Longitudinal Dispersion Coefficient Research Articles

Time-dependent dispersion coefficients for the evolution of displacement fronts in heterogeneous porous media

We present an approach for quantifying displacement fronts in heterogeneous porous media based on the concept of time-dependent apparent dispersion coefficients. The concept of constant asymptotic macrodispersion generally overestimates the area swept by a displacement front and leads to unrealistic upstream dispersion. We show that the large-scale front spreading can be captured by a one-dimensional advection–dispersion equation that is parameterized by a suitably chosen temporally evolving dispersion coefficient. For purely advective front spreading, we derive an analytical expression based on a predictive continuous time random walk approach, which applies to highly heterogeneous porous media. This analysis elucidates the variability of solute travel times as the key longitudinal spreading mechanism. It shows that the evolution of dispersion can be captured as the sum of exponentials that decay on two dominant time scales. In a particle-based picture, these scales mark the short time at which transported particles start exploring the flow variability and the large time at which the slowest particles start decorrelating their transport velocity. Based on these insights, we propose a heuristic formula that accounts for the impact of local-scale dispersion as an additional decorrelation mechanism. The heuristic expression for the longitudinal dispersion coefficient captures solute spreading for a broad range of Péclet numbers and heterogeneity variances. The proposed approach is tested against direct numerical simulations. It provides a robust and fast method for quantifying the evolution of displacement fronts in heterogeneous porous media with possible applications, for example, in groundwater contamination modelling, underground gas storage, and geothermal energy production.

Comparative analysis of tracer studies in the determination of longitudinal dispersion coefficient.

The research presented in this paper is to determine the best tracer studies that will give acceptable estimates of longitudinal dispersion coefficient for Orashi river using rhodamine WT dye and sodium chloride as water tracer. Estimated results obtained for longitudinal dispersion coefficient for the case of rhodamine WT experiment ranges between 71 and 104.4 m2s-1 while that of sodium chloride experiment ranges between 20.1 and 34.71 m2s-1. These results revealed lower dispersion coefficient using sodium chloride as water tracer (WT) indicating that for larger rivers, sodium chloride should not be used as water tracer. The usage of sodium chloride as water tracer in the estimation of longitudinal dispersion coefficient is recommended in smaller streams as NaCl is relatively conservative. The established equations for both cases of investigation are proving satisfactory upon validation as degree of accuracy of 100.0% was obtained using discrepancy ratio (Dr). Standard error (SE), normal mean error (NME) and mean multiplication error (MME) of the developed equations is better when compared with other existing equations. However, Equation (17) is satisfactorily recommended.

Dispersion of artificial tracers in ventilated caves

Artificial CO2 was used as a tracer along ventilated karst conduits to infer airflow and investigate tracer dispersion. In the karst vadose zone, cave ventilation is an efficient mode of transport for heat, gases and aerosols and thus drives the spatial distribution of airborne particles. Modelling this airborne transport requires geometrical and physical parameters of the conduit system, including the cross-sectional areas, the airflow and average air speed, as well as the longitudinal dispersion coefficient which describes the spreading of a solute. Four gauging tests were carried out in one mine (artificial conduit) and two ventilated caves (natural conduits). In this paper, we demonstrate that it is possible to gain reliable airflow rates and geometric information of ventilated karst conduits using CO2 as a tracer. Airflow was gauged along two caves and one mine and compared with punctual measurements made with a hot-wire anemometer. Cross-sectional areas estimated with CO2 tests were compared with those measured in situ. Moreover, breakthrough curve (BTC) analysis displayed an accentuated tailing along the investigated natural conduits due to the presence of dispersive singularities which possibly enable aerosol deposition. The long tailing observed in Milandre and Longeaigue Caves is probably due to cross-section variations. A 1-D advection-dispersion model tested for these sites was unable to fit BTC tailing in natural conduits. In Baulmes artificial conduit, where long tailing is not observed, the dispersion coefficient has been estimated using Chatwin’s method, and compared with the prediction of Taylor’s theory. Despite the regular geometry of Baulmes Mine, Taylor’s correlation significantly underestimates the dispersion coefficient deduced from field data, showing the need for more theoretical work on turbulent dispersion in mines. This paper gives a first insight into air motion and matter dispersion along ventilated karst conduits, preparing for proper aerosol dispersion modelling.

Characterizing suspended particle dispersion in wetland flows: Impact of settling velocity and vegetation factor

Predicting the dispersion process of suspended particles with settling velocity in wetland flows holds significant implications for various ecological and environmental applications. This study analytically investigates the dispersion process of fine settling particles in wetland flows due to an instantaneous release source through the asymptotic expansion method. The effect of high-order terms is incorporated. The impact of vegetation factor and settling velocity on characteristic coefficients (including mass retained in the flow, advection velocity, longitudinal dispersion coefficient, skewness, and kurtosis), vertical mean, and two-dimensional concentration distribution are analyzed. Analytical solution is validated by numerical result through random displacement method. Results demonstrate that the vegetation factor does not influence the vertical mass distribution, and a larger settling velocity results in a higher concentration of mass in the bed wall layer. The longitudinal dispersion coefficient does not exhibit a monotonic relationship with the settling velocity. The position of mass centroid of the vertical mean concentration is biased more to the upstream with the larger settling velocity. At larger times, the vertical mean concentration approximates a normal distribution, with skewness and kurtosis nearing zero. Under the influence of settling velocity, the bed wall layer exhibits a high concentration zone in the two-dimensional concentration distribution. These results can help the understanding of sediment dynamics, nutrient cycling, pollutant transport associated with the wetland flows.

Improvement of the Two-Dimensional Routing Procedure for Observing Dispersion Coefficients in Open-Channel Flow

The dispersion coefficients are crucial in understanding the spreading of pollutant clouds in river flows, particularly in the context of the depth-averaged two-dimensional (2D) advection–dispersion equation (ADE). Traditionally, the 2D stream-tube routing procedure (2D STRP) has been the predominant method for determining both the longitudinal and transverse dispersion coefficients of the 2D ADE under transient concentration conditions. This study aims to quantitatively analyze and address the limitations of the 2D STRP using hypothetically generated data. The findings of these evaluations revealed that the existing 2D STRP failed to accurately reproduce reliable results when the tracer clouds reached wall boundaries. This limitation prompted the development of the 2D STRP-i, which effectively resolves this drawback. The newly developed routing-based observation method, 2D STRP-i, enables the reliable estimation of dispersion coefficients, considering the effect of the wall boundary. The results indicated that the existing 2D STRP yielded 2D dispersion coefficients with relative errors ranging from 40% to 200%, while 2D STRP-i consistently yielded relative errors of 3% to 5% on average. When applied to tracer test data obtained through remote sensing, the 2D STRP-i demonstrated its ability to accurately observe temporal concentration distributions, even when wall boundaries have a significant impact on contaminant transport.

Particle dispersion through porous media with heterogeneous attractions.

Porous media used in many practical applications contain natural spatial variations in composition and surface charge that lead to heterogeneous physicochemical attractions between the media and transported particles. We performed Stokesian dynamics (SD) simulations to examine the effects of heterogeneous attractions on quiescent diffusion and hydrodynamic dispersion of particles within geometrically ordered arrays of nanoposts. We find that transport under quiescent conditions occurs by two mechanisms, diffusion through the void space and intermittent hopping between the attractive wells of different nanoposts. As the attraction heterogeneity increases, the latter mechanism becomes dominant, resulting in an increase in the particle trajectory tortuosity, deviations from Gaussian behavior in the particle displacement distributions, and a decrease in the long-time particle diffusivity. Similarly, under flow conditions corresponding to low Péclet number (Pe), increased attraction heterogeneity leads to transient localization near the nanoposts, resulting in a broadening of the particle distribution and enhanced longitudinal dispersion in the direction of flow. At high Pe where advection strongly dominates, however, the longitudinal dispersion coefficient is insensitive to attraction heterogeneity and exhibits Taylor-Aris dispersion behavior. Our findings provide insight into how heterogeneous interactions may influence particle transport in complex 3-D porous media.

Bimolecular reactive transport in a filled single fracture-matrix system considering the nonequilibrium sorption

Comprehending the transport mechanism of bimolecular reactive solutes in fracture-matrix systems is crucial for improving the efficiency of collaborative remediation using hydraulic fracturing and in-situ chemical oxidation in low-permeability contaminated sites. Previous studies have neglected the effects of physical nonequilibrium (PNE) caused by sedimentation and chemical nonequilibrium (SNE) caused by rete-limited sorption. In this study, a two-dimensional numerical model that considers mobile-immobile mass transfer in the fracture and two-site nonequilibrium sorption in both fracture and matrix is established to investigate the behavior of bimolecular reactive solutes in a filled fracture-matrix system. The results indicate that the PNE and SNE lead to two-stage characteristics and severe tailing effects in contaminant remediation. High tailing occurs when the equilibrium sorption fraction and fracture-mobile/fracture-immobile porosity ratio are relatively small and the longitudinal hydrodynamic dispersion coefficient is relatively large, requiring consideration of multi-nonequilibrium processes. Additionally, the solute concentration in the matrix is most sensitive to the matrix porosity (θk), less sensitive to fracture aperture (2b), and reagent bulk diffusivity (DOA). The remediation area (Sr) in the matrix has an exponential relationship with θk and a linear relationship with 2b and DOA. The quantitative relationship between Sr and key parameters facilitates the prediction of remediation effectiveness.

An improved equation development for longitudinal dispersion coefficient.

The model developed in this paper is an improved equation for the longitudinal dispersion coefficient, which is an important parameter used to monitor and check the assimilatory capacity of rivers. This research incorporates total suspended solids (Ss) and total dissolved solids (Ds) to other selected functional parameters in order to investigate the contributions of Ss and Ds on the longitudinal dispersion coefficient. The results obtained from research indicates that the presence of Ss and Ds affects longitudinal dispersion coefficient as it reduces the magnitude of Dl values. The measured values of longitudinal dispersion coefficient estimated in this study vary between 71 and 104.4 m2 s-1. The percentage of Dr values estimated to be within 0.0 and 0.3 were 50.0% and within -0.3 and 0.0 were 50% for the developed equation and this indicates a degree of accuracy of 100.0%. While for Seo and Cheong, the percentage of Dr values determined to be within 0.0 and 0.3 were 63.3% and within -0.3 and 0.0 were 30% and gives a degree of accuracy of 93.3% and others are poor. SE, NME and MME results show a high accuracy for the derived equation revealing the adequacy of the derived equation in the estimation of D.

Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method

This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.

Performance of equations for the longitudinal dispersion coefficient: a case study in the Orashi River

Abstract Investigation of the water quality of rivers is a key point in Water Resources Engineering. The longitudinal dispersion coefficient is one of the foremost significant parameters in river water quality monitoring. Several parameters such as hydraulic, morphology, total dissolved solids, and total suspended solids are effective parameters in the determination of the longitudinal dispersion coefficient as revealed by this study. The assessment of the river shows mean hydraulic and geometric properties such as flow, depth, velocity, longitudinal slope, and width to be 354.17 m3/s, 9.61 m, 0.69 m/s, 0.0079,101.63 m and the range of the longitudinal dispersion coefficient as (72–104.4) m2/s. Results obtained by employing the established equations revealed standard error indices and RMSE of the developed equation, and Kashefipour and Falconer equation gives correlation coefficient of about 0.819 and 4.182 and 0.421 and 12.186, respectively, as coefficient of determination and RMSE, and they are more accurate among the empirical equations. However, the newly derived equation for the longitudinal dispersion coefficient performed better when compared with others, indicating the fitness of the developed equation to estimate longitudinal dispersion coefficient.

Sub-volume analysis of pore-network simulations: Determining the asymptotic longitudinal dispersion coefficient

This work introduces a new method called sub-volume analysis (SVA) to calculate macroscopic model parameters with their uncertainties from pore-scale simulations. We apply the SVA to calculate the longitudinal dispersion coefficient of the advection–dispersion model (ADM) from continuous tracer injection problems simulated with pore-network models. The SVA application presented here allows for verifying if a given network has enough length to reach an asymptotic dispersion regime where ADM applies. We tested the method using statistically constructed pore networks and pore networks built by joining several network units extracted from Berea sandstone images. There is complete agreement within the error margins for the asymptotic longitudinal dispersion coefficients obtained with the SVA and those obtained from breakthrough curve fitting. We also showed that the SVA gives more accurate results than those from the breakthrough curve fitting and much more accurate results than those from the method of spatial moments. Unlike the other methods, the SVA estimates the parameter uncertainty using a single pore-network realization.

Longitudinal Mixing in Flows with Submerged Rigid Aquatic Canopies

The presence of dense submerged vegetation alters mixing characteristics in open channel flows as they cause differential velocities inside and above canopies. The prediction models for longitudinal mixing in the presence of submerged canopies often use the drag coefficient to represent the canopy, which limits the usability of the models when the canopy properties are not fully understood. Here, attempts were made to present a methodology which can be used for deriving the coefficient of longitudinal dispersion in the presence of submerged vegetation based on velocity measurements, using a mixing length approach to model turbulence. An experimental study was conducted in a large-scale laboratory facility to investigate the longitudinal dispersion characteristics in open channel flow with submerged aquatic vegetation canopies. Detailed velocity and solute tracer measurements were undertaken for a representative range of flow velocities. The velocity measurements were used for deriving turbulent shear stress, mixing length, and diffusivity using established theoretical and empirical relationships to derive the longitudinal dispersion. The longitudinal dispersion measured in two locations in the water column for the two canopy submergences was discussed based on the amount of vertical mixing and differential advection. The canopy with a smaller stem length (i.e., higher submergence ratio) has a higher vertical diffusivity, resulting in increased vertical mixing in the water column. The canopy with the higher stem length (i.e., lower submergence ratio) consists of minimal vertical diffusivity, causing the longitudinal dispersion measured above the canopy to be significantly high, even though the longitudinal dispersion measured inside the canopy is much lower. The mathematical model which was adapted for calculating the coefficient of longitudinal dispersion and the tracer results show good agreement, indicating that the N-zone model can accurately predict the longitudinal dispersion in submerged aquatic canopies when used with the presented methodology.

Simplified dispersion analysis based on dye tests at a small stream

Abstract The modelling of solid transport in open channels requires good knowledge about parameters related to basic processes such as hydrodynamic dispersion, advection and decay rates. Such parameters are usually determined by dye tests. Numerous tracer studies have been performed on laboratory flumes and natural rivers. However, on-site sampling is often difficult, expensive and needs special apparatus. The main aim of the study was to justify simplified method based on the monitoring of the dye cloud shape in order to determine both longitudinal and transversal dispersion coefficients. In this study, four dye tests were carried out on a small local stream (the Lipkovsky) using Rhodamine WT fluorescein dye as a tracer. The tests were carried out in such a manner that both longitudinal and horizontal transversal dispersion data were obtained. For this purpose, the visually determined extent of the dye cloud was interpreted via the analytical solution of the advection-dispersion equation. The results obtained by this simplified approach indicated that the longitudinal dispersion coefficient Dx = 0.051–0.057 m2/s and the coefficient of horizontal transversal dispersion Dy = 0.00024–0.00027 m2/s. The method was justified by corresponding root mean square error (RMSE) counting RMSE = 0.65–1.02 m for the dye cloud centre, RMSE = 1.87–2.46 m for the head and tail of the cloud and RMSE = 0.025–0.11 m for the cloud width, the Nash-Sutcliffe efficiency coefficients ranged from 0.9 to 0.998. The comparison of these values with empirical formulae and other tracer studies indicated significant overestimation of the mentioned values of Dx , which can be attributed to the uniform velocity distribution along the width of Lipkovsky Stream. Much better agreement was achieved for Dy .

Modeling Microplastic and Solute Transport in Vegetated Flows

AbstractPhysical 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.

Application of genetic programming in presenting novel equations for longitudinal dispersion coefficient in natural streams considering rivers geometry - Implementation in assimilation capacity simulation

Precise estimation of the longitudinal dispersion coefficient (LDC) is crucial for the accurate simulation of water quality management tools such as assimilation capacity. Previous research analyzed the LDC of natural streams in two general categories: ignoring or considering the river sinuosity (σ). Genetic programming (GP) is used in this study to investigate both mentioned categories by applying two experimental datasets from 56 to 24 different rivers worldwide. The first proposed LDC equation of this research (without σ) improves the amounts of statistical measures R2 (Determination Coefficient), OI (Overall Index), NSE (Nash-Sutcliffe Efficiency), WI (Willmott's Index of Agreement), RMSE (Root Mean Square Error), and MAE (Mean Absolute Error) by 3.75%, 4.71%, 7.81%, 0.85%, 13.72%, and 0.68%, respectively, compared to the best values of these indicators in the previous investigations. Regarding the second category, relative and absolute sensitivity analyses are conducted, which reveal that σ is the most influential parameter in the accurate prediction of the LDC among all hydraulics and geometric parameters of the river. This part of the investigation presents four unique LDC equations that closely match the experimental results. Significant improvement of the most accurate presented LDC for statistical indices R2, OI, NSE, WI, RMSE, MAE, and accuracy percentage are obtained equal to 3.27%, 2.41%, 3.16%, 0.81%, 35.1%, 24.47%, 3.8%, respectively, in comparison with the best previous relations. Also, a new indicator for measuring the efficiency of mathematical equations called Mean Normalized Statistical Index (MNSI) is introduced and applied in different parts of this research. Finally, the assimilation capacity of the Kashafrud River is determined based on the analytical method of pollution propagation for three types of water demands utilizing the accurately presented LDC in 1993–2020. The average amount of river assimilation capacity using accurate LDC is simulated at 91.93 tons/day, much lower than the currently reported pollution entrance, which equals 540 tons/day.

Study of gas hazard pattern in underground workings after blasting

Determining the sources of hazardous and toxic substances released into mine air, their gas composition, as well as providing each such source of pollution with the required amount of fresh air are important issues in terms of ensuring normal healthy and safe working conditions for miners. This paper studies blasting as one of the most dangerous sources of mine air pollution. The study was carried out for a long dead-end exploration working, and a development (preparatory) working of a copper-nickel mine. In accordance with the federal rules and regulations (FNiP), a number of requirements, including monitoring of gas hazard at a face, is applied to blasting operations.The study examined the behavior of gas-air mixture in dead-end mine workings after blasting. The findings are based on the experimental data obtained in the conditions of two dead-end workings at an operating coppernickel mine. A technique for the experimental studies of gas release after blasting in a dead-end working was developed. The main technical characteristics of the instruments involved in the in-situ measurements are given. Time dependences of the concentrations of toxic gases after blasting at the blasted working mouth, at the return ventilation current, and near a booster were established. In order to assess the reliability of the data obtained, the volume of released carbon oxides was calculated based on the data of gas analyzers and chemical reactions of explosives decomposition during detonation, depending on the types and weights of the explosives. A model of gas-air mixture transfer was described, constructed, and calibrated allowing for longitudinal dispersion. The Voronin model was used to simulate the gradual removal of toxic gases from the working face and solving the problem of boundary conditions. Based on experimental data, the coefficients of longitudinal dispersion, ventilation efficiency, and volume concentration of the considered gas admixture in the mixing zone at initial time were determined for a long dead-end mine working.The constructed gas-dynamic model and longitudinal dispersion coefficients obtained as a result of the analysis enabled the time required for long dead-end mine workings ventilation to be analysed and estimated. Based on the model, the algorithm for calculating the velocity of spreading the combustion products in a mine ventilation network in emergency situations is being improved. The value of longitudinal dispersion coefficient for different operating conditions is also being refined.Based on the gas distribution simulation within the interval of 1,500 m from a working face, the time required for the ventilation of a dead-end mine working was determined.

Solute cloud evolution in channels with suspended vegetation of different configurations

Suspended vegetation's ability to handle solute accumulation in natural waters through their roots has sparked significant interest and research in using them to improve water quality. This research semi-analytically investigates the unsteady solute cloud evolution in channels with suspended vegetation after the point source release on the water surface, by solving the solute transport model with spatially variable flow field coefficients. Results show that regardless of gap ratio (the ratio of the height of the gap region to the water depth) and vegetation density, the solute cloud evolution in the preasymptotic stage (the dimensionless time ⟨Dz*⟩t*/h*2<1, where ⟨Dz*⟩ is the depth-averaged vertical turbulent diffusion coefficient. t* is the time, and h* is water depth.) can be featured by: the cloud centroid shifts upstream; the longitudinal dispersion coefficient increases; the solute cloud is positively skewed; and the solute accumulates in the vegetation layer on the upstream side and the bottom boundary layer on the downstream side. At around ⟨Dz*⟩t*/h*2∼1, the cloud centroid position and the longitudinal dispersion coefficient approach their asymptotic values, and the solute cloud is basically considered to follow the normal distribution longitudinally. In terms of the influences of configurations on the solute cloud during the whole dispersion process, the cloud centroid moves faster and reaches a farther asymptotic location due to a more serious blockage effect for a smaller gap ratio or larger vegetation density. In addition, a small gap ratio enhances the skewness and kurtosis of the cloud, while the vegetation density has little effect on them. Benefiting from the combined action of the violent velocity shear and the strong shear-scale diffusion which dominates the vertical mixing, the smallest gap ratio or highest vegetation density promotes the vertical mixing and yields the largest asymptotic longitudinal dispersion coefficient. Consequently, the vertical concentration distribution is the most uniform and the longitudinal concentration distribution is the flattest in these two cases.

Measurement of the travel time in the upper Yellow River in 2015

The solute travel time in steady and gradually varied flow in rivers is necessary for waste transport studies, in particular, to evaluate the behavior of accidentally spilled soluble substances in streams. This study conducted two dye tests on the Donghe reach within Baotou in the upper Yellow River to measure the travel times in October 2015. It reconstructed the leading and trailing edge missed data by extension from time-concentration curves developed by fitting a three-parameter log-normal (3PLN) equation to the discretely observed data. It also calculated the travel times, dispersion rates, and longitudinal dispersion coefficients. The results show that the calculated travel rates of the centroid are less than the velocities at the Baotou hydrometric station. The calculated longitudinal dispersion rates ranged from about 0.22 meters per second to 0.68 meters per second. Using the nonlinear best fit method, a dispersion model for an instantaneous injection of tracer gave the longitudinal dispersion coefficients ranging from about 76 square meters per second to about 304 square meters per second. However, the ones generated by some commonly used empirical equations are at least 2.6 times them. Tracing tests are essential to obtain helpful information for pollutant transport studies.

A numerical investigation to determine longitudinal dispersion coefficient in ideal and randomized reticulated porous structures using transient direct pore level simulation

The purpose of this numerical investigation is to characterize the longitudinal dispersion coefficients in open-cell reticulated porous structures. Open-cell foams are modelled using idealized Kelvin cell structures. Using the conventional Navier–Stokes equation, airflow has been calculated through various porous structures. Along with the flow, the dispersion of a tracer fluid is traced across the structures and analyzed in terms of the effective dispersion coefficient. Using direct pore level simulations (DPLS), a parametric study is performed to understand the influence of geometrical parameters on the dispersion in porous media. To evaluate the longitudinal dispersion coefficient (LDC), the analytic solution gradients were fitted into the simulated gradients. From the results, a new characteristic length correlation is proposed to calculate the Peclet number, and it is compared with experimental and numerical data that are available in the literature.

Numerical modeling of dispersion of swimming bacteria in a Poiseuille flow

Bacteria have long been assumed to behave as a passive colloid. In this paper, we show that the alignment of bacteria in the flow modifies their dispersion dynamics. We determine here the resulting relation between the macroscopic longitudinal dispersion coefficient and the P\'eclet number.