Longitudinal dispersive coefficient in channels with aquatic vegetation:A review

The determination of longitudinal dispersion coefficient in rivers is necessary for pollution control,environmental risk assessment,and management.In rivers with aquatic vegetation,the flow field is remarkably modified by canopies,which affects velocity profiles and dispersion characteristics dominated by the heterogeneity of the velocity field.The dispersion is deduced from lateral and vertical longitudinal velocity gradients for compound channels with vegetated floodplains and rectangular channels with river-wide vegetation,respectively.Although many efforts have been exerted to clarify the dispersion process in different conditions and predict the diffusion of contaminants in vegetated rivers,no studies have introduced it systematically.This study reviews the dispersion coefficient characteristics,including magnitude,main impacted factors,and relationships with flow and vegetation features,in channels with aquatic canopies considering the variation of impact factors changing with the different vegetation and river morphology scenarios.Several typical methodologies for determining longitudinal dispersion coefficients are also summarized to understand the dispersion processes and concepts.Apart from the pioneer outcomes of previous studies,the review also emphasizes the deficiency of existing studies and suggests possible future directions for improving the theory of dispersion in vegetated channels.

Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.

Influence of Waveguide Properties on Wave Prototypes Likely to Accompany the Dynamics of Four-Wave Mixing in Optical Fibers

In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest.

Horizontal gas mixing in rectangular fluidized bed:A novel method for gas dispersion coefficients in various conditions and distributor designs

In a rectangular fluidized bed combustor, the tracer gas is injected continuously into the bed from a point source at the center of the distributor plate. In this study, a general governing equation is formulated for tracer gas dispersion in the bed. An analytical solution is derived to estimate the dispersion coefficients, Dxand Dy, in a horizontal plane. The concentration profiles at different sampling heights with various gas velocities are plotted.Subsequently, to estimate the dispersion coefficients, surface fitting of the obtained analytical solution to the experimental data is performed. The dispersion coefficients obtained from this model are compared with those of a conventional model. Additionally, the effect of walls, bed height and gas injection rate on the dispersion coefficients in a horizontal plane is investigated, and the effect of distributor design on the dispersion coefficients in a horizontal plane is investigated with different tracer positions. It is found that Dxand Dyare nearly equivalent at a lower tracer gas ratio of the injected gas to the total gas flow rate. It is also demonstrated that the effect of bed height on Dxis minor. This model is also able to estimate the dispersion coefficients in the case of a multihorizontal nozzle distributor.

Use of axial dispersion model for determination of Sherwood number and mass transfer coefficients in a perforated rotating disc contactor

The mass transfer process in a perforated rotating disk contactor(PRDC) using a toluene-acetone-water system was investigated.The volumetric overall mass transfer coefficients are calculated in a PRDC column.Both mass transfer directions are considered in experiments.The influences of operating variables containing agitation rate,dispersed and continuous phase flow rates and mass transfer in the extraction column are studied.According to obtained results,mass transfer is significantly dependent on agitation rate,while the dispersed and continuous phase flow rates have a minor effect on mass transfer in the extraction column.Furthermore,a novel empirical correlation is developed for prediction of overall continuous phase Sherwood number based on dispersed phase holdup,Reynolds number and mass transfer direction.There has been great agreement between experimental data and predicted values using a proposed correlation for all operating conditions.

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.

Experimental Study on Dispersion Coefficient of Dredger Fill in Reclamation Region

In order to satisfy the demand of land use, reclamation engineering has been undertaken in coastal cities for a long time. To study the contaminant transport in the reclamation districts, robust and accurate estimation of dispersion coefficient is essential. In this study, the continuous sodium chloride （NaC1） solution with constant concentration was introduced into the column filled with the dredger fill to get the breakthrough curves （BTCs）. Inverse error function method （IEFM） and CXTFIT program were used for estimating dispersion coefficient. Results showed that the difference between the dispersion coefficients estimated by IEFM and CXTFIT program was slight. The main reason was that the BTC was not strictly linear. IEFM performed poorly in the nonlinear area, while the CXTFIT performed well over the entire BTCs. Moreover, the dispersion coefficient of dredger fill was small. The dispersion property of dredger fill would result in the slow migration of contaminants in the dredger fill.

Diffusion tensor imaging reveals brain structure changes in dogs after spinal cord injury

Based on the Wallerian degeneration in the spinal cord pathways,the changes in synaptic connections,and the spinal cord-related cellular responses that alter the cellular structure of the brain,we presumed that brain diffusion tensor imaging(DTI)parameters may change after spinal cord injury.However,the dynamic changes in DTI parameters remain unclear.We established a Beagle dog model of T10 spinal cord contusion and performed DTI of the injured spinal cord.We found dynamic changes in DTI parameters in the cerebral peduncle,posterior limb of the internal capsule,pre-and postcentral gyri of the brain within 12 weeks after spinal cord injury.We then performed immunohistochemistry to detect the expression of neurofilament heavy polypeptide(axonal marker),glial fibrillary acidic protein(glial cell marker),and NeuN(neuronal marker).We found that these pathological changes were consistent with DTI parameter changes.These findings suggest that DTI can display brain structure changes after spinal cord injury.

Solute transport characteristics of a deep soil profile in the Loess Plateau,China

Understanding solute transport behaviors of deep soil profile in the Loess Plateau is helpful for ecological construction and agricultural production improvement. In this study, solute transport processes of a deep soil profile were measured by a conservative tracer experiment using 25 undisturbed soil cores （20 cm long and 7 cm diameter for each） continuously sampled from the surface downward to the depth of 500 cm in the Loess Plateau of China. The solute transport breakthrough curves （BTCs） were analyzed in terms of the convection-dispersion equation （CDE） and the mobile-immobile model （MIM）. Average pore-water velocity and dispersion coefficient （or effective dispersion coefficient） were calculated using the CDE and MIM. Basic soil properties and water infiltration parameters were also determined to explore their influence on the solute transport parameters. Both pore-water velocity and dispersion coefficient （or effective dispersion coefficient） generally decreased with increasing depth, and the dispersivity fluctuated along the soil profile. There was a good linear correlation between log-transformed pore-water velocity and dispersion coefficient, with a slope of about 1.0 and an average dispersivity of 0.25 for the entire soil profile. Generally speaking, the soil was more homogeneous along the soil profile. Our results also show that hydrodynamic dispersion is the dominant mechanism of solute transport of loess soils in the study area.

Assessment of Fiber Distribution in Steel Fiber Mortar Using Image Analysis

A new test method was introduced to measure fiber distribution in steel fiber reinforced mortar by using image analysis technique. Through specimen preparation, image acquisition, fiber extraction, and measurement of related fiber parameters, quantitative analysis of fiber distribution could be obtained by two parameters, namely dispersion coefficient and orientation factor. Effect of boundaries, size and steel fiber content on fiber distribution was discussed. Results showed that, steel fiber distribution was affected by boundary effect, which would be weakened with the increase of specimen size. If the length and width remained constant, the specimen height had a significant effect on orientation factor of fiber, while its influence on dispersion coefficient was not so obvious. With the increase of steel fiber content, dispersion coefficient decreased slightly, and orientation factor deviated from 0.5.

Inversion of dispersion coeffcient in water quality model using optimal perturbation algorithm

As a primary parameter in the water quality model for shallow bays, the dispersion coefficient is traditionally determined with a trial-and-error method, which is time-consuming and requires much experience. In this paper, based on the measured data of chemical oxygen demand （COD）, the dispersion coefficient is calculated using an inversion method. In the process, the regularization method is applied to treat the ill-posedness, and an operator identity perturbation method is used to obtain the solu- tion. Using the model with an inverted dispersion coefficient, the distributions of COD, inorganic nitrogen （IN）, and inorganic phosphorus （IP） in Bohai Bay are predicted and compared with the measured data. The results indicate that the method is feasible and the inverted dispersion coefficient can be used to predict other pollutant distribution. This method may also be further extended to the inversion of other parameters in the water quality model.

Impact of Soil Water Flux on Vadose Zone Solute Transport Parameters

The transport processes of solutes in two soil columns filled with undisturbed soil material collected from an unsaturated sandy aquifer formation in Belgium subjected to a variable upper boundary condition were identified from breakthrough curves measured by means of time domain reflectometry (TDR). Solute breakthrough was measured with 3 TDR probes inserted into each soil column at three different depths at a 10 minutes time interval. In addition, soil water content and pressure head were measured at 3 different depths. Analytical solute transport models were used to estimate the solute dispersion coefficient and average pore-water velocity from the observed breakthrough curves. The results showed that the analytical solutions were suitable in fitting the observed solute transport. The dispersion coefficient was found to be a function of the soil depth and average pore-water velocity, imposed by the soil water flux. The mobile moisture content on the other hand was not correlated with the average pore-water velocity and the dispersion coefficient.

Lateral Solids Mixing in the Dense Zone of a Circulating Fluidized Bed

Lateral solid mixing was investigated experimentally in the dense zone of a 900mm×100mm×5.2m rectangular circulating fluidized bed riser.Using heated tracer injection,the lateral solid dispersion was determined by measuring the temperature response at different lateral positions. Furthermore, a one-dimensional dispersion model,which describes the solid mixing in the dense zone,is presented.The experimental results were used to determine the lateral particle dispersion coefficient under various operating conditions. A correlation of dispersion coefficient with bed height, gas velocity,and particle size is also proposed.

On controlled propagation of nonautonomous dispersive coupled Whitham-Broer-Kaup equation in shallow water

In this paper,the dispersive coupled Whitham-Broer-Kaup(DCWBK)equation with time-dependent coefficients describing the propagation of the shallow water waves are obtained.The propagation of solitons and elliptic(or chirped)waves can be manipulated by suitable variations of the dispersion coefficient.Here,controllable transmission of the surface waves for soliton similariton pairs with the snoidal backgrounds is considered.It is found that,when the dispersion coefficient is taken as increasing,the velocity is increasing with the dispersion coefficient increasing.While this holds vice versa for the height of propagation wave.

Determination and impact factor analysis of hydrodynamic dispersion coefficient within a gravel layer using an electrolyte tracer method

Hydrodynamic dispersion is a measure for describing the process of solute transport in porous media.Characterizing the dispersion of water flow within gravel is essential for the prediction of solute transport especially nonpoint source pollutants migration in alpine watersheds where the land surface is typically covered with gravel.In this study,an integrated model and experimental method using an electrolyte tracer is proposed for determination of the hydrodynamic dispersion coefficient.Two experimental scenarios were designed to measure electrolyte tracer transport processes in both free water flow and gravel layer flow under different slope gradients and transport distances.Subsequently,the measured data were used to simultaneously calculate both the hydrodynamic dispersion coefficient and flow velocity by fitting the experimental data with the mathematical model.Dispersivity,as a critical feature of hydrodynamic dispersion,was determined as well under the two specified scenarios.Finally,the impact mechanisms of the gravel layer and factors related to the dispersion processes were comprehensively analyzed.The results indicate that the presence of a gravel layer significantly reduces flow velocity and the hydrodynamic dispersion coefficient,but increases solute dispersivity.For the flow within gravel layers,with much lower velocity,the positive effect of the gravel layer on dispersivity may be neutralized or even surpassed by the negative effect of flow velocity.The results should be helpful in characterizing the dispersion processes of water flow within gravel layer and hence in predicting solute transport,especially in nonpoint source pollutants migration in alpine watersheds where the land surface is richly covered with gravel.

Effects of first-order chemical reactions on the dispersion coefficient associated with laminar flow through the lungs

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da （the Damkohler number）, a （phase partitioning number） and F （dimensionless absorption number） on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number （say Da 〉 10） and a small but nonzero value of absorption rate （say P 〈0.5）.

High-Order Dispersion Coefficients for Alkali-metal Atoms

High-order dispersion coefficients C9, C11, C12, and C13 for the ground-state alkali-metals were calculated by combining the 1-dependent model potential of alkali-metal atoms and linear variation method based on B-spline basis functions. The results were compared.

Study and verification on dispersion coefficient in wave field

Transport and diffusion caused by coastal waves have different characteristics from those induced by flows. Through solving the vertical diffusion equation by an analytic method, this paper infers a theoretical formula of dispersion coefficient under the combined action of current and waves. It divides the general dispersion coefficient into six parts, including coefficients due to tidal current, Stokes drift, wave oscillation and interaction among them. It draws a conclusion that the contribution of dispersive effect induced by coastal waves is mainly produced by Stokes drift, while the contributions to time-averaged dispersion coefficient due to wave orbital motion and interaction between current and waves are very small. The results without tidal current are in agreement with the numerical and experimental results, which proves the correctness of the theoretical derivation. This paper introduces the variation characteristics of both the time-averaged and oscillating dispersion coefficients versus relative water depth, and demonstrates the physical implications of the oscillating mixing coefficient due to waves. We also apply the results to the costal vertical circulation and give its characteristics compared to Stokes drift.

Axial gas mixing in conical spouted beds with high density particles

Conical spouted beds operating with high-density particles(ρp>2500 kg/m^(3))have recently gained attention because of their potential use as nuclear fuel coaters for next-generation nuclear reactors.In the literature,the number of axial gas mixing studies in conical and conical-cylindrical spouted beds is very limited and all axial mixing studies were carried out with relatively light particles(ρp≤2500 kg/m^(3)).Therefore,the objective of this study was to generate experimental data that can be used to explain the gas axial mixing behavior in conical spouted beds operating with both low-and high-density particles.Experiments were conducted in two(γ=30°,60°)conical spouted beds with three different types of particles:zirconia(ρp=6050 kg/m^(3)),zirconia toughened alumina(ρp=3700 kg/m^(3))and glass beads(ρp=2460 kg/m^(3)).In order to be able to compare experimental data obtained at different conditions,a 1-D convection-diffusion gas mixing model originally developed by San Joséet al.(1995)was implemented to determine the axial dispersion coefficients.The results show that the axial dispersion coefficients range between m^(2)/s and m^(2)/s,increase with superficial gas velocity and are higher than the corresponding dispersion coefficients of fixed beds,lower than the dispersion coefficients of fluidized beds and in the same range with the cylindrical spouted beds reported in the literature.The corresponding Peclet numbers were in the range of 0.6–7.8 for all operating conditions and slightly higher Peclet numbers were obtained with glass beads indicating the relative importance of gas convective transport over gas dispersion for light particles compared to heavy particles.