Mean Concentration Distribution Research Articles

Unsteady solute dispersion of electro-osmotic flow of micropolar fluid in a rectangular microchannel

This study scrutinizes the two-dimensional concentration distribution for a solute cloud containing a micropolar fluid in a rectangular microchannel under the influence of an applied electric field. The concentration distribution is obtained up to second order approximation using Mei's homogenization method. Analytical formulas are derived for dispersion coefficient, mean and two-dimensional concentration distributions. This study also includes the analytical expressions for electric potential, velocity, and microrotation profiles. This study discusses the impact of coupling number, couple stress parameter, electric double layer thickness, and Péclet number on solute concentration distribution. The results of fluid velocity and dispersion coefficient are validated with available works in the literature. The non-Newtonian parameter and electric double layer thickness are shown to have a significant impact on dispersion. Our study reveals that concentration distribution rises but spreading of solute reduces when the coupling number increases. This is also true when the Debye length decreases. It is also obtained that the solute spreads more in the Newtonian fluid case compared to the micropolar fluid case. Finally, coupling number and electric double layer thickness show a symmetric pattern to the indicator function for the transverse concentration variation rate. The findings of this work have broad implications in deoxyribonucleic acid analysis, chemical mixing, and separation.

Transport of reactive contaminant in a wetland flow with the effects of reversible and irreversible reactions on the bed surface

Wetlands are crucial for maintaining biodiversity in ecosystems. The reversible chemical reactions can significantly affect the pollutant reduction capacity in wetland flow. The spatial transport of contaminants in wetlands is further complicated by phase exchange kinetics due to reversible reactions in the wetland bed. This paper provides an analytical solution for studying the multi-dimensional concentration distribution of solutes in wetland flow, considering both reversible and irreversible boundary reactions. Unlike previous one-dimensional studies (Jiang et al. (2022), Zhan et al. (2024)), our approach offers a comprehensive view of wetland contaminant transport, accounting for complex interactions between different phases and environmental factors. The solute may undergo reversible sorptive phase exchange between the immobile (wetland bed phase) and the mobile phase (fluid phase). Multi-scale homogenization methods are used to determine the dispersion coefficient, mean concentration, longitudinal and vertical real concentration distributions, rate of variation of vertical concentration distribution under the influence of vegetation force, and reversible and irreversible reactions at a stationary wetland bed. The effects of retention parameter (θ), Damkohler number (Da), vegetation effect (α), dispersion time (τ), and first-order irreversible boundary reaction (β′) on solute mixing are thoroughly analyzed. The study's analytical results are validated by numerical results obtained using the finite difference method with a Shishkin mesh, and other comparisons are made with the limiting case of Taylor dispersivity. Results show that an increase in Damkohler number and vegetation force weakens contaminant transport in wetland flow, but an increase in Da enhances contaminant concentration in the mobile phase. The presence of reversible phase exchange kinetics causes non-uniform vertical concentration variation across the wetland cross-section. Critical values where the multi-scale homogenization technique may fail are suggested as θ≤0.5 and Da≥1. The study's findings have potential applications to pollution control in wetlands.

Effect of an inclined magnetic field on dispersion of solute in a pulsatile flow through a channel of absorptive porous walls

The present investigation gives an insight to comprehend the complex mechanism of species transport through porous walls, which has applications for crude oil refining, oil reservoir engineering, and separation of metal from fluids. The paper analyzes the impact of an inclined magnetic field on mass transport phenomena of solute through an unsteady, viscous, incompressible, and electrically conducting fluid flowing between two parallel plates. Both plates are permeable, and the flow is driven by a periodic pressure gradient. At both channel walls, the first order boundary reaction is applied. The governing time depending advection and diffusion equation is solved numerically based on Aris's method of moments. To determine the axial mean concentration distribution of solute, the first four central moments are used in a Hermite polynomial representation. It is significant to note that the dispersion of tracer is more significant for the low frequencies rather than the high frequencies. The behavior of the dispersion process of the tracer is studied for various flow parameters such as the angle of inclination of the magnetic field (α), Hartmann number (M), absorption parameter (β), suction Reynolds number (R), injection Reynolds number (R′), Womersley number (ω), and dispersion time (t) for both purely oscillatory and combined flows. It is significant to note that with the increment of R, α, and M, the amplitude of the dispersion coefficient of the solute reduces. On the other hand, an opposite phenomenon is observed for R′. It is seen that the transport coefficient moves cyclically with a double frequency period for all values of R and R′. Also, it is found that the peak of the mean concentration distribution enhances with the increment of α and M because the flow velocity decreases.

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.

Analyzing the effects of suction and injection Reynolds number on the transport process in a hydromagnetic flow through a channel of reactive porous walls

The present paper analyzes the effects of suction and injection Reynolds number on the dispersion process of solute in an incompressible magneto-hydrodynamics flow through a channel. The walls of the channel are permeable and a first order heterogeneous reaction is applied on it. Also, an inclined magnetic field is employed at both walls of the channel. The unsteady convection-diffusion equation is solved semi-analytically to find out the coefficient of dispersion, skewness and kurtosis of the solute distribution for all time period. Using Hermite polynomial representation, the distribution of mean concentration is obtained. The effects of various parameters such as suction Reynolds number (R), injection Reynolds number (R′), boundary absorption parameter (β), inclination angle of the magnetic field (α), Hartmann number (M) and dispersion time (t) on dispersion process of the solute are examined. It is shown that with the increment of suction Reynolds number, the peak of the mean concentration of solute enhances prominently. But, when injection Reynolds number increases, the amplitude of the mean concentration decreases. The current research gives an insight to understand the complex behavior of transport process of the solute in a hydro-magnetic channel flow with reactive porous walls.

Effect of homogeneous chemical reaction on the dispersion of a solute in a three – dimensional flow of a Newtonian liquid through a porous medium

All-Time dispersion of a reactive solute in a Newtonian fluid flow through a Darcy-Brinkman-Forchheimer Porous medium is carried out using the approach of Gill - Sankarasubramanian (1970) and Doshi et al. (1978). The velocity profile of the non - linear porous medium flow equation is solved using the Maclaurin series of two variables. The three - dimensional model brings into the focus the convective and dispersion coefficients. The chemical reaction is assumed to be homogeneous. The chemical reaction is shown to increase the value of the convective coefficient while it decreases with increase in the value of the reaction rate parameter. The effect of the presence of the porous medium is to decrease the flow and hence the convective coefficient. Similar effect of the porous parameter is seen on the dispersion coefficient. The reaction rate parameter and the porous parameter have opposite effect on the mean concentration distribution.

On scalar transport in an oscillatory Couette–Poiseuille flow under the effects of heterogeneous and bulk chemical reactions: A multi-scale approach

This research presents an analytical solution to explore a two-dimensional concentration transport of solute in an oscillatory Couette–Poiseuille flow between two parallel plates in the presence of homogeneous and heterogeneous reactions. Mei's homogenization method up to second order approximation is used to find the multi-dimensional concentration distributions, namely, transverse concentration distribution, longitudinal concentration distribution, mean concentration distribution, Taylor dispersion coefficient, and the transverse uniformity simultaneously for three different flow conditions: steady, periodic, and the joint effect of steady and periodic Couette–Poiseuille flow for the first time. The distribution of transverse concentration of solute is studied due to its importance in oil lubrication and industrial applications. The transverse variation rate shows that the introduction of heterogeneous reactions cause transverse non-uniformity, but it is significant to note that homogeneous reaction has no effect on it. Furthermore, the maximum variation rate of the concentration cloud is obtained along the upstream and downstream directions when the boundary absorption is considered at steady and moving plates, respectively. To validate the present analytical model, a comparison is performed with the numerical solution and has achieved an excellent agreement. The outcomes of the present study may be helpful to develop a better understanding of the process of contamination and to prevent the pollution in the flow.

Effect of Rayleigh number on transport of solute in a hydromagnetic natural convective flow through a vertical channel with chemical reaction

In the present research, the transport of solute in a hydromagnetic natural convective flow through a vertical channel under the impact of bulk chemical reaction is investigated for the first time using Mei's multi-scale homogenization method. The purpose of this research is to obtain an analytical solution of a physical model for a vertical flow. A uniformly variable axial temperature is considered at both walls. Analytical expressions of Taylor dispersivity, multi-dimensional concentration distributions i.e. horizontal concentration, vertical mean and real concentration distributions are obtained together in the present article. One of the major fact of the present study is to highlight the influence of Rayleigh number (Ra) on mass transfer phenomena in the above mentioned flow. It is observed that both the velocity and Taylor dispersivity reduce due to the increment of the Hartmann and Rayleigh numbers. The Rayleigh number imposes the horizontal uniformity throughout the vertical channel and with the increment of Ra, the variation of horizontal distribution of concentration reduces but it remains tri-modal. It is important to note that, when the Rayleigh number reaches to 275, the non-uniform variation of horizontal concentration distribution becomes bimodal. It is significant to note that a critical value of the Rayleigh number is suggested where the horizontal variation curve becomes bimodal from tri-modal. The outcomes of this study may have a wide range of industrial applications, including metal casting, crystal growth and liquid metal cooling blankets for fusion reactors.

Multi-scale analysis of solute dispersion in non-Newtonian flows in a tube with wall absorption

This study presents the two-dimensional concentration distribution of a solute cloud for non-Newtonian fluid in a tube flow with wall absorption. The non-Newtonian fluid models, such as the Carreau–Yasuda and Carreau fluid models, are helpful in investigating solute dispersion in the bloodstream and have also been effective in understanding hemodynamics. The multi-scale method of homogenization is used here to analyze the dispersion of solute through a straight tube for Carreau–Yasuda and Carreau fluids, which represents the shear-thinning nature. Most of the previous studies are mainly focused on determining the dispersion coefficient and mean concentration distribution for non-Newtonian fluids. Apart from those in our study, we also derived analytical expressions for the two-dimensional concentration distribution for Carreau–Yasuda and Carreau fluids. As the exact peak position of the two-dimensional concentration is a concern in real-life applications rather than that of mean concentration, the effects of wall absorption parameter (α*), the Weissenberg number (We), Yasuda parameter (a), and power-law index (n) on solute concentration distribution are discussed. Comparison between the present results and previous results of solute dispersion for non-Newtonian as well as Newtonian fluids are also enclosed in this study. Results reveal that the mean concentration decreases with increasing values of We because of an increase in the dispersion coefficient. Carreau–Yasuda and Carreau fluids act like Newtonian fluid for very small values of We. At the initial stage, the solute concentration exhibits transverse non-uniformity and then becomes uniform over a larger timescale. The effects of non-Newtonian parameters such as We, a, and n on transverse variation are also studied. It is noted that parameters n, We, and a have no significant impacts on the non-uniformity of the transverse concentration variation on both sides of the tube centroid, but that is not the case for the wall absorption parameter. It is observed that wall absorption results in significant transverse concentration non-uniformity across the tube cross section even after large times.

Transient solute dispersion in electro‐osmotic viscoplastic flow in a microchannel

AbstractThe transport of a neutral solute in incompressible electro‐osmotic flow of Bingham plastic non‐Newtonian liquid flowing through a microchannel is studied theoretically. The flow is driven by a constant axially applied electric field. The non‐dimensional conservation equations with associated boundary conditions are solved with Gill's series expansion technique. The whole transport process is analyzed using three transport coefficients, namely, advection coefficient, dispersion coefficient and the apparent asymmetry coefficient, respectively. The mean concentration distribution of the solute is calculated via a third‐order approximation of the series expansion. The study investigates the collective effects of yield stress and electric double layer (EDL) thickness (inverse Debye length) on the transport of solute. The long‐term behaviour of mean concentration distribution is shown to be accurately predicted by second‐order approximations; however, utilizing third or higher order approximations in Gill's series expansion enables a more refined analysis of the small and moderate time behavior of transport coefficients. The present analysis is relevant to emerging applications in bio‐microfluidics exploiting electroviscous fluent media.

Unsteady solute dispersion in pulsatile Luo and Kuang blood flow (K - L Model) in a tube with wall reactive absorption

Unsteady solute dispersion in pulsatile non-Newtonian flow in a circular tube has been investigated considering higher order moments using the Aris’s method of moments. The Luo and Kuang(1992) (K - L Model) constitutive relation is used for the non-Newtonian fluid. The axial mean concentration of solute is estimated by considering exchange, convective, dispersion coefficients. In addition, considering the 3rd and 4th central moments, the skewness, and kurtosis in the mean concentration is examined. Variations of these five moments against the absorption parameter, K-L fluid parameters, and Womersley frequency parameter are thoroughly investigated. The increase in the Womersley frequency parameter led to the occurrence of a double frequency period for the dispersion coefficient, which influenced the skewness and kurtosis coefficients that led to the deviation from usual normal distribution of the mean concentration distribution at the starting of the dispersion process. The concentration distribution is skewed towards the central region of the tube. The concentration contours also reveal that the solute convection is more in the central region of the tube. The results for Newtonian, Bingham, and Casson fluid models are retrieved as special cases. The mean concentration has the highest peak for the K-L model and the lowest for the Newtonian fluid model. It is scattered axially more for the Bingham fluid than the Casson fluid. This investigation emphasizes that higher moments provide precise information about the solute dispersion in the flow field and its deviation from the normal distribution at small time scales. • This investigation examining the unsteady axial dispersion of a solute in the non-Newtonian pulsatile flow in a cylindrical tube, considering the impact of an irreversible first-order boundary reaction. Solute dispersion in K-L model has been introduced, which gives the shear thinning and thickening behaviour of blood flow even if yield stress is zero. • The present study initiated skewness and kurtosis analysis for steady/ unsteady, non-pulsatile/ pulsatile and Newtonian/ non-Newtonian fluid flow by using method of moments. Here analytical results for all transport coefficient with skewness and kurtosis has been discussed. • The perturbation and numerical solution of coupled and non-linear equation of shear stress and momentum equation has been obtained to get the velocity profile. A new class of computationally explicit Runge–Kutta (CERK) numerical method (Yadav et. al. (2022)) has been used to solve this stiff problem. A detailed comparison of perturbation and numerical solutions is also given in this manuscript. • The solution of the concentration equation is obtained analytically adopting the Aris0 s method of moments, with fourth-order precision. In the presence of boundary reaction, the transport coefficients are affected not only by time but also by the Womersley frequency parameter, other chemical variables, the wall absorption parameter, the yield stress, the amplitude of the fluctuating pressure component, and plasma viscosity. The non-Gaussian distribution of solute is visible for small time after injection. • The mean concentration as well as the two-dimensional concentration distribution are accurately described. The results for the Bingham model, the Casson model, and the Newtonian model are derived directly from this analysis.

Dispersion of fine settling particles in a tidal wetland flow

An investigation on transport of fine sediment particles in a tidal wetland flow is presented in the current research. The model of this work is based on an advection diffusion equation whose solution reveals the water phase based concentration of settling particles. Using the method of moments, a system of moment equations are derived from the governing equation. A finite difference implicit scheme is employed to solve the equations of moment. The behavior of Taylor effective dispersivity due to the variation of settling velocity of fine particles for oscillatory current with or without nonzero mean is predicted. The mean concentration distribution along the longitudinal direction is obtained using the Hermite polynomial and first four central moments. It is shown that for greater settling velocity, the dispersion procedure is inhibited. Some significant effects of vegetation factor, time period, oscillation parameter on environmental dispersivity, skewness and mean concentration profile are shown. The results of the present study are very important to understand the process of sedimentation and wastewater treatment in a tidal wetland flow.

On solute dispersion in an oscillatory magneto-hydrodynamics porous medium flow under the effect of heterogeneous and bulk chemical reaction

It is well known to all of us that there is a shortage of pure drinking water across the globe. Different types of pollutants (metallic and nonmetallic) mix with the water, and they cause several diseases such as cholera, typhoid, and various kinds of skin diseases, and even it is found that these kinds of particles may cause skin cancer. In the current study, an analytical solution of a two-dimensional convection–diffusion equation is obtained using Mei's multi-scale homogenization technique to investigate the influences of homogeneous and heterogeneous reactions on dispersion phenomena of the solute in an oscillatory magneto-hydrodynamics porous medium flow. In the appearance of the applied transverse magnetic field and oscillatory pressure gradient, a mathematical model of magneto-hydrodynamics dispersion between two parallel plates is presented. The analytical expressions of Taylor dispersivity, longitudinal mean and real concentration distributions, transverse concentration distribution, and transverse uniformity rate of the concentration are obtained. Also, the effect of various flow parameters such as Péclet number, Hartmann number, Schmidt number, Darcy number, oscillatory Reynolds number, porous parameter, dispersion time, downstream and upstream locations, chemical heterogeneous boundary reaction, and bulk reaction is discussed. How the transport phenomena of the solute display different natures with the various ranges of Darcy and Hartmann numbers with the aid of homogeneous and heterogeneous boundary reactions are highlighted. To show the effect of the absorption parameters on the transport coefficient, the third-order approximation of concentration is performed. It is seen that the dispersion coefficient (DT1) corresponding to the purely time-dependent flow increases with the enhancement of the Darcy number (Da). Moreover, it is found that as the Hartmann number (M) enhances, the total dispersivity (DT) decreases. Also, the transverse concentration distribution becomes flat for larger values of the Hartmann number. It is noticed that when Da≥1, the transverse variation curve turns into a trimodal distribution from a bimodal. This model may be helpful for separating various metallic and nonmetallic particles from the water to reduce the water pollution.

The effect of solute release position on transient solute dispersion in floating wetlands: An analytical study

Considering the stochastic and complex pollutant emissions in the application of floating wetlands, we investigate the effects of release position on the solute transport in this work. On the basis of the analytical expressions derived from concentration moments, the temporal evolutions of dispersion intensity, the cloud distortion, and the displacement of the cloud centroid at the preasymptotic stage are all analyzed. Owing to the nonhomogeneous flow field, the location of the point source determines the strength of the initial advection, diffusion, and velocity shear acting on a solute cloud, which in turn affects the dispersion process. As a result, the waiting time before the dispersion enters the anomalous regime, the dispersion mechanism, the normality of mean concentration distribution, and the form of spatial concentration distribution are all influenced by the initial condition. The time at which the Taylor dispersion model is capable to depict the mean concentration distribution is t = 0.3 for the line source case and t = 0.5 for point sources released in the outer shear layer, and t = 1 for point sources released in the canopy region and the bottom boundary layer. The point source releases below the internal canopy layer and the line source release cause the initial accumulation of solute in the bottom boundary layer, even for the cases with relatively strong longitudinal dispersion. The depende-

Survey of residential indoor particulate matter measurements 1990-2019.

We surveyed literature on measurements of indoor particulate matter in all size fractions, in residential environments free of solid fuel combustion (other than wood for recreation or space heating). Data from worldwide studies from 1990 to 2019 were assembled into the most comprehensive collection to date. Out of 2752 publications retrieved, 538 articles from 433 research projects met inclusion criteria and reported unique data, from which more than 2000 unique sets of indoor PM measurements were collected. Distributions of mean concentrations were compiled, weighted by study size. Long-term trends, the impact of non-smoking, air cleaners, and the influence of outdoor PM were also evaluated. Similar patterns of indoor PM distributions for North America and Europe could reflect similarities in the indoor environments of these regions. Greater observed variability for all regions of Asia may reflect greater heterogeneity in indoor conditions, but also low numbers of studies for some regions. Indoor PM concentrations of all size fractions were mostly stable over the survey period, with the exception of observed declines in PM2.5 in European and North American studies, and in PM10 in North America. While outdoor concentrations were correlated with indoor concentrations across studies, indoor concentrations had higher variability, illustrating a limitation of using outdoor measurements to approximate indoor PM exposures.

Multi-scale analysis for transport of fine settling particles through an ice-covered channel in a laminar flow condition

The current research deals with the dispersion of fine settling particles in a fluid flowing through an ice-covered channel under the laminar flow condition. An analytical solution of the two-dimensional convection–diffusion equation, based on the multi-scale homogenization technique, is obtained. To validate the current study, analytical results for the dispersion coefficient are compared with the available earlier research work. Moreover, the proposed analytical solutions for mean concentration distributions of the tracers are compared with the numerical results obtained from the finite difference technique. From the industrial and environmental points of view, the vertical concentration distribution provides a very significant information. The downstream evolution of the concentration distribution also is shown for typical time periods at different values of the settling velocity. The approach to the vertical uniformity shows that it is too slow a process in comparison to that of longitudinal normality. It was found that settling velocities of particles disturb the vertical uniformity and the centroid of the solute cloud rises due to the increase in settling velocity. Results illustrate that in the downstream direction, the vertical concentration distribution increases near the bed surface and it decreases in the proximity of the ice-covered surface of the channel with the increase of settling velocity, but the mean concentration of the solute increases. The current study may play an important role to understand the mechanism of the sedimentation process in a closed channel system.

Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption—Deviation from the Gaussianity

Unsteady solute dispersion in a pulsatile Herschel–Bulkley fluid flow in a tube is reinvestigated to examine the significance of the skewness and kurtosis on the concentration distribution using Aris' method of moments considering Hermite polynomials. This study is also an initiation in the direction of solute dispersion in a pulsatile non-Newtonian flow considering the first five moments. This investigation not only brings in the accuracy in the estimation but also measures the deflection and decrease in the axial mean concentration distribution of a solute in a tube. Significant variations in the skewness and kurtosis coefficients against various values of the flow governing parameters, such as the yield stress τy, the wall absorption parameter β, the power law index a, the Womersley frequency parameter α, and the amplitude of fluctuating pressure component e, are presented graphically along with the variations in the mean concentration distribution of the solute in the tube. For larger values of the Womersley frequency parameter, the occurrence of double frequency period for the convection and dispersion coefficients is noticed, which has significant influence on the skewness and kurtosis coefficients. The results for solute dispersion in Newtonian fluid, Bingham fluid, and power law fluid flows are also reported as special cases of this analysis.

Comparison of quantitative elemental depth distribution analyses of Ni and Ti in co-sputtered Ni-Ti alloy thin films using MCs+ and M+ secondary ions

Compositional uniformity in Ni-Ti thin alloy films, both at the surface and in the depth, significantly enhances their performance in various engineering applications. Quantitative depth distributions of Ni and Ti in magnetron co-sputtered Ni-Ti thin alloy films of various composition and thickness, were determined through an effective depth profiling technique. Secondary ion mass spectrometry (SIMS) was utilized to determine the qualitative elemental depth distribution of Ni and Ti in the films using MCs+-SIMS (Cs+ primary ion beam; MCs+ secondary ions, 'M' is the element of interest) and M+-SIMS (O2+ primary ion beam) approaches. The qualitative depth profiles were converted to quantitative depth profiles using the relative sensitivity factor values determined from the elemental concentrations obtained through energy dispersive x-ray spectroscopy analysis of one of the Ni-Ti thin film taken as reference. Thickness of the deposited films determined by x-ray reflectivity was used for depth scale calibration of SIMS raw profile. A comparison of the analytical capabilities of MCs+-SIMS and M+-SIMS approaches for determining the mean concentration and quantitative depth distribution of elements Ni and Ti in deposited Ni-Ti thin films has been presented.

Analyzing the health risk assessment of particles in Isfahan Steel Company by AERMOD model

Introduction: One of the effects of air pollution in the community was increasing mortality rate. Determination of contamination was the first step in improving the existing conditions. Therefore, the way of pollutants distribution and the timing and spatial changes were important. This study aimed to evaluate the risk of Parental Emissions (PE) of Isfahan Steel company using AERMOD. Materials and methods: In this research, the distribution of suspended particles of the Isfahan Steel company were modeled in the AERMOD for 1 h, 24 h and yearly average (30×30 km2), then the comparison of the average concentrations modeled with air standards clean country and Environmental Protection Agency (EPA) regional risk maps were provided in Arc GIS. Results: The prediction of the distribution of 24-h mean concentrations indicated that the maximum value for the 24-h average was equal to 8.52 EPA and 25.25 times, the standard Iran's clean air. Also, the prediction of the distribution of average annual concentrations indicated that the maximum value for the average annual time was 91.1 times, the EPA standard and 4.78% higher than Iran's clean air standard. Conclusion: Health risk maps show that the risk spot was not regional in the direction of the region's wind and topography of the region was the main factor in the distribution of risky spots in the region. Legitimate use of the AERMOD could be useful in managing, controlling, and evaluating air pollutants especially in industrial units of the country.

Solute dispersion in an open channel turbulent flow: Solution by a generalized model

In this work, the classic problem in environmental hydraulics of solute dispersion in an open channel turbulent flow is analytically investigated by Gill’s generalized dispersion model to account for all the basic characteristics as dispersivity, skewness and kurtosis of the mean concentration evolution. A complete solution is presented for the whole process and three typical time-scales are determined: after a convection-dominated initial stage, a transient stage with essential transverse diffusion effect begins at a dimensionless time-scale of t∼0.1 and gives way to an asymptotic stage of normal distribution of mean concentration from t∼1, slowly approaching to a final stage with relative uniformity in transverse concentration distribution at t∼10. Two-dimensional concentration distribution shows that there is a high concentration zone near the free water surface at a small time due to the small velocity gradient, indicating that it is not enough to characterize the dispersion process by the mean concentration, especially for the transient stage. The obtained analytical solutions of concentration distribution consist well with numerical simulation results by the random displacement method (RDM).