Axial Equilibrium Distance and Positioning of Particles in a Laminar Tube Flow

Particle transport in a laminar tube flow at low Reynolds numbers leads to accumulation of particles at specific equilibrium radii. The equilibrium radius depends on the particle size. Small particles find their equilibrium radius near the wall and large particles near the tube axis. During their radial migration to the equilibrium position, the particles move in axial direction with the flow. In an experimental setup, the axial equilibrium distance is measurement for several tube Reynolds numbers. The axial equilibrium distance is the distance a particle migrates in the flow direction, until it reaches its radial equilibrium position. The results are compared with CFD‐simulations of single particle movement in a laminar tube flow.     

A measure of the degree of inhomogeneity in a distribution and its application in characterising the particle circulation in a fluidized bed

A quantitative method to evaluate variational processes such as particle circulation in a fluidized bed is presented. It involves the calculation of H, an index of the degree of inhomogeneity in the tracer circulation in standard measure. The position of a given particle in a rectangular fluidized bed was followed using Positron Emission Particle Tracking. This technique is able to locate a labelled solid and construct a three-dimensional trajectory of its movement. The degree of inhomogeneity in the tracer distribution was then calculated from the observations. The values of H for the tracer movement when the bed is operated with a differential air supply across the distributor to stimulate gross solids circulation, suggest that there are relatively large regions of the bed in which the presence of the tracer is much less frequent than elsewhere. This lack of homogeneity in the tracer particle circulation is consistent with visual observation of particle circulation in the investigated bed. Increase in H with increasing length of the duration of the test is consistent with a stable circulation pattern. H affords a quantitative measure of how the fluidized bed parameters influence the particles movement.     

Solids motion in flowing froths

Flotation is a widely used process within the minerals processing industry, as well as being used for water treatment and de-inking of recycled paper. The froth phase and its role in the separation achieved is as yet ill understood. A fundamentally based model of the behaviour of solids within a flowing froth allows for a fuller understanding of the froth phase of flotation vessels and process optimisation.This paper outlines a model for the motion of solids within a flowing froth. It builds on earlier work on the modelling of bubble and liquid motion within a flowing froth and includes all the effects of same phenomena that effect liquid motion, as well as including the effect of solids concentrations on liquid motion.The solids are divided into two classes for the purposes of modelling, namely the attached material, which follows the bubbles, and the unattached material, which mainly follows the liquid, but can move relative to the water by means of hindered settling and geometric and Plateau border dispersion. The attached material consists of hydrophobic particles, while the unattached material can consist of both hydrophobic and hydrophilic particles. Attached particles can become unattached due to coalescence or bursting.Results from simulations are shown to illustrate the movement and concentration of the solids from the pulp-froth interface to the upper, bursting surface and overflowing the weir.     

Network simulation for deep bed filtration of Brownian particles

The effect of different interaction energy curves of DLVO theory on the permeability reduction in a filter bed is investigated by using the Brownian dynamics simulation method and the modified square network model to track the individual particles movement through the filter bed. When energy barrier exists and both particle and pore size distributions are of the Raleigh type, it is found that particles with Brownian motion behavior are easier to get straining at small pores, and cause higher permeability reduction than those without considering the Brownian motion behavior. But, this result was not observed for the constant particle and pore sizes case. The permeability reduction for the Raleigh size distribution is higher than that of the constant size. Similar results are also obtained for the “barrierless” type interaction energy curve for the case of Raleigh type size distribution, with the exception that the decreasing rate of permeability reduction of Brownian particles is smaller than that without considering the Brownian motion behavior. When comparing with the permeability reduction experimental data, it is found that the present model shows fair agreement between the theory and the experimental results when the direct deposition mechanism is dominant.     

Effect of particle characteristics on particle pickup velocity

Particle entrainment is investigated by measuring the velocity required to pick up particles from rest, also known as pickup velocity. Pickup velocity is a function of individual particle characteristics and interparticle forces. Although 5-200 μm particles are investigated, the work presented here focuses on the pickup of particles in a pile in the size range of 5-35 μm. These smaller particle sizes are more typical for pharmaceutical and biomedical applications, such as dry powder inhalers (DPIs). Pickup velocities varied from 3.9 to 16.9 m/s for the range of particle sizes investigated.There is a strong correlation between particle size and the dominating forces that determine the magnitude of the pickup velocity. Preliminary data investigating pickup velocity as a function of particle size indicate the existence of a minimum pickup velocity. For larger particle sizes, the mass of the particle demands a greater fluid velocity for entrainment, and for smaller particle sizes, greater fluid velocities are required to overcome particle-particle interactions. Pickup velocity remains relatively constant at very small particle diameters, specifically, less than 10 μm for glass spheres and 20 μm for nonspherical alumina powder. This can be attributed to the negligible changes in London-van der Waals forces due to a hypothesized decrease in interparticle spacing. At intermediate particle diameters, electrostatic forces are dominant.     

水力旋流器内颗粒运动的几个问题

简要论述了水力旋流器内颗粒运动的几个主要问题,包括固液两相以及颗粒间的相互作用,旋流器内不同区域的颗粒运动特征,颗粒运动与流体运动的联系与区别,流体湍流对颗粒运动的影响,颗粒粒度与浓度在旋流器内的分布等。     

INSTANTANEOUS RESPONSE OF PULVERIZED COAL PARTICLES TO FLUCTUATING TEMPERATURE IN A HOT GAS FLOW

The instantaneous temperature response of pulverized coal particles to fluctuating gas temperature in a hot airflow is investigated. The particle relaxation time for temperature is analyzed. Both numerical and analytical approaches are adopted to solve the instantaneous particle energy equation. The results obtained by the two approaches are quite close. The gas temperature fluctuation has an obvious influence on the particle instantaneous temperature, especially for particles with relatively small diameters. The effects of fluctuation intensity and frequency of the gas temperature, as well as particle Reynolds number, on the particle instantaneous temperature response are delineated. The present study provides a basis for further exploring the impacts of gas turbulence on the particle reactive behaviors.     

INSTANTANEOUS RESPONSE OF PULVERIZED COAL PARTICLES TO FLUCTUATING TEMPERATURE IN A HOT GAS FLOW

The instantaneous temperature response of pulverized coal particles to fluctuating gas temperature in a hot airflow is investigated. The particle relaxation time for temperature is analyzed. Both numerical and analytical approaches are adopted to solve the instantaneous particle energy equation. The results obtained by the two approaches are quite close. The gas temperature fluctuation has an obvious influence on the particle instantaneous temperature, especially for particles with relatively small diameters. The effects of fluctuation intensity and frequency of the gas temperature, as well as particle Reynolds number, on the particle instantaneous temperature response are delineated. The present study provides a basis for further exploring the impacts of gas turbulence on the particle reactive behaviors.     

Rapid growth of particles by coagulation between particles in silane plasma reactor

The changes of particle size distribution were investigated during the rapid growth of particles in the silane plasma reactor by the discrete-sectional model. The particle size distribution becomes bimodal in the plasma reactor and most of the large sized particles are charged negatively, but some fractions of small sized particles are in a neutral state or even charged positively. As the mass generation rate of monomers increases or as the monomer diameter decreases, the large sized particles grow more quickly and the particle size distribution becomes bimodal earlier. As the mass generation rate of monomers decreases, the electron concentration in the plasmas increases and the fraction of particles charged negatively increases. With the decrease in monomer diameter, the electron concentration decreases in the beginning of plasma discharge but later increases.     

十二烷基吗啉选择性浮选氯化钠颗粒的作用机理

通过研究十二烷基吗啉（DMP）在饱和卤水中对氯化钠颗粒的浮选行为,揭示了氯化钠颗粒通过增强体系泡沫的稳定性而提高了十二烷基吗啉的浮选性能;运用红外光谱法研究证明,DMP分子以物理作用力吸附于氯化钠颗粒表面;同时,研究了十二烷基吗啉分子在氯化钠颗粒表面的吸附行为及精光卤石颗粒与各种条件下氯化钠颗粒表面的接触角.研究结果表明,十二烷基吗啉选择性浮选分离氯化钠颗粒的作用原理是：十二烷基吗啉分子在饱和卤水介质中由于受到很强的疏水力,选择性吸附于氯化钠颗粒表面;且因精光卤石（KCl•MgCl₂•6H₂O）颗粒表面有很强的水合斥力,十二烷基吗啉分子不能吸附于精光卤石颗粒表面;因此,在浮选过程中,吸附在气泡界面的DMP分子因受到疏水作用力,使气泡吸附在氯化钠颗粒表面,氯化钠颗粒被浮选分离.     

Convective-dispersive gangue transport in flotation froth

The transport of gangue through flotation froth has been described by solving the convection-diffusion equation. Gangue recovery is predicted to be proportional to liquid recovery, which is consistent with experimental observation. In addition, it is seen that the dependency of gangue recovery upon particle size is due to processes within the pulp phase rather than the froth, insofar as the transport of particles in a given froth is approximately independent of size. The importance of maintenance of positive bias in column flotation, previously stressed by other workers, is reinforced. This model utilises a simplified representation of the froth and, as a consequence, it does not necessarily give accurate gangue recovery estimates for practical flotation processes. However, the convective-diffusive model does illuminate the physical processes behind gangue recovery in the concentrate which will aid the development of automatic control strategies.     

Mixing of granular materials, part II: effect of particle size under periodic shear

Although the study of mixing of granular particles in the last years has shown notable advances, it continues being moderately understood. In this work, a low shear mixing device consisting of a box with two moving walls and three static walls was used again to study granular mixing as a function of particle size. The goal is to obtain a more in depth understanding of the internal behavior of granular material in the three dimensions when particle size is changed. Experiments at different particle size distributions and wall displacements were run. Results show that faster mixing is achieved with particles of high diameter. The particle size affected the granular movement at the three directions. The phenomenon of dilation varied proportionally with the particle size.     

An improved estimation of size distribution from particle profile measurements

Several methods are available to measure particle size. The majority of them, such as sieving, are off-stream techniques where samples must first be separated from the main stream for analysis.Therefore, the search for on-line particle size analysis systems has provided the impetus for the introduction of image-based particle size analysers to the mineral industry in the past three decades. Generally, the estimation of particle size distribution on the basis of image analysis depends on measuring a single parameter of particle profile. For example the equivalent area diameter (d_A) or mean Feret's diameter (d_F) distributions, then transforming this data to the equivalent size distribution. However, due to the irregularity of particles being analysed, it is believed that this kind of analysis may increase the error in estimation of particle size distribution since profiles of irregular particles carry more information than can be represented by a single parameter.In this paper, a proposed technique which measures two parameters, equivalent area diameter (d_A) and mean Feret's diameter (d_F), for each particle profile has been developed. The accuracy of the technique has then been investigated in the laboratory by successfully estimating (unfolding) the size distribution, where size refers to sieve size, of three samples of different particle shapes with known size distribution.     

A Comparative Study on the Separation of Different‐Shape Particles Using a Mini‐Hydrocyclone

The separation efficiency from water of different‐shape particles was studied experimentally using a mini‐hydrocyclone. Spherical and flaky (plate‐like) aluminum particles with the same particle size distributions were employed. Also, the effects of the feed flow rate and the temperature on the separation performance were studied. The results were investigated in terms of slurry recovery, total efficiency, and partition curves. The separation efficiency of the spherical particles increased with increasing particle size, temperature, and feed flow rate, as expected. The fishhook effect, as a noticeable phenomenon, was observed for the spherical particles. In case of the flaky particles, the separation showed an unusual behavior: The separation efficiency decreased with increasing particle size in the largest particle fraction, which has so far not been reported and addressed in this way.     

Direct numerical simulation of particle collisions in two-phase flows with a meshless method

The element-free Galerkin (EFG) method was used to simulate particle motion in two-phase flows with a new node distribution arithmetic suitable for meshless methods. The control equations were discretized with the standard Galerkin method in space and a fractional step finite element scheme in time. Regular background cells were used for the quadrature. The forces of the fluid on the particles were obtained by integrating the stress and shear forces on the particle surfaces. Simulation of the movement of a particle in a channel showed the Karman vortex street forming behind the particle with increasing particle velocity. Simulation of the movement of two particles in a channel showed the well-known drafting, kissing and tumbling, which has been obtained experimentally. Multi-particle flows were simulated with the results showing that meshless methods are capable of dealing with real particle collisions, which makes meshless methods superior to all mesh-based methods. Moreover, the theoretical relation of interparticle collision rate derived using kinetic theory was compared with the present numerical results and it is found that the collision rate is much lower than the theoretical estimation based on kinetic theory.     

Particle size distribution of PM-10 and heavy metal emission with different temperature and HCl concentrations from incinerators

Emission characteristics of particulate matter and heavy metals from 12 small waste incinerators, whose capacity ranged from 25 to 200 kg/h of waste, were investigated to determine the factors affecting the particulate matter generation and growth mechanisms. The ratio of fine particles to coarse particles increased with the flue gas temperature. Particulate matter showed bimodal forms in particle size distributions. The finer particle mode in particle size distribution shifted toward the coarser particle mode with a decrease in flue gas temperature. Experimental results were in agreement with coagulation theory: It is thought that the coarser particles were mechanically generated and the finer particles were generated by gas-to-particle conversion mechanisms such as nucleation, condensation, and coagulation. Heavy metal enrichment in finer particulate matter was also observed and related to particle formation and growth from vaporized metals. Emission of all heavy metals except zinc was affected by hydrogen chloride concentrations, while some metal emissions such as manganese, chromium, and copper were not varied with flue gas temperature. This paper is dedicated to Professor Dong Sup Doh on the occasion of his retirement from Korea University.     

An investigation of the recovery of cryolite from alumina-electrolyte froth by flotation

In the industrial production of aluminium by the electrolysis of alumina, electrolyte froth, which is a mixture of carbon and cryolite is obtained at a rate of 50 kg of froth per ton of aluminium produced. Cryolite can be recovered from this mixture by flotation. In this study, the effects of the following parameters on flotation were experimentally investigated: particle size, type, combination, dosage and ratio of reagents, and conditioning time. It is found that it is possible to decrease the carbon content of cryolite below 1% by suitably choosing the operating parameters. Electrolyte froth must be ground to —100 mesh size for the liberation of carbon particles captured in the cryolite matrix. Any combination of two of the reagents, kerosene, fuel oil, creosote and terebenthene yield good results if used together with pine oil. Pine oil is found to be a more effective frother compared to Pril, a commercial detergent. Satisfactory separations are obtained when a kerosene-fuel oil mixture (50:50, v/v) is used as the collector with a dosage of 3.7 kg per ton of feed together with pine oil, the frother, with a dosage of 0.095 kg per ton of feed.     

Direct measurement of entrainment in large flotation cells

A key response variable to describe the metallurgical performance in a flotation cell is the concentrate grade. The mineral feed characteristics and conditioning determine the grade of the particles attached directly to the surfaces of the bubbles by true flotation, while the operating conditions, such as gas rate, bubble size, froth depth and others, determine the amount of gangue recovered by entrainment, which finally decreases the concentrate grade.In this paper, the recovery of liquid and solids by entrainment was evaluated by direct measurement of the fraction of liquid and solids reported to the concentrate in a 130 m³ mechanical flotation cell.The liquid and solids entrainment, per size classes (+ 150; − 150 + 45; − 45 µm), was measured by the radioactive tracer technique. The procedure consisted of introducing a tracer impulse at the cell feed entrance. The tracer time response was monitored on-line at the concentrate overflow and at the tailings discharge. Also, in order to obtain the quantitative distribution of the feed, samples were taken periodically from the concentrate and tailings streams, for a period of 4 residence times, during the tracer tests. This allowed the quantification of the mass of tracer reporting to both streams.Experimental results confirmed that solids entrainment with the froth was strongly dependent on particle size, and that the entrainment factor (EF = solid/water recovery ratio) was similar to that reported for smaller size cells under similar operations conditions.     

Entrainment behaviour of high-density Geldart A powders with different shapes

Atomised and milled Ferrosilicon with average particle diameters of 38 and 50 µm respectively were fluidised with air at ambient conditions. The entrainment rate of the more spherical atomised particles was on average six times that of the irregularly shaped milled particles over the range of superficial velocities investigated. In an attempt to decouple the effect of particle size from shape, the bed was divided into theoretically isolated bins based on the distributions of particle sizes. This indicated that the atomised particles had a higher entrainment rate for particles smaller than approximately 25 µm whereas the opposite was true for particles greater than this size. None of the entrainment correlations investigated was able to predict the switch in entrainment behaviour as a function of particle sphericity and diameter. Furthermore, the traditional critical particle diameter associated with cohesive Geldart A particles was not observed for either of the two particle shapes. It is therefore concluded that neither the hydrodynamic nor Van der Waals forces acting on the particles can adequately explain the entrainment rate behaviour of differently shaped high-density Geldart A particles.     

Variation of particle size and its distribution during the synthesis of silicalite-1 nanocrystals

Recent studies imply that the external surface area of the nanozeolite product may, at least in some cases, be related to the average size of the particle population participating in aggregative nucleation, a population which itself is a product of aggregation of even smaller primary nanoparticles. This possibility puts more importance on our understanding of the variation of particle size and its distribution during the crystallization of zeolite nanoparticles. Variation of the particle size and PSD during nanoparticle silicalite-1 crystallization was followed with respect to time by a laser light scattering device with a scattering angle of 173°, for several starting synthesis compositions. Effects of varying TPAOH and water contents in the starting synthesis mixtures on the variation with time of the particle sizes and PSDs, especially across the two distinct aggregation events, were investigated. The products were also analyzed by XRD and AFM. Parallel to the decrease in the average particle size of the final product population with increasing alkalinity and organic template content, its PSD was observed to become narrower too. A reversal in the dependence on TPAOH content, of the average size of the population formed by aggregation, with respect to that of the population participating in aggregation, was observed across both aggregation events, implying that smaller particles aggregated to form larger particles, while larger particles aggregated to form smaller particles during these processes, and this was also seen from the AFM images, to be reflected to the surface features of the final product particles.