The separation mechanism and application of a tapered diameter separation bed

Research on recycling waste printed circuit boards is at the forefront of preventing environmental pollution and finding ways to recycle resources. A wet process for reclaiming metals from printed circuit boards applying a tapered diameter separation bed is described, and the separation mechanism of the device is proposed. The motion of a particle in the tapered diameter fluid flow field and particle separation within this field were studied. As the material passes through the fluid field, along with the water, differences in particle density, granularity, and shape cause particles to follow at different trajectories. A tapered diameter separation bed was used to process 1?C0.074?mm-sized crushed material from discarded printed circuit boards. The separation efficiency of 91.77?% and the recovery rate of 95.79?% for recovered metal were achieved with a discharge water flow rate of 4.5m³/h, a material feed rate of 300?g/min, and an obliquity of 30°. For ?0.074?mm printed circuit boards, the metal recovery is 93.42?% and the separation efficiency is 77.63?% when the water discharge is 2?m³/h, the obliquity is 35o, and the material feed rate is 450?g/min. The superfine products in a size range of ?0.074?mm can be recovered effectively under suitable operating condition using the tapered diameter separation bed. It indicates that the lower separation limit of the tapered diameter separation bed can be close to zero. The technique will prevent environmental pollution from waste printed circuit boards and allow efficient recovery.     

Entrainment threshold of cohesionless sediment grains under steady flow of air and water

Existing formulations for bed sediment entrainment under steady flow are incapable of explaining two well-documented observational facts: (i) water flow requires considerably higher dimensionless shear stresses to move the bed grains than air flow; and (ii) under open channel flow, steep granular beds are more stable than beds with milder slopes. These two facts, together with recent direct measurements of forces acting on bed grains giving time-mean negative drags ( Schmeeckle et al. , 2007 ), question the conventional models of forces used so far. Here, fluid forces acting on bed particles are treated in a new way in order to take into consideration the fundamental interference effects, thus obtaining appropriate magnitude estimates that exhibit good agreement with direct force measurements by Schmeeckle et al. (2007) . Impulsive pressure fluctuations generated by turbulence are shown to be capable of dislodging the bed grains by saltation under air flow, whereas they can only produce a rocking effect under water flow, thus explaining the first anomaly. On the other hand, previous work by the authors allows a direct estimate of space averaged time-mean drag and lift forces exerted on bed grains. Both components have the same order of magnitude but, contrary to the common belief, the mean lift is downward, which provides an explanation for the second anomaly. Finally, spatial disturbances of pressure, both positive and negative, appear to generate maximum, persistent, local forces considerably greater than mean forces, thus allowing an explanation for the observed negative time-mean drag. A new formula for predicting incipient motion of sediment under open channel flow is derived, which incorporates all dynamically significant effects and gives very good agreement with observation for the entire range of bed slopes.     

The physics of “falling curtain” dry magnetic separation

The separation process in a “falling curtain” of particles is investigated in detail. Each particle experiences gravity, air drag and magnetic forces, as well as collisions with other particles. A simple kinetic theory model is used to model these processes and the separation distance between two different minerals is calculated. The maximum throughput of a superconducting magnet can be as high as 10 tons/hour per meter of effective magnet length, with a recovery in excess of 90%.     

Initiation of ripple marks under oscillating water

It was observed that a monolayer of glass beads which were scattered sparsely on a rigid plane floor grew into regular waves of particles under oscillatory water flow. The relative displacement of two nearby particles due to viscous fluid forces seems to be responsible for the initiation of these particle waves. It was also observed that the similar particle waves were formed on the initially flat surface of a thick sand bed and subsequently developed into oscillatory sand ripples of a common type. On the basis of these observations, it is suggested that the particle waves may be the basic cause of the initiation of general ripple marks under oscillatory flow.     

Direct numerical simulation of bedload transport using a local, dynamic boundary condition

ABSTRACT Temporally and spatially averaged models of bedload transport are inadequate to describe the highly variable nature of particle motion at low transport stages. The primary sources of this variability are the resisting forces to downstream motion resulting from the geometrical relation (pocket friction angle) of a bed grain to the grains that it rests upon, variability of the near‐bed turbulent velocity field and the local modification of this velocity field by upstream, protruding grains. A model of bedload transport is presented that captures these sources of variability by directly integrating the equations of motion of each particle of a simulated mixed grain‐size sediment bed. Experimental data from the velocity field downstream and below the tops of upstream, protruding grains are presented. From these data, an empirical relation for the velocity modification resulting from upstream grains is provided to the bedload model. The temporal variability of near‐bed turbulence is provided by a measured near‐bed time series of velocity over a gravel bed. The distribution of pocket friction angles results as a consequence of directly calculating the initiation and cessation of motion of each particle as a result of the combination of fluid forcing and interaction with other particles. Calculations of bedload flux in a uniform boundary and simulated pocket friction angles agree favourably with previous studies.     

Pore‐scale modeling of surface erosion in a particle bed

A fully coupled transient two‐dimensional model was employed to study fundamentals of flood‐induced surface erosion in a particle bed. The interaction of the liquid and solid phases is the key mechanism related to surface erosion. The solid phase was idealized at a particle scale by using the discrete element method. The fluid phase was modeled at a mesoscale level and solved using the lattice Boltzmann method. The fluid forces applied on the particles were calculated on the basis of the momentum the fluid exchanges with the particle. The proposed approach was used to model both single particles and particle beds subjected to Couette flow conditions. The behavior of both the single particle and the particle bed depended on particle diameter and surface shear fluid velocity. The conducted simulations show that the fluid flow profile penetrates the bed for a small distance. This penetration initiates sheet‐flow and surface erosion as the fluid interacts with particles. The effect of suppressing particle rotation on the fluid‐induced forces on the particle was also examined. Suppressing particle spinning may lead to underestimated erosion rate. Results of fluid and particle velocities were compared against experimental results and appeared to agree with the observed trends.Copyright © 2013 John Wiley & Sons, Ltd.     

Applications of grain-pivoting and sliding analyses to selective entrapment of gravel and to flow-competence evaluations

Models of sediment threshold by grain pivoting or sliding over underlying particles are examined in order to explore their application to evaluations of selective entrainment of gravel by flowing water. Of special interest is whether such process-based models provide satisfactory evaluations of flow competence and the movement of large clasts by floods. A detailed derivation is undertaken, focusing first on the fluid flow and forces at the particle level. The resulting threshold equation for the particle-level velocity is then modified to yield the mean entrainment stress for the flow as a whole. This approach is appropriate for considerations of selective entrainment of grains of varying sizes within a deposit, the sorting being due to their relative projection distances above the bed and the dependence of their pivoting angles on grain size and shape. The resulting threshold equations contain a number of coefficients (e.g. drag and lift) whose values are poorly known, but can be constrained by requiring agreement with the Shields curve for the threshold of grains in uniform deposits. If pivoting coefficients based on laboratory measurements with tetrahedral arrangements of particles are used in the models, smaller degrees of selective sorting are predicted than found in the field measurements of gravel entrainment. However, if reasonable modifications of those coefficients are made for expected field conditions, then the models yield good agreement with the data. Sliding models, where sorting is due entirely to projection distances of the grains above the bed, yield somewhat poorer agreement with the field data; however, the sliding models may have support from laboratory experiments on gravel entrainment in that the data and theoretical curves have similar concave trends. The existing measurements lack documentation of the mechanisms of grain movement, so it is not possible to conclusively determine the relative importance of grain pivoting versus sliding. In spite of such uncertainties, the results are encouraging and it is concluded that pivoting and sliding models for grain entrainment do have potential for field computations of selective entrainment and flow competence.     

A simple model for the prediction of the deflation threshold shear velocity of dry loose particles

A very important parameter in aeolian equations is the deflation threshold shear velocity, which quantifies the instant of particle motion. In this paper, a simple model is presented for the prediction of the threshold shear velocity of dry loose particles. It has the same functional form as the widely used models of Bagnold (1941) and Greeley & Iversen (1985), but differs in its treatment of the so‐called threshold parameter. As the new expression was based on the moment balance equation used by Greeley & Iversen, it includes a function for the aerodynamic forces, including the drag force, the lift force and the aerodynamic moment force, and a function for the interparticle forces. The effect of gravitation is incorporated in both functions. However, rather than using an implicit function for the effect of the aerodynamic forces as in the Greeley & Iversen model, a constant aerodynamic coefficient was introduced. From consideration of the van der Waals' force between two particles, it was also shown that the function for the interparticle cohesion force is inversely proportional to the particle diameter squared. The model was calibrated on data reported by Iversen & White (1982). The new expression compared, at least for terrestrial conditions, very well with the Greeley & Iversen model, although it is much simpler. It was finally validated with data from wind‐tunnel experiments on different fractions of dune sand and sandy loam soil aggregates. The soil aggregates were treated as individual particles with a density equal to their bulk density. The good agreement between observations and predictions means that, when predicting mass transport of particles above a given soil, minimally dispersed particle‐size distributions should be considered rather than the granulometric composition of the soil.     

Bedload transport and bed resistance associated with density and turbidity currents

Turbidity currents in the ocean are driven by suspended sediment. Yet results from surveys of the modern sea floor and turbidite outcrops indicate that they are capable of transporting as bedload and depositing particles as coarse as cobble sizes. While bedload cannot drive turbidity currents, it can strongly influence the nature of the deposits they emplace. This paper reports on the first set of experiments which focus on bedload transport of granular material by density underflows. These underflows include saline density flows, hybrid saline/turbidity currents and a pure turbidity current. The use of dissolved salt is a surrogate for suspended mud which is so fine that it does not settle out readily. Thus, all the currents can be considered to be model turbidity currents. The data cover four bed conditions: plane bed, dunes, upstream‐migrating antidunes and downstream‐migrating antidunes. The bedload transport relation obtained from the data is very similar to those obtained for open‐channel flows and, in fact, is fitted well by an existing relation determined for open‐channel flows. In the case of dunes and downstream‐migrating antidunes, for which flow separation on the lee sides was observed, form drag falls in a range that is similar to that due to dunes in sand‐bed rivers. This form drag can be removed from the total bed shear stress using an existing relation developed for rivers. Once this form drag is subtracted, the bedload data for these cases collapse to follow the same relation as for plane beds and upstream‐migrating antidunes, for which no flow separation was observed. A relation for flow resistance developed for open‐channel flows agrees well with the data when adapted to density underflows. Comparison of the data with a regime diagram for field‐scale sand‐bed rivers at bankfull flow and field‐scale measurements of turbidity currents at Monterey Submarine Canyon, together with Shields number and densimetric Froude number similarity analyses, provide strong evidence that the experimental relations apply at field scale as well.     

An electromagnetic device for automatic detection of bedload motion and its field applications

A new sensor for the continuous and unmanned detection and recording of bedload motion is described. The sensor acts in the same fashion as a conventional metal detector but is elongate and installed permanently in the bed of an alluvial channel. Artificial clasts are labelled with short lengths of ferrite rod and are seeded upstream from the sensor, replacing bed particles. The entrainment of seeded clasts takes them over the sensor where they distort the magnetic field and produce a change in inductance that is detected and recorded. A field installation demonstrates the value of the sensor by revealing for the first time in coarse-grained alluvium the spasmodic nature of particle motion reminiscent of kinematic waves. It also illustrates the importance of pebble clusters in delaying particle entrainment.     

黏性泥石流对球型大颗粒启动的临界条件分析

泥石流是一种破坏力巨大的地质灾害,其破坏力主要来源于浆体中裹挟的大颗粒。相近速度情况下,相同体积的大颗粒比液相浆体拥有更大的冲击力。本文针对黏性泥石流沟内大颗粒的滚动启动,建立了合理并且较为简洁的计算模型。水流条件是泥石流爆发的关键因素,通过分析计算球型大颗粒在浆体冲击下受到的上举力、推移力、有效重力等,考虑支承颗粒和启动颗粒相对位置的随机分布问题,求解大颗粒临界启动时的力矩平衡方程,得到对应的上游来流临界条件。临界启动流速公式符合普适性规律,并且通过计算流体软件FLUENT对3个典型算例的数值模拟,得到的数值解与理论解吻合得较好。本文结论对黏性泥石流沟的防治工程设计,特别是水石分流中排水流量的计算具有一定借鉴意义。     

The motion of sediment-water mixtures during intense bedload transport: computer simulations

A new model, which couples fluid and particle dynamics, has been developed to study the motion of the sediment-water mixture during intense bedload transport, including the velocity profiles of both sediment and water, the roughness length of an upper plane bed and the thickness of moving sediment layers. Standard mixing length theory is used to model the motion of water above the boundary between the overlying water and the sediment-water mixture. The turbulent flow within the moving sediment layers is described by a shear stress model, in which the effective viscosity of the flowing water is proportional to the velocity difference between the fluid and the sediment. The particle dynamics method, in which the equations of motion of each of many particles are solved directly, is applied to model the movement of sediment particles. The particle-fluid interaction is expressed by a velocity-squared fluid drag force exerted on each sediment particle. Both computer simulation results and theoretical analysis have shown that the velocities of both sediment and fluid during intense sediment transport decrease exponentially with depth in the top layers of a fast-moving sediment—water mixture. The thickness of the moving sediment layers, obtained from the computer simulation results, is proportional to the shear stress, which agrees with previous experimental observations.     

Effects of bed longitudinal inflexion and sediment porosity on basal entrainment mechanism: insights from laboratory debris flows

Channel morphology and bed sediment erodibility are two crucial factors that significantly affect debris flow entrainment processes. Current debris flow entrainment models mostly hypothesize the erodible beds are infinite with uniform slopes. In this study, a series of small-scale flume experiments were conducted to investigate the effects of bed longitudinal inflexion and sediment porosity on basal entrainment characteristics. Experimental observations revealed that sediment entrainment is negligible at early stages and accelerates rapidly as several erosion points appear. Continual evolution of flow-bed interfaces changes interactions between debris flows and bed sediments, rendering the interfacial shear action involved into a mixed shear and frontal collisional action. Lower bed sediment porosity will change the spatial arrangement and orientation of particle mixture, strengthen the interlocking and anti-slide forces of adjacent sediment particles, and promote the formation of particle clusters, all of which will increase bed sediment resistance to erosion. By examining the post-experimental bed morphology, the slope-cutting amounts and topographic reliefs are determined to positively correlate with longitudinal transition angles. These high topographic reliefs may indicate the propensity of triangular slab erosion, rather than strip-shaped slab erosion, in non-uniform channels with relatively steep erodible beds. Empirical formulas are obtained that denote the relationships among bed sediment strength, channel curvature radius, and sediment porosity through a multi-parameter regression analysis. This study may aid in clarifying the complex coupling effects of spatial variations in debris flow dynamics as well as sediment erodibility and bed morphology in non-uniform channels with abundant seismic loose material.

     

Magnetic and coagulation forces on a suspension of magnetic particles

It is shown that the magnetic force on a highly-magnetic particle in a slurry is a strong function of the particle shape and the concentration density of the magnetic particles in the suspension. An expression is derived for the coagulation forces between magnetized particles as a function of magnetic moment, size, and concentration.     

CFD simulation of fine coal segregation and stratification in jigs

The literature review on discrete element (DEM) model analysis of jigging reveals that an idealized fluid behavior is assumed and the damping of the fluid motion across the mineral bed is generally ignored. A microscopic model based on the principles of Computational Fluid Dynamics (CFD) is used to simulate the liquid flow and stratification of coal particles with a wide size range and density distribution in jigging. Fluid motion is calculated by directly solving the Navier–Stokes equations. Coal particles are moved in a Lagrangian frame through the action of forces imposed by the fluid and gravity. Particle effects on fluid motion are fed back at each time step through calculating the velocity disturbance caused by the particle. Particle–particle and particle–wall collisions are also considered. The snapshots of particle configurations for the simulation of stratification in oscillating flow show that the model predicts the macroscopic behavior, such as segregation and stratification, of particles reasonably well.     

Porosity and size gradation of saturated gravel with percolated fines

Fine particles may infiltrate through coarse alluvial beds and eventually saturate the subsurface pore space. It is essential to understand the conditions that lead to bed saturation, and to forecast the packing characteristics of saturated beds to assess the effect of excess fine sediment supply on a number of processes that occur in the stream–sediment boundary. To address this problem, in this study, a new method is introduced to predict the grain‐size distribution for the saturated condition, and the resulting porosity decrease, given the characteristics of the bed and the supplied sediments. The new method consists of the numerical aggregation of infilling fines in a finite bed volume, during which the bed properties change to affect further infilling. An existing semi‐empirical, particle packing model is implemented to identify these properties. It is shown that these types of models are adequate to describe regimes of natural sediment fabric quantitatively, and are thus useful tools in the analysis of sediment infiltration processes. Unlike previous developments to quantify saturated bed conditions, which assume that the supplied material is uniform and finer than the bed pore openings, the method developed herein considers poorly sorted fines, and can identify size fractions that are able to ingress into the bed due to being smaller than the particles that form the bed structure. Application of the new method to published experimental data showed that the final content of infiltrated fines is strongly sensitive to the initial bed packing density, highlighting the need to measure and understand open‐work gravel deposits. In addition, the new method was shown to be suitable for assessing the degree of bed saturation, when it was applied to a published data set of field samples.     

Threshold for particle entrainment into suspension

ABSTRACT Laboratory observations regarding the limit conditions for particle entrainment into suspension are presented. A high‐speed video system was used to investigate conditions for the entrainment of sediment particles and glass beads lying over a smooth boundary as well as over a rough bed. The results extend experimental conditions of previous studies towards finer particle sizes. A criterion for the limit of entrainment into suspension is proposed which is a function of the ratio between the flow shear velocity and particle settling velocity. Observations indicate that particles totally immersed within the viscous sublayer can be entrained into suspension by the flow, which contradicts the conclusions of previous researchers. A theoretical analysis of the entrainment process within the viscous sublayer, based on force–balance considerations, is used to show that this phenomenon is related to turbulent flow events of high instantaneous values of the Reynolds stress, in agreement with previous observations. In the case of experiments with a rough bed, a hiding effect was observed, which tends to preclude the entrainment of particles finer than the roughness elements. This implies that, as the ratio between particle and roughness element sizes becomes smaller, progressively higher bed shear stresses are required to entrain particles into suspension. On the other hand, an overexposure effect was also observed, which indicates that a particle moving on a smooth bed is more prone to be entrained than the same particle moving on a bed formed by identical particles.     

The influence of sediment thickness on energy delivery to the bed by bedload impacts

Fluvial bedrock erosion rates due to impacting sediment particles are thought to be proportional to the energy delivered to the bedrock. When sediment particles cover the bed, they reduce the energy transmitted to the bed by an impacting particle. We measured the decline of energy transferred through sediment cover of increasing thickness in laboratory experiments. The energy arriving at the bed is a function both of the cover thickness and the grain size of the covering sediment. Using a simple stochastic model of cover distribution, the experimental results were upscaled to the reach scale. Although cover thickness influences energy delivery heavily at a given point, when averaging over the whole bed, cover-free areas dominate total energy delivery, making partial energy transfer through the cover negligible when a small or intermediate fraction of the bed is covered by sediment. Partial energy delivery through the bed cover is not negligible when a large fraction or the complete bed is already covered, but in this situation, an erosion threshold may become important. On grounds of the presented data, we expect that the areal distribution of sediment in a bedrock channel dominates total energy delivery and that partial energy delivery to the bed through a sediment layer can be neglected for most modelling purposes.     

Interrelationships between bed morphology and bed-material transport for a small,gravel-bed channel*

Bed conditions (micro-relief, textural associations and packing structural arrangements) in the gravel-bed channel of Seale's Brook are shown to be closely interrelated; various categories are identified and related to mode of bed material transport and deposition. Entrainment of bed material, commonly treated as a simple function of particle weight and channel hydraulics, is also shown to be strongly affected by varying and variable bed conditions. In particular, the classic concept of competence appears to be of restricted utility in such channels; resistance of bed material to fluid drag and to particle impact is augmented, over large parts of the channel bed, by its interlocking structure, made possible by the wide range in particle calibre, and by the characteristic disc and blade shapes of the slate debris. Particle mobility, as indicated by distance of travel of labelled bed material, is only partly a function of particle weight; indeed, although particle mobility decreases from small pebbles to large cobbles, it also decreases for the finest bed material (very small pebbles). This appears to be explicable, partly in terms of the ease of entrainment (and duration of travel), and, partly in relation to the ease of transport of material over an uneven channel bed surface. Particle mobility is greatest for material in open and infilled structures and smallest for sediment in tight structural arrangements. Local bed slope also exerts an influence on the probability of particle entrainment and on particle mobility. The findings emphasize the need for combining sedimentological and engineering approaches to bed material transport in coarse-bedded channels, and, at the same time, illustrate some of the reasons for the existence of indeterminacy in the modelling of bed-material transporting processes.