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Physical interactions of microplastics within vegetation and turbulent flows of freshwater systems are poorly understood. An experimental study was conducted to investigate the underlying physical transport mechanisms of microplastics over submerged canopies across a range of flow conditions common in the natural environment. The effects of changing canopy heights were investigated by testing two model canopies of varying stem heights, simulating seasonal variation. This study determined and compared the mixing and dispersion processes for microplastics and solutes utilizing fluorometric tracing techniques. A hydrodynamic model was developed based on the advection‐dispersion equation for quantifying microplastic mixing in submerged canopies. Longitudinal dispersion coefficients for neutrally buoyant microplastics (polyethylene) and solutes were significantly correlated within submerged model vegetation irrespective of the complexity of the flow regime. Hydrodynamic and solute transport models were shown to be capable of robust predictions of mixing for neutrally buoyant microplastics in environmental flows over a canopy, facilitating a new approach to quantify microplastic transport and fate. We compare the mixing processes for microplastics and solutes then propose a hydrodynamic model for quantifying the mixing in submerged canopies. Plain Language Summary: Microplastic movement and fate within vegetation and turbulent flows of freshwater systems is poorly understood. A study was conducted within a laboratory flume, scaled for real‐world river systems, to investigate the transport of microplastics over submerged canopies across a range of flow conditions common in the natural environment. The effects of changing vegetation heights were investigated by testing two model canopies of varying stem heights, simulating seasonal variation. To measure microplastic movement in real‐time this study determined and compared the mixing of microplastics and solutes using fluorometric techniques that measure fluorescence at specific wavelengths of light produced by the stained microplastics and Rhodamine WT dye (solute). Models utilizing velocities over depth and solute dispersion were adapted to quantify microplastic mixing in submerged canopies. The dispersion of neutrally buoyant microplastics (polyethylene), microplastics of a similar buoyancy to water, and solutes were significantly correlated within submerged vegetation irrespective of the complexity of the flow regime. The models were shown to be capable of reliable predictions of mixing for neutrally buoyant microplastics in environmental flows over a canopy, facilitating a new approach to measure microplastic transport and fate. Key Points: Neutrally buoyant microplastics disperse analogous to solutes within the water column of fluvial environments with submerged vegetationA novel fluorometric tracing and particle staining technique is proven to accurately trace stained microplastics within vegetated flowsA robust hydrodynamic model is proven to predict mixing of neutrally buoyant microplastics [ABSTRACT FROM AUTHOR]

We report new measurements of the concentration‐dependent longitudinal dispersion coefficient of aqueous urea and ethyl acetate solutions in a porous medium at a wide range of concentrations. The longitudinal dispersion coefficient was obtained by injection of a pulse of an aqueous solution of urea (or ethyl acetate) into a carrier phase flowing through a porous column and analysis of the effluent peak using the Taylor dispersion theory. The measured longitudinal dispersion coefficients for different velocities and concentrations showed an increasing trend with concentration and pore velocity. The longitudinal dispersion coefficient measurements show a power‐law relationship with the Peclet number KL∝αlPemβl. The results are compared with experimental data and empirical formulas available in the literature, and a reasonable agreement is achieved over the range of Peclet numbers studied. [ABSTRACT FROM AUTHOR]

Vegetation notably influences transport and mixing processes and can thus be used for controlling the fate of substances in the hydro‐environment. Whilst most work covers fully vegetated conditions, the novelty of this paper is to focus on flows with real‐scale flexible willow patches. We aimed to investigate how longitudinal dispersion varies according to the spatial distribution, density and coverage of the patches and to evaluate the explanatory power of predictors that consider the hydraulics, vegetation and channel geometry. Salt tracer experiments were performed in a trapezoidal channel where we established 3–4 m long and 1–1.6 m wide patches of artificial foliated willows that reproduced the shapes and plant densities observed on woody‐vegetated floodplains. We examined sparsely distributed patches with low areal/volumetric coverage of 6–11%, and non‐vegetated conditions for reference. Flow depths and surface widths were 0.7–0.9 and 6–7 m, respectively, and the mean flow velocities ranged at 0.3–0.6 m/s. The emergent patches generated from a negligible to over a four‐fold increase in the longitudinal dispersion when compared with non‐vegetated conditions. The patches with a preferential location in low‐velocity areas, such as near banks, or with a high plant density and a blockage of the cross‐sectional flow area ⪆0.4, led to the largest dispersion and residence times. Patches under such configurations enhanced the normalized differential velocity defined as the difference between the highest (90th percentile) and lowest (10th percentile) cross‐sectional flow velocities divided by the mean velocity, thus increasing shear dispersion. As existing analytical predictors failed to estimate the effect of different patch configurations, we proposed the change in the normalized differential velocity between vegetated and corresponding non‐vegetated conditions as a basic predictor of the reach‐scale longitudinal dispersion coefficient under patchy vegetation. In contrast, we observed no clear relationship between flow resistance and dispersion. Thus, our findings indicated that bankside vegetation may allow for reduced peak concentrations and lengthened residence times, supporting pollutant management, while ensuring good flow conveyance. Such rare field‐scale analyses improve the estimation of solute transport in real vegetated flows. [ABSTRACT FROM AUTHOR]

Numerous studies focus on flow and mixing within cylinder arrays because of their similarity to vegetated flows. Randomly distributed cylinders are considered to be a closer representation of the natural distribution of vegetation stems compared with regularly distributed arrays. This study builds on previous work based on a single, fixed, cylinder diameter to consider non‐uniform cylinder diameter distributions. The flow fields associated with arrays of randomly distributed cylinders are modeled in two dimensions using the ANSYS Fluent Computational Fluid Dynamics software with Reynolds Stress Model turbulence closure. A transient scalar transport model is used to characterize longitudinal and transverse mixing (Dx and Dy) within each geometry. The modeling approach is validated against independent laboratory data, and the dispersion coefficients are shown to be comparable with previous experimental studies. Eight different cylinder diameter configurations (six uniform and two non‐uniform) are considered, each at 20 different solid volume fractions and with seven different transverse positions for the injection location. The new dispersion data cover a broad range of solid volume fractions, for which simultaneous estimates of Dx and Dy have not been available previously. There are no systematic differences in non‐dimensional Dx and Dy between uniform and non‐uniform cylinder diameter distributions. When non‐dimensionalized by cylinder diameter, both dispersion coefficients are independent of solid volume fraction. When non‐dimensionalized by cylinder spacing, both longitudinal and transverse dispersion can be described as linear functions of the ratio of cylinder diameter to cylinder spacing. Key Points: New dispersion data for non‐uniform and uniform cylinder diameter distributions have been generated using a two‐dimensional numerical modelNon‐dimensional dispersion coefficients are unaffected by cylinder diameter distributionBoth longitudinal and transverse dispersion coefficients can be modeled as linear functions of cylinder diameter and cylinder spacing [ABSTRACT FROM AUTHOR]

Mixing in the hyporheic zone plays a key role in controlling the fate and transport of contaminants in streams and rivers. Consistently with recent experimental and numerical results, a physically based one‐dimensional solute transport model is presented that represents hyporheic mixing as a diffusion process exponentially attenuated with depth. When vertical diffusion in the sediment bed is not limited by an impermeable boundary, the moments of the breakthrough curves (BTCs) generated by the model exhibit persistent non‐Fickian behavior and are shown to scale consistently with existing experimental evidence. The ability of the exponentially attenuated mixing model to represent experimental BTCs was tested using data from field and flume tracer experiments, and its performance was compared with that of a classic two‐storage zone model. While both models provided an equally good approximation for the BTCs observed in field tracer tests, the exponentially attenuated mixing model provided better fits for the flume experiments. Analysis of the model equations and their solutions shows that, if the flow cross‐sectional area and wetted perimeter are not predetermined, there are infinite sets of parameter values that produce the same space‐time concentration distributions. The result implies that the physical parameters of hyporheic exchange cannot be determined by sole measurements of the solute BTCs in the surface water unless flow cross‐sectional area and average flow depth can be independently estimated. Key Points: A physically based one‐dimensional solute transport model with vertically attenuated hyporheic mixing is presentedThe behavior of the model breakthrough curves is consistent with experimental evidencePhysical transport parameters cannot be identified solely from surface breakthrough curves unless the cross‐sectional geometry is known [ABSTRACT FROM AUTHOR]

In nature, aquatic vegetation is one of the important factors—along with hydraulic characteristics and geometric configuration—determining the dispersion of scalars. Previous research has studied the effects of vegetation on longitudinal dispersion, varying plant population with uniform arrangement. However, since vegetation grows more often in clumped and heterogeneous rather than uniform patterns, the present work investigates the effects of the vegetation arrangement on the flows characteristics such as longitudinal dispersion, mean velocities, and drag coefficients. Several types of vegetation arrangement are described with the isometric and allometric concept and quantified with the standardized Morisita index. Laboratory experiments were performed to investigate variations of hydraulic parameters and longitudinal dispersion coefficients according to vegetation arrangements, which were quantified with the standardized Morisita index. The hydraulic parameters of mean velocity, turbulent kinetic energy, and drag depend on the vegetation arrangements, and in particular, the longitudinal dispersion coefficient varies with these arrangements by a factor of 4 or more. Key Points: The standardized Morisita index can compare vegetation arrangements quantitatively and varies with dispersion parametersThe longitudinal dispersion gets larger as the patterns of vegetation become more allometric even with the same densityVegetation in 2‐D allometric arrangement generates velocity fluctuations in the lateral direction, increasing of longitudinal dispersion [ABSTRACT FROM AUTHOR]

The one‐dimensional advection dispersion equation (1D ADE) is commonly used in practice to simulate pollutant transport processes for assessment and improvement of water quality conditions in rivers. Various studies have shown that the longitudinal dispersion coefficient used within the 1D ADE is influenced by a range of hydraulic and geomorphological conditions. This study aims to quantify the impact and importance of the parameter uncertainty associated with the longitudinal dispersion coefficient on modeled pollutant time‐concentration profiles and its implications for meeting compliance with water quality regulations. Six regression equations for estimating longitudinal dispersion coefficients are evaluated, and commonly used evaluation criteria were assessed for their suitability. A statistical evaluation of the regression equations based on their original calibration data sets resulted in percent bias (PBIAS) values between −47.01% and 20.78%. For a case study, uncertainty associated with the longitudinal dispersion coefficient was propagated to time‐concentration profiles using 1D ADE and Monte Carlo simulations, and 75% confidence interval bands of the pollutant concentration versus time profiles were derived. For two studied equations, the measured peak concentration values were above the simulated 87.5th percentile, and for the other four equations it was close to the 87.5th percentile. Subsequent uncertainty propagation analysis of four diverse rivers show the potential considerable impact on concentration‐duration‐frequency‐based water quality studies, with 1D ADE modeling producing predictions of quality standard compliance which varied over hundreds of kilometers. Key Points: Uncertainty associated with longitudinal dispersion coefficients is quantified and propagated to time‐concentration profiles using 1D ADEApplication to case study found highly variable and considerable levels of uncertainty, influencing assessment of regulatory complianceStatistical criteria for evaluation of dispersion coefficient equations are less suitable for water quality regulation compliance evaluation [ABSTRACT FROM AUTHOR]

Solute transport in rivers has been traditionally represented using one-dimensional models assuming advection and Fickian dispersion along the main flow direction and transient storage in surface and subsurface dead zones. Experimental evidence from several stream tracer studies has shown that the longitudinal scaling of the moments of the breakthrough curves (BTCs) is inconsistent with classic 1-D solute transport models. In this work, simulations of advection and diffusion in a 2-D and 3-D channel flow over a porous bed are presented assuming an exponentially attenuated profile of the transverse mixing coefficient in the porous medium, as suggested by recent experimental and numerical studies. It is shown that the longitudinal transport in the channel is superdiffusive, and the skewness of the concentration distributions can be almost constant over a broad temporal range, with no sign of approaching zero at large times. A sensitivity analysis shows that, at large times, longitudinal dispersion is controlled by the cross-sectional profile of the in-bed transverse mixing coefficient, and by the difference between the average velocity in the channel and in the porous bed. The normalized concentration distributions can be approximated by beta-distributions with time-dependent parameters, and relationships are derived between the scaling of the parameters under power-law approximation and the scaling of the spatial and temporal moments. The results provide new insights into the physical mechanisms that control the anomalous scaling of the moments observed in field tracer studies and opens new possibilities for predictive and inverse modeling of transport processes in rivers and their catchments. [ABSTRACT FROM AUTHOR]

Dye tracing field data were collected in small, steep streams in Ontario and used to calculate longitudinal dispersion coefficients for these headwater streams. A predictive equation for longitudinal dispersion coefficient is developed using combined data sets from five steeper head - water streams and 24 milder and larger rivers. The predictive equation relates the longitudinal dispersion coefficient to hydraulic and geometric parameters of the stream and has been developed using multiple regression analysis. The newly developed equation shows impressive accuracy of predictions for longitudinal dispersion coefficient ( R2 = 0.86, RMSE = 25, Nash-Sutcliffe coefficient Ens = 0.86 and Index of Agreement D = 0.96) for both small, steep headwater streams as well as large, mild rivers. The Froude number has been introduced as a third key parameter to capture the effect of slope of the reach - in addition to the aspect ratio and bed material surface roughness - on the longitudinal dispersion coefficient. The pronounced improvement in the accuracy of the prediction is due to the addition of the Froude number to capture the effect of the slope of the reach on longitudinal dispersion coefficient. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The longitudinal (DL) and transverse (DT) dispersion coefficients for flow through randomly packed beds of discrete monosized spherical particles are studied. The three-dimensional (3-D) porous-medium model consists of thousands of spherical particles that are divided into cells using Voronoi diagrams. The relationship between the variation of the dual stream function and the vorticity between neighboring particles is derived using Laurent series. The whole flow pattern at low particle Reynolds number is then obtained by minimization of the dissipation rate of energy with respect to the dual stream function. The DL is obtained by fitting the resulting effluent curve to a 1-D solution of a continuous model. The DT is obtained by fitting the numerical concentration profile to an approximate 2-D solution. The derived DL and DT values are in agreement with 3-D experimental data from the literature enabling a study of the effects of pore structure and porosity on DL and DT. © 2013 American Institute of Chemical Engineers AIChE J 60: 749-761, 2014 [ABSTRACT FROM AUTHOR]

Perturbations of temperature or solute concentration in a porous medium spread out by heat or molecular diffusion, respectively. If the pore-filling medium (e.g., water in soil) flows, this causes additional spreading of the perturbation due to the variation of local flow velocities and the tortuous flow lines through pore space. Together, this is termed dispersion, which plays an important role in geothermal energy production, contaminant transport, and reactor beds. Numerous models have been proposed to describe the dispersion coefficient as a function of flow rates, diffusion rates and other parameters, such as pore geometry. These models are either for heat (thermal) or solute dispersion, and often only valid for a limited range of flow rates, typically expressed in terms of the Péclet number. Here we present a single, universal expression for both the heat and solute dispersion coefficient in homogeneous porous media, valid over a wide range of Péclet numbers. Only three parameters have to be determined, which depend mainly on the pore geometry of the material. The expression facilitates the physical understanding of dispersion and may be helpful for the interpretation of numerical microscopic modeling results. It has the practical advantage that the heat dispersion coefficient can easily be calculated from the solute dispersion coefficient (or vice versa) and that dispersion coefficients over a wide range of Péclet numbers can be estimated from measurements over only a limited range. [ABSTRACT FROM AUTHOR]

Stream tracer injection experiments are useful for characterizing hydrological and biogeochemical processes in streams. We used nonconservative synthetic DNA and conservative NaCl in six instantaneous tracer injection experiments in streams in the Benelux. The main aim was to compare the performance of injected synthetic DNA tracer 'T23' with NaCl. In all experiments, the shapes of the T23 and NaCl breakthrough curves (BTCs) were similar. Recovered T23 mass ranged from 2.9 to 52.6%, while recovered NaCl tracer mass ranged from 66.7% to complete mass recovery. In batch experiments, T23 decay was not detected. However, in those batches, we observed an unexplained initial T23 mass loss of 40-97%. In batches with sediment, T23 attachment rate coefficients ranged from close to zero to 0.2 hr−1. Advective and dispersive transport parameters of both NaCl and T23 fitted with STAMMT-L were similar. However, compared to T23, fitted storage zone areas of NaCl were 2-5 times larger, while storage zone exchange coefficients were two times larger. Fitted mass dilution factors of T23 ranged from 1.6 to 34.8. Together, these results pointed toward the disappearance of a part of the T23 mass due to both initial losses and attachment or sorption of T23 mass in those storage zone(s), while decay was not important. Our research demonstrated that artificial DNA can be a valuable tool to determine advective and dispersive transport in brooks, but not to assess solute mass exchange processes related to surface transient storage or hyporheic exchange. [ABSTRACT FROM AUTHOR]

The longitudinal ( D L) and transverse ( D T) dispersion coefficients in two-dimensional (2-D) randomly packed beds of circular particles in a laminar flow regime are derived. A 2-D discrete system of particles is divided into cells using modified Voronoi diagrams. The relationship between the variation of the stream function and the averaged vorticity is obtained from computational fluid dynamics (CFD) simulations. The whole flow pattern is then obtained by using the principle of energy dissipation rate minimization. The obtained values of D L agree well with 3-D experimental data for all velocities investigated. At very high velocities, D T in 2-D appears to be higher than 3-D experimental data. In addition, the effects of particle-size distributions, packing structure, and porosity on the D L and D T were studied. One result was that an increase in the width of the particle-size distribution resulted in higher values of D L and D T at high velocities. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1002-1011, 2013 [ABSTRACT FROM AUTHOR]

Longitudinal dispersion of solute released in an unsteady flow between two coaxial cylinders is studied by employing the method of moments. The flow unsteadiness is caused by the oscillation of the outer cylinder in its own plane around the inner. A finite difference implicit scheme is adopted to solve the Aris integral moment equations arising from the unsteady convective-diffusion equation for all time period. The behaviour of dispersion coefficient due to periodic flow with the variation of radius ratio, absorption parameter and frequency parameter has been examined. Assuming that the distribution of concentration is initially uniform over the cross-section of the annulus, it is shown that, like the case of oscillatory flow caused by periodic pressure gradient, dispersion coefficient can be diminished by increasing absorption at the boundary. The radius ratio of the annular tube is found to have variable effect on the dispersion coefficient depending on the position (inner or outer) of the oscillatory tube. The axial distributions of mean concentration are approximated using Hermite polynomial representation from the first four central moments for a range of different radius ratios, absorption parameters, and frequencies of the wall oscillation. It has been found that the peak of the concentration distribution increases with increase in frequency parameter and radius ratio but opposite trend follows for the absorption parameter. Longitudinal dispersion of solute released in an unsteady flow between two coaxial cylinders is studied by employing the method of moments. The flow unsteadiness is caused by the oscillation of the outer cylinder in its own plane around the inner. A finite difference implicit scheme is adopted to solve the Aris integral moment equations arising from the unsteady convective-diffusion equation for all time period. The behaviour of dispersion coefficient due to periodic flow with the variation of radius ratio, absorption parameter and frequency parameter has been examined. Assuming that the distribution of concentration is initially uniform over the cross-section of the annulus, it is shown that, like the case of oscillatory flow caused by periodic pressure gradient, dispersion coefficient can be diminished by increasing absorption at the boundary. The radius ratio of the annular tube is found to have variable effect on the dispersion coefficient depending on the position (inner or outer) of the oscillatory tube. The axial distributions of mean concentration are approximated using Hermite polynomial representation from the first four central moments for a range of different radius ratios, absorption parameters, and frequencies of the wall oscillation. It has been found that the peak of the concentration distribution increases with increase in frequency parameter and radius ratio but opposite trend follows for the absorption parameter. [ABSTRACT FROM AUTHOR]

The article reports on a research on the longitudinal dispersion coefficient modeling. This paper focuses on the development of a fuzzy model to predict longitudinal dispersion coefficient in natural channels. It is a deviation away from differential and empirical equations. However, these equations are recommended to be used with precautions and reservations. Variables in the proposed model are depth, width, and mean cross-sectional velocity of flow, shear velocity and longitudinal dispersion coefficient.

The shear layer at the top of a submerged canopy generates coherent vortices that control exchange between the canopy and the overflowing water. Unlike free shear layers, the vortices in a canopy shear layer do not grow continuously downstream but reach and maintain a finite scale determined by a balance between shear production and canopy dissipation. This balance defines the length scale of vortex penetration into the canopy, δ e, and the region of rapid exchange between the canopy and overflow. Deeper within the canopy, transport is constrained by smaller turbulence scales. A two-box canopy model is proposed on the basis of the length scale δ e. Using diffusivity and exchange rates defined in previous studies, the model predicts the timescale required to flush the canopy through vertical exchange over a range of canopy density and height. The predicted canopy retention times, which range from minutes to an hour, are consistent with canopy retention inferred from tracer observations in the field and comparable to retention times for some hyporheic regions. The timescale for vertical exchange, along with the in-canopy velocity, determines the minimum canopy length for which vertical exchange dominates water renewal. Shorter canopies renew interior water through longitudinal advection. Finally, canopy water retention influences longitudinal dispersion through a transient storage process. When vertical exchange controls canopy retention, the transient storage dispersion increases with canopy height. When longitudinal advection controls water renewal, dispersion increases with canopy patch length. [ABSTRACT FROM AUTHOR]