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.     

Experiments on the settling, overturning and entrainment of bivalve shells and related models

An experimental and theoretical examination has been made of the settling, entrainment and overturning of 176 valves representing 16 common Northwest European marine bivalve species, together with a comparative study of 15 plastic models in the form of segments from cylindrical tubes. Settling behaviour in both stagnant and moving water depends on particle mass, symmetry and concavo-convexity. Separated empty bivalve shells spin and spiral while settling and, if sufficiently elongated, also pitch. At the observed Reynolds numbers, the shells and models fall concave-up, the terminal fall velocity increasing as the square root of the unit immersed mass or weight. The drag coefficient is independent of Reynolds number but increases with surface roughness and, particularly, particle elongation. Turbulence slightly lowers the critical elongation for pitching. A separation vortex lies captive on the upper side of each descending particle. Consequently, an empty bivalve shell traversing a suspension of sand traps grains on its upper side at a rate proportional to their volume concentration and terminal fall velocity. This process, increasing the effective shell mass, is limited only by the capacity of the shell and grain spillage due to the possible onset of pitching. The ratio (non-dimensional) of a quantity proportional to the applied fluid force and the particle unit immersed weight consistently describes the entrainment of concave-up and convex-up particles, and also the immediate overturning of a valve on settling concave-up to the bed. These thresholds vary in relative magnitude with bed-particle friction and particle concavo-convexity. In general, convex-up particles are the most stable; the concave-up entrainment and overturning thresholds are of a substantially lower but similar magnitude. The high frequency of concave-up bivalve attitudes in turbidites is understandable largely in terms of the ability of a settling valve to increase in effective mass by grain entrapment. Convex-up attitudes in the lower parts of turbidites may record currents stronger than the overturning threshold.     

Drag on non-spherical particles in power law non-Newtonian media

The free settling velocity of cylinders and disks falling in quiescent Newtonian and power law liquids has been measured over wide ranges of experimental conditions of the particle Reynolds number (10^− 5–∼300), power law flow behaviour index (0.31–1) and the length-to-diameter ratio, ∼0.4–∼14. The corresponding range of sphericity is 0.62 to 0.86. An existing drag expression which has been tested extensively for spherical particles falling in Newtonian and in power law fluids has been slightly modified here for non-spherical particles. In particular, the use of this drag expression necessitates a knowledge of an equal volume sphere diameter (to evaluate the Reynolds number and drag coefficient) and the ratio of the surface area to the projected area of a non-spherical particle. With these modifications, the approach outlined here reproduces the present and the literature data for a wide range of non-spherical particles including cones, prisms, needles, cylinders settling in both Newtonian and power law fluids with reasonable levels of accuracy.     

考虑钙质砂细观颗粒形状影响的液体拖曳力系数试验

钙质砂作为南海岛礁填筑常用的岩土材料,其渗透性很大程度上决定着填筑后土体的固结和沉降。拖曳力系数是表达流体对土体颗粒表面力的参数,也是表征颗粒状土体渗透能力的一个重要参数,目前国内外对钙质砂拖曳力系数的研究十分有限。首先引入一个修正的三维参数 对钙质砂这种天然非规则颗粒材料的形状进行定量描述,然后开展一系列单个钙质砂颗粒在液体中沉降试验,利用高速相机记录颗粒沉降过程,结合图像处理技术获得颗粒沉降平衡速度Ut,进而计算出拖曳力系数CD和雷诺数Re,最后拟合出包含CD、Re及 三个参数的钙质砂拖曳力系数半经验模型。结果发现,在相同雷诺数条件下钙质砂的形状系数 越大,拖曳力系数越小。通过与其他研究结果对比发现,其表面微孔隙越发育,拖曳力系数越小的规律。该模型能够考虑不规则颗粒形状对拖曳力系数的影响,从而提高对土体渗透性预测的精度,对南海岛礁填筑工程中钙质砂固结和沉降的计算也具有重要意义。     

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 (\( \frac{Z_{rel}}{h}=0.81 \)).     

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.     

Interference phenomena between particle flattening and particle rounding in free vertical sedimentation processes

In this paper interference phenomena between particle flattening and particle rounding during the free vertical sedimentation of natural particles are investigated. Particle flattening is measured by the Corey Shape Factor (CSF), particle rounding by the Powers Index (P). Using Dietrich's equation, the effect of the flattening and the effect of the rounding on the terminal fall velocity of the particle can be studied separately. This is done by examining the influence of particle flattening and particle rounding on the Particle Sedimentation Coefficient (PSC), which is the ratio of the nominal diameter D_n of the particle to the equivalent sedimentation diameter D_b. It appears that particle flattening and particle rounding are interdependent so that interference phenomena occur. In the case of positive interference, the combined effect of flattening and rounding on the PSC is larger than the sum of the effects of both parameters separately. If, on the other hand, the combined effect is smaller than the sum of the single effects, negative interference occurs. For fine-grained particles, the more the shape of a particle differs from a sphere in one variable (flattening or rounding), the higher will be the influence of the other variable on the free vertical fall. For coarse-grained particles, the inverse occurs. For very fine-grained particles (D_n < 200 μm (air) or < 370 μm (water)) the influence of particle rounding on free vertical settling is negligibly small. For coarser grained particles, flattening is the most important parameter if the grains are strongly flattened. If not, rounding will be the governing parameter.     

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.     

Quickclays as products of glacial action: a new approach to their nature,geology, distribution and geotechnical properties

Essentially, quickclays are products of glaciation which accounts for their limited distribution; other modes of development being of lesser importance. Glacial grinding provides the fine silt and clay sizes required to constitute quickclays. Two major factors account for the geotechnical properties, a composition factor related to material comprising the soil system and a leaching factor, the effectiveness of which is related to the clay-mineral content of the soil.Soils can be divided into three types, based on criteria of particle size and type of interparticle bond. Among the latter are long-range active bonds, typical of true clay-mineral systems; and short-range inactive bonds such as are observed between two quartz particles. The three main soil types have: (a) small particles and long-range forces - the bond/weight ratioR is high; (b) small particles and short-range forces ? R > 1 ; and (c) large particles and short-range forces - i.e., the sands, andR < 1. Quickclays fall more conveniently into type (b) than into type (a) in as much as the most important property is a preponderance of inactive bonds in the soil system. This is achieved by a high content of non-clay mineral particles, and also may be assisted by leaching and cementation. If more than a critical proportion of long-range bonds are present, the required very high sensitivity does not occur.The initial failure of the soil might be treated as tensile using a volume failure criterion; the low settling velocity of the very small (≈ 1?2 μm) particles allows the solid-liquid transformation to occur after a modest shock loading. Observations of low thixotropy, lack of secondary settlement and sudden failure in compression tests can be explained by requirements of particle size and material.     

激光测速粒子对复杂流动的响应研究——Ⅰ颗粒非恒定运动数学模型及其数值方法

流体激光测速的精度与示踪粒子的跟随特性即流体中异质粒子的非恒定运动特性密切相关。首先对粒子非恒定运动方程进行了探讨,着重考虑了在高颗粒雷诺数时该方程的修正问题,简要分析了该方程的数学属性,并构造了这类方程的数值计算方法。分析表明,高颗粒雷诺数下的粒子非恒定运动方程为非线性奇异积分方程,而当颗粒雷诺数小于1时,则线性化为第二类渥尔特拉(Volterra)积分方程。以几种均匀流中球形小颗粒的非恒定运动为算例,计算结果与其解析解及有关实验数据的比较表明,数值方法具有良好的计算精度。     

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.     

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.     

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。     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

Steady-state vertical distribution of cohesive sediments in a flow

Settling velocity of diluted suspended aggregates is examined under steady-state conditions. It is shown that if the local settling velocity of the suspended mass of sediments at the bottom is gamma distributed, then, the vertical variation of the local mean settling velocity $\overline{W}$ is proportional to a power $1/r$ of the local concentration C, where r is the gamma distribution parameter. That is a consequence of the suspended-sediment sorting produced by the vertical dynamics. The parameter r characterizes the range of settling velocity values for all the aggregates simultaneously in suspension. To cite this article: M. Sánchez et al., C. R. Geoscience 337 (2005).     

The shape of loess particles reviewed

An important property of loess is a tendency to collapse on loading and wetting (hydroconsolidation) which can have serious consequences worldwide for civil engineering projects. This paper describes the use of Monte Carlo and other analytical techniques to predict the shape of naturally occurring loess particles. Randomly generated particles are classified according to Zingg shape categories: disc, sphere, blade and rod. By assuming a uniform distribution for the basic particle, average relative dimensions are calculated for the blade category, into which most loess particles have been shown to fall.     

Particle shape effect on thermal conductivity and shear wave velocity in sands

This study presents the correlations between quantified shape parameters and geotechnical properties for nine sand specimens. Four shape parameters, sphericity, convexity, elongation and slenderness, were quantified with two-dimensional microscopic images with the aid of image processing techniques. An instrumented oedometer cell is used to measure compressibility, thermal conductivity and shear wave velocity during loading, unloading and reloading stages. As the particle shape inherently determines the initial loose packing condition, initial void ratio and shape parameters are well correlated with compressibility. The applied stress in soils increases the interparticle contact area and contact quality; round particles tend to achieve higher thermal conductivity and shear wave velocity during stress-induced volume change. Multiple linear regression is implemented to capture the relative contributions of involved variables, revealing that the thermal evolution is governed by the initial packing density and particle shape. The experimental observations underscore the predominant effect that particle shape has on the geomechanical and physical properties upon stress-induced soil behavior.     

The pressure-field characteristics around porous wind fences: results of a wind tunnel study

Using detailed measurements of the instantaneous velocity fields around fences with different heights and porosities, the pressure fields around the fences were calculated using the Reynolds equations. Based on the results of calculation, the relationships among the pressure field, fence porosity (i.e., the β coefficient), fence height, and free-stream wind velocity were examined. For all fences, a high-pressure region exists upwind of the fence, and a low-pressure region exists downwind of the fence, the change of mean pressure is gradually less to a long distance from the fence. The pressure value at the center of the low-pressure area downwind of the fence decreases with increasing fence height and free-stream wind velocity. The impact of the fence’s porosity on pressure is large, when β < 0.2, the mean pressure upwind of the fence is relatively small, and the center value of the low-pressure area downwind of the fence increases with increasing fence porosity; when β > 0.3, the mean pressure increases around the fence.     

A Fluid-Dynamical Study of Crystal Settling in Convecting Magmas

Thermal convection in magma chambers is believed to be almostalways highly time-dependent, or ‘turbulent’, andpredicted convective velocities are commonly orders of magnitudelarger than settling velocities for typical crystals calculatedfrom Stokes' Law. To understand crystal settling in magma chamberswe have therefore undertaken a theoretical and experimentalstudy of particle settling in a turbulently convecting fluid. The regime of interest is where the ratio, S, of the Stokes'Law settling velocity, v_s, to the root mean square verticalcomponent of convective velocity, W, at mid-depth in the fluidis less than unity. Although v_s < W, settling is still possiblebecause convective velocities are height-dependent and mustdecrease to zero at the boundaries of the fluid. Particles immediatelyadjacent to the bottom boundary settle out with their full Stokes'settling velocities. At the same time, convection is vigorousenough to ensure that the distribution of particles in the fluidis uniform. It follows that the number of particles in suspensiondecays with time according to an exponential law, and the decayconstant is simply the ratio of v_s to h, the depth of the fluid.Experiments confirm this relationship, at least for low particleconcentrations, provided S < 0.5 and there is no re-entrainmentof particles from the floor of the tank. We apply this relationship to crystals in magma chambers andso calculate residence times for typical crystals. We find thatfor basaltic magmas the predicted residence times are smallcompared with the many thousands of years that a chamber takesto solidify if cooling is dominated by conduction through thecountry rock. We therefore conclude that crystal settling maybe an efficient differentiation mechanism. Significant magmaticevolution may, however, take place on time-scales that are competitivewith these residence times. If the settling of crystals is the rate-limiting step duringthe crystallization of a magma chamber it is expected that asteady state will be achieved at which the rate of supply ofcrystals into the convecting magma by crystallization balancesthe rate at which crystals settle out. We show how this ideacan explain both the lack of hydraulic equivalence in cumulaterocks and the commonly observed discrepancy between the relativeproportions of phenocrysts of various phases in fractionatedbasaltic lavas and the calculated relative proportions of thesemineral phases in the fractionating assemblage. Finally, anattempt is made to calculate the steady-state crystal contentof convecting magma chambers. Comparison of the predicted crystalcontents with the observed phenocryst contents of typical basalticlavas suggests that magma chambers may often cool more rapidlythan would be expected for conduction through the country rockalone.     

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.