A comparative study of slip velocity models for the prediction of performance of floatex density separator

The separation features of the floatex density separator (FDS) are investigated through experimental and computational approaches. It has been shown that the performance of the FDS can be predicted reasonably well using a slip velocity model and steady-state mass balance equations. The approach for the formulation of the slip velocity model makes a difference in the prediction of FDS performance. The computed data from four different slip velocity models have been compared and contrasted with the experimental observations. It has been shown that a slip velocity model based on the modified Richardson and Zaki equation, in which the dissipative pressure gradient is considered to be the primary driving force for separation, predicts the performance more accurately than the other three. A deslimed feed is recommended for better performance of the FDS.     

Alteration of the equal settling ratio of fine particles by vertically-oscillating water

An equal settling ratio is an important factor in estimating particle separation accuracy. However, this factor is often calculated using the settling velocity in stationary water, there are no examples of calculation of the equal settling ratio in an actual separator. This is difficult because particle movement in a separator is very complicated, and even simple periodic motions, such as the oscillation field used with many separators, are ignored in many cases. The authors have previously reported on the relation between the equal settling ratio and the oscillation frequency by analysis of particle movement in vertically oscillating water, using spherical particles of glass (average size 435 μm) and zirconia (202 μm) which have the same settling velocity in stationary water. In this study, the influence of particle diameter on the change in the settling velocity in oscillating water was experimentally investigated for three pairs of glass and zirconia particles having different sizes under 0.5 mm, which have the same settling velocity in stationary water. The settling velocities of different-sized particles decreased at different rates in oscillating water, indicating that the equal settling ratio is reduced by water oscillation. We conclude that water oscillation improves the accuracy of size separation for glass particles over 300 μm and zirconia particles over 150 μm when glass and zirconia particles are separated from each other with the difference of these settling velocities.     

Hindered settling of sand grains

The sedimentation rate of sand grains in the hindered settling regime has been considered to assess particle shape effects. The behaviour of various particulate systems involving sand has been compared with the widely used Richardson–Zaki expression. The general form of the expression is found to hold, in as much as remaining as a suitable means to describe the hindered settling of irregular particles. The sedimentation exponent n in the Richardson–Zaki expression is found to be significantly larger for natural sand grains than for regular particles. The hindered settling effect is therefore greater, leading to lower concentration gradients than expected. The effect becomes more pronounced with increasing particle irregularity. At concentrations around 0·4, the hindered settling velocity of fine and medium natural sands reduces to about 70% of the value predicted using existing empirical expressions for n. Using appropriate expressions for the fluidization velocity and the clear water settling velocity, a simple method is discussed to evaluate the sedimentation exponent and to determine the hindered settling effect for sands of various shapes.     

Estimating the settling velocity of bioclastic sediment using common grain‐size analysis techniques

Most techniques for estimating settling velocities of natural particles have been developed for siliciclastic sediments. Therefore, to understand how these techniques apply to bioclastic environments, measured settling velocities of bioclastic sedimentary deposits sampled from a nearshore fringing reef in Western Australia were compared with settling velocities calculated using results from several common grain‐size analysis techniques (sieve, laser diffraction and image analysis) and established models. The effects of sediment density and shape were also examined using a range of density values and three different models of settling velocity. Sediment density was found to have a significant effect on calculated settling velocity, causing a range in normalized root‐mean‐square error of up to 28%, depending upon settling velocity model and grain‐size method. Accounting for particle shape reduced errors in predicted settling velocity by 3% to 6% and removed any velocity‐dependent bias, which is particularly important for the fastest settling fractions. When shape was accounted for and measured density was used, normalized root‐mean‐square errors were 4%, 10% and 18% for laser diffraction, sieve and image analysis, respectively. The results of this study show that established models of settling velocity that account for particle shape can be used to estimate settling velocity of irregularly shaped, sand‐sized bioclastic sediments from sieve, laser diffraction, or image analysis‐derived measures of grain size with a limited amount of error. Collectively, these findings will allow for grain‐size data measured with different methods to be accurately converted to settling velocity for comparison. This will facilitate greater understanding of the hydraulic properties of bioclastic sediment which can help to increase our general knowledge of sediment dynamics in these environments.     

吹填泥浆中土颗粒沉降-固结规律研究

吹填泥浆中土颗粒沉降-固结过程十分复杂,其中土颗粒的沉降固结规律并不明确。室内沉降试验采用一种改进的方法--分层抽取法,先得到土颗粒体积分布规律,再利用体积通量函数法计算不同粒组颗粒平均沉速。计算结果表明,吹填泥浆在沉降过程中会出现3个区域,分别是干涉沉降区、絮体压缩沉降区和自重固结区;在沉降初期0～1 h和1～7 h内,干涉沉降区内土颗粒沉速远小于Stokes公式沉速计算值,颗粒沉速分别与颗粒直径的0.488 1和0.111 7次方有关。絮体压缩沉降区和自重固结区内颗粒基本不出现分选现象,均属于泥浆颗粒的沉积物;该试验中絮体压缩沉降区的密度约为1.04 g/cm3。     

Threshold of motion and settling velocities of mollusc shell debris: Influence of faunal composition

Bioclastic particles derived from mollusc shell debris can represent a significant fraction of sandy to gravelly sediments in temperate and cool‐water regions with high carbonate productivity. Their reworking and subsequent transport and deposition by waves and currents is highly dependent on the shape and density of the particles. In this study, the hydrodynamic behaviour of shell debris produced by eight mollusc species is investigated for several grain sizes in terms of settling velocity (measurements in a settling tube) and threshold of motion under unidirectional current (flume experiments using an acoustic profiler). Consistent interspecific differences in settling velocity and critical bed shear stress are found, related to differences in shell density, shell structure imaged by scanning electron microscopy and grain shape. Drag coefficients are proposed for each mollusc species, based on an interpolation of settling velocity data. Depending on the shell species, the critical bed shear stress values obtained for bioclastic particles fall within or slightly below empirical envelopes established for siliciclastic particles, despite very low settling velocity values. The results suggest that settling velocity, often used to describe the entrainment of sediment particles through the equivalent diameter, is not a suitable parameter to predict the initiation of motion of shell debris. The influence of the flat shape of bioclastic particles on the initiation of motion under oscillatory flows and during bedload and saltation transport is yet to be elucidated.     

滑源区粒序分布及颗粒粒径对碎屑流冲击作用的影响研究

滑体的运动速度、堆积形态、冲击力等因素决定了碎屑流的致灾程度。滑源区不同岩性特征和结构分布的差异导致了滑体粒序分布和颗粒粒径的差异。在运动过程中产生的碰撞、摩擦、跳跃,影响着滑坡碎屑流的致灾程度。在物理模型试验的基础上,运用三维离散元软件PFC3D,探究滑源区粒序分布及颗粒粒径对滑体运动速度、堆积形态、冲击力的影响。研究结果表明:碎屑流中各粒径颗粒的平均速度受颗粒粒径及滑源区初始粒序的共同影响,且初始粒序对各颗粒平均速度影响更大;在堆积形态方面,粒径大小对厚度方向上的粒序排布影响较大,而滑源区粒序分布对单种颗粒的堆积形态影响较大;在颗粒分选作用下,颗粒粒径成为控制峰值冲击力的主要因素,而滑源区粒序分布则通过决定滑体堆积形态控制了准静态堆积阶段碎屑流的冲击力。     

Particle Retention in a Submerged Meadow and Its Variation Near the Leading Edge

The retention of particles within meadows of submerged aquatic vegetation impacts the fate of organic matter, pollen, and larvae. Because flow conditions near the leading edge differ from those over the bulk of the canopy, particle retention is likely to differ as well. In particular, near the leading edge of a wide meadow, flow deceleration generates a vertical updraft, which impacts particle fate. In the fully developed region of the meadow, shear layer vortices at the top of the meadow may also influence particle fate. In this study, the retention of particles was measured along the length of a 10-m model meadow (height h?=?0.1 m) and was connected to the evolving flow field. Two particle sizes, with settling velocity w _s50?=?0.00075?,?0.018 m s^?1, were released at two heights within the model meadow \( \left(\frac{Z_{rel}}{h}=0.31,0.81\right). \) The retention of particles was measured using microscope slides distributed along the flume bed. Retention increased with distance from the leading edge, associated with the decrease in vertical updraft. Retention was also greater for the particles with higher settling velocity. In the fully developed region of the meadow, particle retention was lower for particles influenced by the shear layer vortices at the top of the meadow (\( \frac{Z_{rel}}{h}=0.81 \)).     

Analogue study of particle segregation in pyroclastic density currents, with implications for the emplacement mechanisms of large ignimbrites

Abstract Analogue flume experiments were conducted to investigate the transport and sedimentation behaviour of turbulent pyroclastic density currents. The experimental currents were scaled approximately to the natural environment in three ways: (1) they were fully turbulent; (2) they had a very wide range of particle sizes and associated Rouse numbers (the ratio of particle settling velocity to effective turbulent eddy velocity in the current); and (3) they contained particles of two different densities. Two sets of surge‐type experiments were conducted in a 5 m long, water‐filled lock‐exchange flume at five different volumetric particle concentrations from 0·6% to 23%. In one set (one‐component experiments), the currents contained just dense particles; in the other set (two‐component experiments), they contained both light and dense particles in equal volume proportions. In both sets of experiments, the population of each component had a log‐normal size distribution. In the two‐component experiments, the size range of the light particle population was selected in order to be in hydrodynamic equivalence with that of the dense particles. Dense particles were normally graded, both vertically and downstream, in the deposits from both sets of experiments. The mass loading (normalized to the initial mass of the suspension) and grain size of the dense component in the deposits decreased with distance from the reservoir and were insensitive to initial total particle concentration in the currents. On the other hand, in the two‐component experiments, the light particles were extremely sensitive to concentration. They were deposited in hydrodynamic equivalence with the dense particles from dilute currents, but were segregated efficiently at concentrations higher than a few per cent. With increasing particle concentration, the large, light particles were carried progressively further down the flume because of buoyancy effects. Deposits from the high‐concentration currents exhibited reverse vertical grading of the large, light particles. Efficient segregation of the light component was observed even if the bulk density of the current was less than that of the light particles. In both sets of experiments, marked inflexions in the rate of downstream decline in mass loading and maximum grain size of the dense component can be attributed to the presence of two different particle settling regimes in the flow: (1) particles with Rouse numbers >2·5, which did not respond to the turbulence and settled rapidly; and (2) particles with Rouse numbers <2·5, which followed the turbulent eddies and settled slowly. The results are applied to the transport and sedimentation dynamics of pyroclastic density currents that generate large, widespread ignimbrites. Field data fail to reveal significant departures from aerodynamic equivalence between pumice and lithic clasts in three such ignimbrites: the particulate loads of some large ignimbrites are transported principally in turbulent suspensions of low concentration. In some ignimbrites, the well‐developed inflexions in curves of maximum lithic (ML) size vs. distance can be attributed to the existence of distinct high and low Rouse number particle settling regimes that mark the transition from an overcharged state to one in which the residual particulate load is transported more effectively by turbulence.     

激光测速粒子对复杂流动的响应研究——Ⅱ典型流场中粒子跟随性的数值分析

以修正后适用于高颗粒雷诺数的粒子非恒定运动方程为基础,将该方程无量纲化,定义了一般流场中粒子跟随性的概念,给出了粒子跟随性的数学表述。据此对典型流场中粒子的运动进行了数值计算,并定量分析了粒径、密度等参数对不同流动中示踪粒子跟随特性的影响。     

Experimental and modeling investigation of sewage solids sedimentation based on particle size distribution and fractal dimension

Sewage solids are usually characterized by non-specific parameters such as suspended solids. The suspended solids has been shown to be an inadequate index for advanced water treatment processes. In this study, the sewages solids particle size distribution was used to provide more detailed information on sewage characteristic. It is hoped that, by introducing particle size distribution, the mechanism of sewage solids sedimentations can be better understood. The particle size distribution of the domestic sewage was measured by the Malvern® laser scattering technique to link to its settlement efficiency. Experimental results show that 77 % of particle volume was removed during the 90 min settling, of which 71.2 % of particle volume was removed in the initial 30 min. The submicron particles were found to be removed by co-settling with large particles. The fractal dimensions of sewage solids could also be derived from the laser scattering measurement. The fractal dimension could also provide useful information on the shape and density of sewage solids. A mathematical model considering the particle sizes, shapes and density changes was then constructed to simulate the settlement of raw sewage particles. Comparison of the modeling results based on discrete and flocculant settling theory shows that settlement can be better predicted by considering the fractal nature of particles. The particle size distribution and fractal dimension data measured by Malvern® laser scattering technique have been shown to be valuable data for in-depth understanding of the mechanisms of sewage solids sedimentation.     

Microstructural study of a natural slip zone: quantification and deformation history

Microstructure of a natural slip zone was comprehensively examined using a combination of images captured systematically by optical microscopy (OPM) and backscattered electron microscopy (BEM) techniques. Microstructural features identified on these images were processed and evaluated using an advanced image analysis system, which proved that quantitative analyses could considerably enhance the understanding of shear behavior of slip zones. It was found that variations of porosity, abundance of platy clay particles and alignments of particles are significant indicators revealing nature of deformation processes. These indicators show that global mechanical behavior of the investigated slip zone can be conceptualized as that of normally consolidated clayey soils under drained conditions.

The geometric patterns of the microstructure of the slip zone are similar to the S–C fabrics seen in tectonic shear zones. It is suggested that combined progressive bulk simple shear and pure shear modes enable to realistically reconstruct the kinematic history of the slip zone, through which particle movements and microstructural evolution were accomplished via various types of particulate flows. The results of this study show that clay mineralogy plays a more important role in the development of the slip zone than abundance of clay-size particles, while both clay mineralogy and relative proportions of each particle size fraction control the response of particles to shear deformation. Among the fractions present in the slip zone, fine silts are the strongest indicator of global shear stress characterized by their highest degree of alignment, whereas clay particles are the weakest. Highest degree of shape preferred orientation is also found within fine silt domains.     

Grain size distribution in suspension from bed materials

Experimental results show that the grain size distribution of suspended material is related to flow parameters and grain size distribution in the bed. A theoretical model has been developed to compute the suspension grain size distribution on the basis of diffusion equations, taking into account the effect of hindered settling due to the increased concentration in suspension. Fluid velocity closest to the bed is estimated by using the concept of migration velocities of particles in the bed layer. Comparisons of data computed by the proposed method and data from actual observations show generally good agreement.     

A numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.     

Sensitivity of incipient particle motion to fluid flow penetration depth within a packed bed

A discrete element method is applied to a three‐dimensional analysis related to sediment entrainment on a micro‐scale. Sediment entrainment is the process by which a fluid medium accelerates particles from rest and advects them upward until they are either transported as bedload or suspended by the flow. Modelling of the entrainment process is a critically important aspect for studies of erosion, pollutant resuspension and transport, and formation of bedforms in environmental flows. Previous discrete element method studies of sediment entrainment have assumed the flow within the particle bed to be negligible and have only allowed for the motion of the topmost particles. At the same time, micro‐scale experimental studies indicate that there is a small slip of the fluid flow at the top of the bed, indicating the presence of non‐vanishing fluid velocity within the topmost bed layers. The current study demonstrates that the onset of particle incipient motion, which immediately precedes particle entrainment, is highly sensitive to this small fluid flow within the topmost bed layers. Using an exponential decay profile for the inner‐bed fluid flow, the discrete element method calculations are repeated with different fluid penetration depths within the bed for several small particle Reynolds numbers. For cases with slip velocity corresponding to that observed in previous experiments with natural sediment, the predicted particle velocity is found to be a few percent of the fluid velocity at the top of the viscous wall layer, which is a reasonable range of velocities for observation of incipient particle motion. This method for prescribing the fluid flow within the particle bed allows for the current discrete element method to be extended in future studies to the analysis of sediment entrainment under the influence of events such as turbulent bursting. Additionally, predictions for the slip velocities and fluid flow profile within the bed suggest the need for further experimental studies to provide the data necessary for additional improvement of the discrete element method models.     

Physical model study on the clay–sand interface without and with geotextile separator

In most marine reclamation projects, sand fill is placed directly on soft marine seabed soils. The sand particles can easily penetrate into the soft marine soils, and the soft soil can also move into the pore spaces inside the sand at the initial contact interface between the sand and the soft marine soil. In this case, the permeability and the volume of the sand above the initial surface are reduced. To avoid this problem, a geotextile separator is often placed on the surface of the soft marine soils before placing the sand. In this study, a two-dimensional physical model is utilized to study the geotextile separator effects. The initial conditions of a clayey soil, sand fill, and surcharge loading were kept the same in the physical model test with the only difference being that a geotextile separator was either placed on the clay surface or omitted. The settlements of the initial interface were recorded and compared for the two cases without or with the geotextile separator. The particle size distribution of the soils taken across the interface zone for different time durations was then measured, analyzed, and compared. Based on an analysis of the results, the sand percolation depth was 40 mm and fine particle suffusion was apparent when the sand was placed directly on the marine slurry surface without a geotextile separator. However, when a geotextile separator was used sand percolation was avoided, and the fine particle suffusion was effectively diminished. A relative fine particle fraction is defined to illustrate the migration of fine particles from the clay to the sand soils. The fine particle percentages of the Hong Kong Marine Deposits–sand mixtures were calculated for the cases with and without a geotextile separator using an empirical formula and micromechanical modeling to obtain a better understanding of the effects of geotextile separators in practice.

     

The settling of consecutive spheres in viscoplastic fluids

One of the factors contributing to the uncertainties involved in the estimation of particle settling velocity in viscoplastic fluids is the time-dependent effect where the viscous parameters of the fluid change as a particle flows through and shears the medium. These changes, particularly at low shear Reynolds numbers, are reflected in the settling velocity of a following sphere that is released some time after an initial one, with the following sphere having a significantly greater velocity. This study found that changes in both fall velocity and equivalent viscosity can be correlated satisfactorily by a power law equation to the dimensionless form of the time interval between releases, and the rheogram shape factor for the fluid. A collision of particles occurs in cases where the time interval between releases is small, after which the particles combine and travel at a terminal velocity. A new variable, β, which takes into account the different surficial stress of the combined spheres, was introduced to the correlation of Wilson et al. [Wilson, K.C., Horsley, R.R., Kealy, T., Reizes, J.A., Horsley, M.R., 2003. Direct prediction of fall velocities in non-Newtonian materials. Int. J. Miner. Process. 71, 17–30] β was found to depend on the rheogram shape factor for the fluid and the shear Reynolds number for the particle. The validity of this approach was supported by experimental data.     

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.     

颗粒沉降的格子Boltzmann模拟与PIV实验验证

在格子Boltzmann方法中引入大涡模拟,对球形颗粒在静水中沉降引起的紊动流场进行了数值模拟。数值模拟沉速与理论值以及粒子图像测速系统(PIV)实验结果吻合,验证了模型的合理性。同时分析比较了颗粒沉降过程中尾部紊动流场分布以及尾流流速值,发现数值模拟结果与实测结果趋势、数值基本一致,进一步说明了利用格子Boltzmann方法与大涡模拟技术相结合可以合理模拟泥沙颗粒在紊流区的沉降。     

Evaluation of slurry settling rate using fuzzy rule-based modeling

The pressure acid leach process is the most widely used method of metal extraction from laterite ores. The self-weight settling rate of the ore slurries governs the throughput of the process and is improved by adding synthetic polymers. The charge density, molecular weight, and dosage of the polymers are the key factors influencing the settling rate of the slurries. This interdisciplinary paper uses the geotechnical understanding of hindered sedimentation for a mining engineering application. A conceptual fuzzy rule-based model was developed to evaluate the initial hydraulic conductivity of polymer-modified laterite ore slurries. Identification of control parameters and selection of the model architecture (fuzzy rule-base) were based on expert judgment. The developed model was trained and validated using bench-scale settling test data. The model reasonably predicts the initial hydraulic conductivity of polymer-added laterite ore slurry with a coefficient of determination of 0.75. Rank correlation coefficient-based sensitivity analyses indicated that charge density was the most significant polymer parameter followed by molecular weight and then by dosage. Charge density accounted for more than 97% of variability in the initial hydraulic conductivity estimates for both anionic and cationic polymers.