface are considered. The slow motion of a liquid aerosol sphere subject to the combination of thermophoresis and sedimentation is obtained by superposition of the individual solutions for pure thermophoresis and pure body-force-driven motion, since both the governing equations and boundary conditions in this problem are linear. The stream functions of the internal and external flows, which are displayed in both the laboratory frame and a reference frame moving with the droplet, as well as the migrating velocity of a droplet, are formulated generally. The flow structures manifest more remarkable topologies than do those of common intuition developed from sedimentation. Our results can be simplified to the corresponding motion for solid aerosol particles.     

Colloidal Filtration and (Simultaneous) Sedimentation of Alumina and Silica Suspensions: Influence of Aggregates

Colloidal filtration and (simultaneous) sedimentation is studied for suspensions of alumina particles and monodisperse silica spheres. A comparison is made between stable suspensions and systems which are aggregated due to salt addition (silica) or absence of a deflocculant (alumina). From separate sedimentation experiments we conclude that the stable silica settles as an ordered particle array, that the unstable silica sediments as separate aggregates, and that aggregated aluina behaves as a densifying network. The filtration results show that settling of aggregates during filtration changes the filtration kinetics in accordance with our model for simultaneous filtration and sedimentation. Further, aggregates in suspension are shown to have little influence on the silica compact microstructure, whereas they clearly increase porosity and permeability of the alumina compact. We also find that for all suspensions porosities of compacts prepared by sedimentation are clearly larger then porosities of filter compacts.     

Incipient motion of individual particles in horizontal particle-fluid systems: B. Theoretical analysis

This paper presents a theoretical analysis of the force and moment balance during incipient motion of a single particle. The analysis showed that large particles start their motion by rolling for spherical particles and by sliding for non-spherical particles. It also showed that fine spherical or near spherical powders start their motion by rolling. The theoretical analysis shown that the incipient motion velocity of individual particles for all fluid, system and particle properties might be presented as power relationships between the Reynolds and Archimedes numbers.     

微颗粒实时在线监测仪在固液体系测量中的应用

使用自研的微颗粒实时在线监测仪对微颗粒在液相中的悬浮和沉降过程进行了在线定量测量研究。首先,通过与商用离线仪器Multisizer 4e的对比验证了自研的微颗粒监测仪实时、在线测量的可靠性。然后,选用了标准物质乳胶微球、Al₂O₃和 ZrO₂三种密度不同的百微米量级的微颗粒,对磁力搅拌器中稳定转速下的悬浮特性以及搅拌停止后颗粒的重力沉降过程进行实时在线观测,得到了这两种情形下测量点的颗粒浓度和粒度分布信息。实验结果表明,即使搅拌速度超过临界悬浮转速,搅拌容器中的Al₂O₃颗粒仍存在不同程度的非均匀分布状态,呈现出一定的浓度和粒度分布。在重力沉降的瞬变过程中,固体颗粒的粒径和密度在固液两相分离的过程中有着显著的作用。     

Study on the mechanism of hindered sedimentation by ‘unified theory on solid-liquid separation’

The entire procedure of hindered sedimentation has been calculated by the introduction of new boundary conditions to the ‘unified theory on solid-liquid separation.’ During this study, the hindered sedimentation was defined as ‘a process of sedimentation with transmission of the gravitational force between the particles due to contact.’ The lower concentration limit, on which the ‘unified theory on solid-liquid separation’ is based, could not be applied. To understand the mechanism of hindered sedimentation, variations in the porosity during sedimentation were calculated by using our theory.     

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.     

Features of micro and nano-particles produced by pulsed arc submerged in ethanol

Ni-C powders were synthesized using a pulsed arc between Ni electrodes submerged in pure ethanol. The arc pulses with energies 7.7, 22.7 or 48 mJ and 20 μs duration, and a repetition rate of 100 Hz were applied for 5 min. Powder samples were obtained by extracting liquid from the treatment vessel after a pre-determined sedimentation time, or by collecting the residue after the liquid evaporated. The particles size distribution was studied using a High Resolution Transmission Electron Microscope (HRTEM). The particle diameters after 25 min sedimentation time were in the range of 3-30 nm, and the distribution depended weakly on the discharge energy. Effects of applied electric and magnetic fields on the particle motion in ethanol were also studied. The particles moved in an applied electric field with velocities increasing with the field strength and the particle diameter. The as-produced particles with diameter ∼80 μm had velocities ∼2-2.5 mm/s in an electric field of ∼800 V/cm. The powder had soft ferromagnetic properties at room temperature, and the particles in the liquid moved in the direction of increasing magnetic field.     

On the stochastic nature of the motion of nonspherical aerosol particles. II: The overall drift angle in sedimentation

The sedimentation of cylindrical aerosol particles in a gravitational field was studied experimentally and theoretically in relation to the overall drift caused by the interaction with rotational Brownian motion. Experimentally, the location of glass fibers settling in a sedimentation cell through a hole onto a horizontal collecting surface was checked with the aid of a scanning electron microscope, the maximally drifted particle noted and its dimensions measured by a photogrammetric technique. Theoretically, the distribution of the settling points of the particles on the horizontal surface was calculated by a Monte Carlo method. In both sides of the study, it was found that the particles have a non-negligible overall drift the angle of which decreases with the duration of fall.     

The effect of brownian motion on particle size analysis by sedimentation

The influence of Brownian motion on the results of particle size measurements obtained by gravity sedimentation methods has been investigated by mathematical simulation of the process. It is shown that the effects can be directly correlated with an effective mean Péclet number (which expresses the ratio of settling velocity to diffusive velocity) for the particular system. For very small Péclet numbers, diffusion effects dominate in all cases and sedimentation methods should not be used. For larger values of the Péclet number, the errors introduced by Brownian motion are most important for very narrow and very broad distributions. In general, the effects can be reduced by increasing the sedimentation height, but it must be remembered that this will lead to increased settling times and may increase errors due to other factors such as thermal convection.     

Comparison of Dissolved Air Flotation and Sedimentation in Treatment of Typical North China Source Water

The treatment of typical north China water by dissolved air flotation (DAF) and sedimentation process was examined. A pilot plant with a water treatment capacity of 120 m3/d constructed in the Jieyuan Water Treatment Plant (JWTP) of Tianjin, China, was utilized for the comparison of the two processes. The results show that during the pilot test, DAF process can remove particles and organic mater more efficiently than sedimentation process. The removal rate for turbidity by DAF process is 5.5% higher than that by sedimentation in normal turbidity period, and 40% higher in low turbidity period, it is 5%~10% higher for removals of algae, total organic carbon (TOC), trihalomethane formation potential (THMFP) and bacteria in all periods. The removal rates for turbidity, TOC, THMFP, algae and bacteria by DAF process can reach 95%, 30%, 20%, 94% and 97% respectively. From the results of the pilot test, it can be concluded that DAF is a feasible clarification process, especially for source water with low turbidity and high algal blooming.     

Streaming diffusion effect on spheres falling in a circular cylinder

In quantitative research on the sedimentation of particles in liquid state, the sphere paths inside a glass tube and the dependence of the transverse force exerted on them by the components of the motion are studied. The movement of the spheres in a direction normal to the main axis of the tube and the parameters which regulate the falling velocity such as: the dimensions and the density of the particles and the viscosity of the fluid, are thus correlated.