Dimensionless Particle Diameter Research Articles

Experimental Investigation of Settling Velocity of Spherical Microplastic Particles

Research on the effects of microplastics on water environments is being widely conducted because the discharge of microplastics into the ocean and freshwater systems is rapidly increasing. For the numerical simulation of the transport and diffusion of microplastics introduced into water systems and evaluation of the ecological impacts, the settling velocities of microplastics must be investigated first. The settling behavior of microplastics has been commonly assumed to be similar to that of sediment particles, but this has not been sufficiently verified for various types of microplastic. In this study, a laboratory experiment was performed to measure the settling velocities of spherical microplastic particles in freshwater using a particle tracking technique, and a new calibration coefficient of the settling velocity was proposed based on the experimental data. The experimental results showed a clear linear relationship between the settling velocity and dimensionless particle diameter in the laminar flow region, as suggested by Stokes' law. However, the settling velocities in the transition region had a nonlinear relationship, which was also clearly demonstrated in the relationship between the drag coefficient and the particle Reynolds number. The evaluation of the existing equations for settling velocity showed that previous empirical equations based on experiments on sediment particles produced relative errors of 20% or more. However, the proposed calibration coefficient provided a more accurate prediction of the settling velocities of microplastic particles than the existing empirical equations based on sediment studies.

Experimental study of sediment washout from stormwater sumps.

Sumps are commonly used in urban stormwater systems, which can be considered as a simple pretreatment device for stormwater quality control. However, they may function as pollution sources due to sediment washout under high flow conditions. An experimental study was conducted to investigate the scour process of predeposited sediments from a sump and its influencing parameters. Under conditions with large inflows or high sediment deposit, the sediment particles could be resuspended, entrained and flushed out. The washout mass decreased exponentially with time if the sediment bed surface depth was larger than a threshold value; otherwise, the amount of washout would be much smaller. The same scour pattern was observed for all the testing cases, of which the largest scour depth always occurred below the outlet. The deposit below the inlet might increase under conditions with high flow rates and low levels of sediment bed. Dimension analysis was performed and principal non-dimensional parameters were found, including the Péclet number, the pipe Froude number, and the dimensionless particle diameter, which can be used to determine whether the washout would occur and its intensity in a stormwater sump under given conditions.

Developing a generic relation for predicting sediment pick-up rate using symbolic soft computing techniques.

Sediment pick-up rate has been investigated using experimental and numerical approaches. However, the use of soft computing methods for its prediction has received less attention so far. In this study, genetic programming (GP), grammatical evolution (GE), and gradient boosting machine (GBM) algorithms are employed to develop a relation in dimensionless form for predicting sediment pick-up rate in open channel flow based on two experimental datasets. Dimensionless Froude number, particle diameter, and depth-averaged turbulent kinetic energy are input variables for prediction. Prediction performance is evaluated with performance indices (root mean square error, mean absolute error, and coefficient of correlation), visual comparisons (scatter, dot, and Bland-Altman plots), and uncertainty indicators (Tsallis and Renyi entropies). Three mathematical expressions for sediment pick-up rate prediction are obtained, with GE producing the most accurate results.

Incipient Motion of Exposed Microplastics in an Open-Channel Flow.

The incipient motion threshold of microplastics (MPs), defined as the condition that is just sufficient to initiate MP movement, is key to assessing the transport and fate of MPs in water bodies, yet only a few studies have focused on its prediction. This study experimentally investigated the effects of bed roughness (smooth and rough beds) and MP properties (shapes, sizes, and densities) on the incipient velocity (Ui) and critical shear stress (τc) of exposed MPs in an open-channel flow. For a total of 19 types of MPs, Ui and τc were found to range from 0.06 to 0.21 m/s and 0.01 to 0.075 N/m2, respectively. The commonly used thresholds for sediment transport, for example, critical shield parameter Θc and movability number Λc, were established for MPs based on τc. Based on the experimental data of the literature and this study, it was found that predictions of Θc and Λc for sediments do not apply to MPs. A new explicit formula for Λc was proposed for predicting the incipient motion of MPs by introducing the dimensionless particle diameter (d*) and a new dimensionless parameter related to the particle size, density, and shape. The new formula has an absolute error of 12.3%, which is smaller than the existing formula for MPs (55.6%).

A new model for the terminal settling velocity of microplastics

Microplastic (MP) settling process is important for the transport of microplastic particles (MPs, <5 mm) in water bodies. However, for the control parameter of the drag coefficient (Cd), no generalized formula has been proposed for MPs of different shapes and materials. In this study, a total of 1343 MP settling data were collected from the literature. It was found that the drag law for perfect spheres cannot reasonably predict Cd for MPs with particle Reynolds number of 1–103. A new formula for Cd was developed by introducing the dimensionless particle diameter (d⁎) and two shape descriptors. The absolute error of the new formula is 15.2%, smaller than those (42.5–72.8%) of other existing formulas. Moreover, an explicit model was developed for MP settling velocity by correlating Cd, d⁎, and shape descriptors, with lower absolute error (8.8%) than those (15.4–77.2%) of existing models.

Attrition rate of CO2 adsorbent in bubbling fluidized beds

Particle attrition induced by bubbles in a bubbling fluidized bed was investigated with CO2 adsorbent particles (0.128 mm in diameter, 1770 kg/m3 in apparent density). The theoretical relationship between the rate of attrition by gas jets on the perforated plate distributor (Ra,j) and the rate of attrition by bubbles (Ra,b) in the bed was revealed that the rate constant of attrition by bubbles (Ka,b) was the product of the rate constant of attrition by gas jets (Ca) and dimensionless particle diameter (dpbc). An attrition tube (0.035 m-i.d.) using the perforated-plate distributor designed for reducing the attrition by gas jets was employed as the fluidized bed, and the air as the fluidizing gas. The mode of attrition by bubbles was identified as abrasion. The rate of attrition by bubbles (Ra,b) was linearly proportional to the power given to the bed solids by bubbles. The top size of the fine particles formed by attrition (dpm,ab) increased exponentially with an increase of bed mass and gas velocity. The effects of temperature, pressure, and area of internal surface contacting particle bed on the Ra,b and dpm,ab were negligible under the tested condition. Empirical relationships on Ra,b and dpm,ab were proposed based on the experimental data. When both jet and bubble attrition were significant, there existed the static bed heights that gave respectively the minimum attrition rate and the minimum of the top size of fine particles formed by attrition. Each optimal static bed heights increased with an increase of the orifice jet velocity of the perforated plate distributor.

The Mass Settling Flux of Suspended Particulate Matter in Venice Lagoon, Italy

Amos, C.L.; Kassem, H.; Bergamasco, A.; Sutherland, T.F., and Cloutier, D., 2021. The mass settling flux of suspended particulate matter in Venice Lagoon, Italy. Journal of Coastal Research, 37(6), 1099–1116. Coconut Creek (Florida), ISSN 0749-0208. A multidisciplinary study of the stability of the tidal flats of Venice Lagoon has provided field and laboratory data on the factors influencing the mass settling rates of material in suspension. This work was performed using two in situ benthic flumes (Sea Carousel and Mini Flume) in association with a wide range of physical and biological measurements undertaken during the summer of 1998 and the subsequent winter. Also, controlled experiments on erosion/sedimentation of prepared beds were carried out using Lab Carousel, a laboratory equivalent of Sea Carousel. Particle size and mass settling rates were found to be largely independent of suspended sediment concentration but strongly controlled by the antecedent bed shear stresses that led to the suspension. Results between the three flume types differed because of differences in the induced stress history created in each case. Comparable results were obtained by normalizing mass settling rate to the mean friction velocity of the flow during settling, i.e. the Rouse parameter () , and by use of the mean dimensionless particle diameter (D*). Results fell in line with results on carbonate and silica sands of the inlets of the lagoon. The mean particle diameter (df) varied in proportion to the applied shear stress and shear rate (G) suggesting that the suspended particles were eroded aggregates not floccules. The effective density of these aggregates was least (∼16 kgm–3) at the largest sizes (df > 1 × 10–4 m) and greatest (∼160–1600 kgm–3) at the smallest sizes (df < 1 × 10–4 m). The lack of an increase in df at low shear rates suggests that flocculation was not taking place. The mean deposition threshold (all experiments) was 0.68 Pa, which is less than the mean erosion threshold from these sites (0.78 Pa).

Development of Elastic Drag Coefficient Model and Explicit Terminal Settling Velocity Equation for Particles in Viscoelastic Fluids

Summary Viscoelastic fluids are frequently used as drilling or fracturing fluids to enhance cuttings or proppant transport efficiency. The solid transport performance of these fluids largely depends on the settling behaviors of suspended particles. Different from viscoinelastic fluids, the elastic and viscous characteristics of viscoelastic fluids both affect particle settling behaviors. In this study, to separately quantify the contribution degrees of the shear viscosity and fluid elasticity on the terminal settling velocity, we decompose the total drag force into a viscous drag force and an elastic drag force. Based on the experimental data from the available literature, it is concluded that the elastic drag force is a function of the fluid elasticity, particle diameter, particle terminal settling velocity, and density difference between the fluid and particle. The formula for the elastic drag force is determined on the basis of the force analysis, and a relationship between the elastic drag coefficient and particle Reynolds number (Re) is developed. An explicit equation that directly predicts the terminal settling velocity in viscoelastic fluids is determined by correlating the dimensionless particle diameter and Re. To validate the proposed model, a total of 108 settling experiments in viscoelastic fluids are conducted. The absolute percentage error (APE) between the predicted and measured terminal settling velocities is 15.26%, which indicates that the proposed explicit terminal settling velocity equation can provide satisfactory prediction accuracy of the terminal settling velocity for particles in viscoelastic fluids. Furthermore, an illustrative example is provided to show that the proposed model can be used to calculate the required fluid elasticity to obtain the desired terminal settling velocity when the fluid shear viscosity is fixed. The proposed models are valid with a consistency index range of approximately 0.16 to 1.2 Pa⋅sn, flow behavior index range of approximately 0.282 to 0.579, an Re range of approximately 0.005 to 30, and a fluid relaxation time range of approximately 0.183 to 110 seconds. This study can help operators choose proper drilling/fracturing fluids to enhance the cuttings/proppant transport and maximize drilling/fracturing performance.

Combined Effects of Mean Flow and Turbulence on Sediment Pickup Rate

AbstractThis paper aims to explore the combined main flow and turbulence influence on sediment pickup rates by investigating four purposely devised cases, namely, (1) unobstructed flow over a plane bed; (2) unobstructed flow over a rigid‐dune bed; (3) flow obstructed by a horizontal pipe; and (4) flow obstructed by a vertical pipe. The four cases were used to represent typical scenarios of mean flow combined with turbulence of varying intensities. By analyzing the dependence of sediment pickup rate on different combinations of the mean and turbulent flow parameters, a modified densimetric Froude number, incorporating both the bulk‐averaged velocity and maximum root‐mean‐square value of the fluctuating velocity, is found to be reasonably correlated with the measured pickup rates for all the four cases. Consequently, by relating the pickup rate with the dimensionless particle diameter and the modified densimetric Froude number, a generalized equation that predicts the pickup rates under both unobstructed as well as obstructed flow conditions is obtained.

Determination of cleaning mechanisms by measuring particle size distributions

Knowledge of the dominant removal mechanism (diffusive vs. convective mass transport) is important for understanding, modelling and predicting cleaning behavior of food soils. The size of the detached particles is thereby a useful physical quantity, since small particles, which are fully immersed within the viscous sublayer of the flow, will rather be removed due to diffusion than caught from the flow itself. The dimensionless particle diameter relates the particle size to the thickness of the viscous sublayer and has therefore been chosen to identify whether the particles were removed rather by diffusive or convective mass transport.This contribution presents the online measurement of particle size distributions during cleaning of starch and egg yolk soils in an automated laboratory test rig. To achieve accurate results for the particle sizes, measurements with Fraunhofer and Mie theory were compared. Furthermore, the influence of the cleaning temperature on the dimensionless particle diameter was examined for both soils.

An explicit analytical expression for bed-load layer thickness based on maximum entropy principle

The present study aims to derive an analytical model on bed-load layer thickness in an open channel turbulent flow carrying sediments. Determination of the thickness of the bed-load layer is of utmost importance in the study of bed-load transport as it is required to determine the bed-load transport rate, as well as in the study of suspended load transport as it acts as reference level for the particles in suspension. Apart from the several deterministic approaches available in the literature, the work adopts probabilistic approach based on entropy theory to determine the bed-load layer thickness. The concept of entropy theory developed by Shannon is used and the method of Lagrange multipliers is employed for the maximization of entropy function to find the least biased probability distribution. To calculate the Lagrange multipliers, present in the probabilistic model of dimensionless bed-load layer thickness, two different methodologies are presented. The model of bed-load layer thickness is a function of dimensionless shear stress and also depends on three other parameters which are found to be functions of specific gravity of sediment particle and dimensionless particle diameter from a non-linear regression analysis. The proposed model is validated with wide sets of experimental data available in literature and a good agreement is achieved. Apart from comparison with data, the model is also compared with existing deterministic model and computation of relative percentage error proves the better efficiency of the present model.

A new model for predicting drag coefficient and settling velocity of spherical and non-spherical particle in Newtonian fluid

The settling process of particles occurs in many natural and industrial processes and the knowledge of drag coefficient and settling velocity of spherical and non-spherical particles is of fundamental significance in practical applications. In this paper, a visualization apparatus and high-speed camera system are used to record the settling behavior of spherical and non-spherical particles in Newtonian fluid. 336 tests involving particle density (2680, 4450, 7960kg/m3), fluid viscosity (0.135, 0.289, 0.6685Pa·s), and particle shape (sphere, cube, cylinder) are conducted. A new and accurate correlation for the drag coefficient of spherical and non-spherical particles is been developed. This correlation has been formulated including the effect of the particle sphericity and the particle settling orientation. Besides, an explicit settling velocity equation which directly predicts settling velocity of both spherical and non-spherical particles in Newtonian fluid is proposed by correlating drag coefficient, the dimensionless particle diameter, sphericity and settling orientation. The average relative error is 3.52%, which indicates predictions of settling velocity are in good agreement with measured settling velocity. The model for predicting drag coefficient and settling velocity is valid with particle Reynolds number ranging from 0.001 to 100 and sphericity ranging from 0.471 to 1. And suitable particle shape range of this model is sphere, cube and cylinder. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate drag coefficient and settling velocity in Newtonian fluid with known particle and fluid property.

Primary Fragmentation Characteristics of Coal Particles during Rapid Pyrolysis

Experiments were carried out to investigate the rapid pyrolysis of Nei-meng (NM) lignite, Shen-fu (SF) bituminous coal, and Jin-cheng (JS) anthracite with the duration time of 0–500 ms and the temperature of 1173–1773 K using a high-frequency induction furnace. Interest was centered on the primary fragmental characteristics of particles, including the changes of mass loss, particle density, and size distribution, during the pyrolysis. A pair of fragmental parameters, i.e., dimensionless particle diameter δ and particle distribution Sf, was proposed to characterize the fragmentation during the different stages of pyrolysis. The result showed that the pyrolysis progress increases with time and temperature. The fragmentation extent is also positively related to the time and temperature. The progress of primary fragmentation is lignite ≈ bituminous coal > anthracite. However, the particle morphology changes little during the pyrolysis fragmentation. Evidence reveals that major fragmentations of NM and SF occu...

Solids velocity fields in a cold-flow Gas–Solid Vortex Reactor

In a Gas–Solid Vortex Reactor (GSVR), also referred to as a Rotating Fluidized Bed in Static Geometry, a fluidized bed is generated in a centrifugal field by introducing the gas via tangential inlet slots to the reactor chamber. Better heat and mass transfer are observed, making this a promising reactor type for Process Intensification. Developing GSVRs on industrial scale requires, amongst other, a good insight and understanding of the hydrodynamics of the granular flow. In the present work experiments are performed over a wide range of operating conditions in a cold flow pilot-scale set-up. The set-up has a diameter of 0.54m, a length of 0.1m and 36 tangential inlet slots of 2mm. Different materials with solids density between 950–1800kg/m3 and particle diameters of 1–2mm, at varying gas injection velocities from 55 to 110m/s are tested between minimum and maximum solids capacities. All these operating conditions are used to follow the change of granular flow by performing PIV. The rotating fluidized bed can change from a smoothly rotating, densely fluidized bed to a highly bubbling rotating fluidized bed depending on the operating conditions. Bubbling diminishes with increasing solids density and particle diameter. Experimental measurements of azimuthal particle velocity fields in a GSVR are for the first time reported. Azimuthal solids velocity is found to decrease with higher solids density and larger particle diameter. The critical minimum fluidization velocity, that is the minimum velocity at which the complete bed is fluidized, is calculated and the centrifugal bed behavior is mapped in terms of a dimensionless radial gas velocity and a dimensionless particle diameter, as conventionally done for gravitational beds.

Simple settling velocity formula for calcareous sand

From the analysis of 1557 calcareous sand grains, a new equation for the computation of particle settling velocity is derived. The proposed expression involves only the dimensionless particle diameter and the Reynolds number, meaning that the estimation of the settling velocity is quick and easy. This formula is compared with expressions available elsewhere and its improved accuracy is demonstrated. When the formula was applied to Hallermeier's database [(1981). Terminal settling velocity of commonly occurring sand grains. Sedimentology 28(6), 859–865], which has been used in previous studies to develop settling velocity equations, it was also found to have the smallest root mean square error. The equation reported in the paper is one of very few expressions specifically developed for calcareous sand.

Single droplet drying step characterization in microsphere preparation

Spray drying processes are difficult to characterize since process parameters are not directly accessible. Acoustic levitation was used to investigate microencapsulation by spray drying on one single droplet facilitating the analyses of droplet behavior upon drying. Process parameters were simulated on a poly(lactide-co-glycolide)/ethyl acetate combination for microencapsulation. The results allowed quantifying the influence of process parameters such as temperature (0–40°C), polymer concentration (5–400mg/ml), and droplet size (0.5–1.37μl) on the drying time and drying kinetics as well as the particle morphology. The drying of polymer solutions at temperature of 21°C and concentration of 5mg/ml, shows that the dimensionless particle diameter (Dp/D0) approaches 0.25 and the particle needs 350s to dry. At 400mg/ml, Dp/D0=0.8 and the drying time increases to one order of magnitude and a hollow particle is formed. The study demonstrates the benefit of using the acoustic levitator as a lab scale method to characterize and study the microparticle formation. This method can be considered as a helpful tool to mimic the full scale spray drying process by providing identical operational parameters such as air velocity, temperature, and variable droplet sizes.

A macroscopic two-energy equation model for turbulent flow and heat transfer in highly porous media

In this paper, a model for turbulent flow and heat transfer in a highly porous medium is proposed and applied to a porous channel bounded by parallel plates. Macroscopic continuity, momentum and energy equations are presented. Local non-thermal equilibrium is considered by means of independent equations for the solid matrix and the working fluid. The numerical methodology used is based on the control-volume approach. The effects of thermal dispersion, Reynolds number, dimensionless particle diameter, thermal conductivity ratio and Darcy number, on the Nusselt number, are presented. For laminar and turbulent flows the thermal dispersion mechanism leads to larger local temperature differences. Increase in Re number causes values for Nu, of both phases, to increase. Porosity increase causes the solid phase Nusselt number to decrease whereas the fluid Nusselt number in augmented. In general, an increase in the particle diameter increases Nusselt number. Also, the thermal conductivity ratio causes the most pronounced effect on Nusselt numbers.

Three-dimensional saltating processes of multiple sediment particles

The purpose of this study was to investigate the interacting mechanism between the saltating particles near a channel bed. A three-dimensional real-time flow visualization technique was developed to measure the interparticle collision behaviors during the saltating process. Based on the experimental data, the distribution of the collision points was found to be symmetric. This confirms the assumption that the projections of the collision points onto the reasonable plane are uniformly distributed. A three-dimensional saltating model was also developed. This model produced satisfactory results. The model is able to simulate the continuous saltating trajectories of several particles. The simulated dimensionless saltating height, longitudinal and vertical saltation velocity components were found to increase as the dimensionless particle diameter and the dimensionless flow transport capacity parameter increase, while the simulated lateral saltation velocity component varies inversely with the dimensionless flow transport capacity parameter. A regression equation for the bed load transport rate was also obtained.

A numerical study of particle wall-deposition in a turbulent square duct flow

The deposition of dense solid particles in a downward, fully developed turbulent square duct flow at Re τ = 360, based on the mean friction velocity and the duct width, is studied using large eddy simulations of the fluid flow. The fluid and the particulate phases are treated using Eulerian and Lagrangian approaches, respectively. A finite-volume based, second-order accurate fractional step scheme is used to integrate the incompressible form of the unsteady, three-dimensional, filtered Navier–Stokes equations on an 80 × 80 × 128 grid. A dynamic subgrid kinetic energy model is used to account for the unresolved scales. The Lagrangian particle equation of motion includes the drag, lift, and gravity forces and is integrated using the fourth-order accurate Runge–Kutta scheme. Two values of particle to fluid density ratio ( ρ p/ ρ f = 1000 and 8900) and five values of dimensionless particle diameter ( d p/ δ × 10 6 = 100, 250, 500, 1000 and 2000, δ is the duct width) are studied. Two particle number densities, consisting of 10 5 and 1.5 × 10 6 particles initially in the domain, are examined. Variations in the probability distribution function (PDF) of the particle deposition location with dimensionless particle response time, i.e. Stokes number, are presented. The deposition is seen to occur with greater probability near the center of the duct walls, than at the corners. The average streamwise and wall-normal deposition velocities of the particles increase with Stokes number, with their maxima occurring near the center of the duct wall. The computed deposition rates are compared to previously reported results for a circular pipe flow. It is observed that the deposition rates in a square duct are greater than those in a pipe flow, especially for the low Stokes number particles. Also, wall-deposition of the low Stokes number particles increases significantly by including the subgrid velocity fluctuations in computing the fluid forces on the particles. Two-way coupling and, to a greater extent, four-way coupling are seen to increase the deposition rates.

Analysis of bedload transport in laminar flows

Bedload transport generally depends on the bed shear stress and Reynolds number. Many studies conducted for the condition of turbulent flows have revealed the dependence of the transport rate on the bed shear stress, while knowledge of the Reynolds number effect on the transport rate is very limited. As an extreme case to reflect the viscous effect on sediment transport, sediment transport in laminar flows is considered in this paper. A stochastic approach is adopted to explore how the transport rate can be associated with characteristics of laminar flows. First, the probability of erosion in the absence of turbulence is assumed to depend only on the randomness of bed particles. The probability is then applied to formulate the sediment transport rate, of which the derivation is made largely based on Einstein’s bedload theory. The theoretical result indicates that the dimensionless transport rate for laminar flows is dependent on the dimensionless shear stress and dimensionless particle diameter or the shear Reynolds number. Comparisons are finally made between the derived formula and an empirical correlation available in the literature.