Longitudinal dispersion in laboratory and natural streams

This study concerns the longitudinal dispersion of fluid particles which are initially distributed uninformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream.

Taylor's method of determining a dispersion coefficient, previously applied to flow in pipes and two-dimensional open channels, is extended to a class of three-dimensional flows which have large width-to-depth ratios, and in which the velocity varies continuously with lateral cross-sectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel cross-sectional geometry, the cross-sectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required.

Large values of the dimensionless dispersion coefficient D/rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio.

A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for two-dimensional flow, and gives results in good agreement with laboratory and field experiments.

Both laboratory and field experiments are described. Twenty-one laboratory experiments were conducted: thirteen in two-dimensional flows, over both smooth and roughened bottoms; and eight in three-dimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the Green-Duwamish River, Washington.

Both laboratory and flume experiments prove that in three-dimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factory of ten by roughening the channel banks. In three-dimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor's analysis within a maximum error of 15%. For the Green-Duwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.

Traveltime, unit-concentration, longitudinal-dispersion, and reaeration characteristics of upstream reaches of the Yampa and Little Snake Rivers, Colorado and Wyoming /

Mode of access: Internet.

Longitudinal dispersion in spiral wound RO modules and its effect on the performance of batch mode RO operations

Operation of reverse osmosis (RO) in cyclic batch mode can in principle provide both high energy efficiency and high recovery. However, one factor that causes the performance to be less than ideal is longitudinal dispersion in the RO module. At the end of the batch pressurisation phase it is necessary to purge and then refill the module. During the purge and refill phases, dispersion causes undesirable mixing of concentrated brine with less concentrated feed water, therefore increasing the salt concentration and energy usage in the subsequent pressurisation phase of the cycle. In this study, we quantify the significance of dispersion through theory and experiment. We provide an analysis that relates the energy efficiency of the batch operation to the amount of dispersion. With the help of a model based on the analysis by Taylor, dispersion is quantified according to flow rate. The model is confirmed by experiments with two types of proprietary spiral wound RO modules, using sodium chloride (NaCl) solutions of concentration 1000 to 20,000 ppm. In practice the typical energy usage increases by 4% to 5.5% compared to the ideal case of zero dispersion.

Survival analysis with internal covariates modelled using a longitudinal dispersion model and flexible links

Poster presented at the From Basic Sciences to Clinical Research: 1st International Congress of CiiEM. Egas Moniz, Caparica, Portugal, 27-28 November 2015

Wave dispersion in a cellular composite with modulated microstructure

In this paper we report a modeling technique and analysis of wave dispersion in a cellular composite laminate with spatially modulated microstructure, which can be modeled by parameterization and homogenization in an appropriate length scale. Higher order beam theory is applied and the system of wave equations are derived. Homogenization of these equations are carried out in the scale of wavelength and frequency of the individual wave modes. Smaller scale scattering below the order of cell size are filtered out in the present approach. The longitudinal dispersion relations for different values of a modulation parameter are analyzed which indicates the existence of stop and pass band patterns. Dispersion relations for flexural-shear case are also analyzed which indicates a tendency toward forming the stop and pass bands for increasing values of a shear stiffness modulation parameter. The effect the phase angle (θ) of the incident wave indicates the existence more number of alternative stop bands and pass bands for θ = 45°.

Longitudinal distribution and lateral pattern of megalopal settlement and juvenile recruitment of Carcinus maenas (L.) (Brachyura, Portunidae) in the Mira River Estuary, Portugal

Settlement is a critical process in the life history of crabs, and thus affecting the abundance, distribution and structure of estuarine communities. The spatial pattern of settlement of megalopae of the shore crab Carcinus maenas along a longitudinal estuarine gradient (Mira River Estuary, Portugal) was examined, as well as its effects on the juvenile population. To measure megalopal settlement, four replicate collectors were deployed in six equally spaced stations along the estuarine axis. Juveniles were collected on the same locations with a quadrat randomly deployed on the substrate. To assess fine-scale megalopal settlement within a curved region of the estuary, replicate collectors were deployed on both margins along Moinho da Asneira curve. Megalopae settled differently along the six longitudinal points, with a tendency to attenuate their settlement upstream. Within the curved region, megalopae preferentially settled on the left margin collectors, probably due to the weaker velocity speeds felt on this margin. Concerning the overall juvenile density, there were significant differences among the stations distributed along the estuary, but they did no reflect a longitudinal dispersion attenuation pattern. Size-frequency distribution of the juvenile population showed that the average size is higher on the left margin. Recruits (carapace length between 1.0 mm and 3.4 mm) were more abundant on the upstream stations. Density of early juveniles (3.4 mm-6.5 mm) and juveniles (6.5 mm-10 mm) was more stable throughout the estuary axis than that of recruits. This distribution pattern may result from tidal excursion processes or mechanisms to avoid biotic interactions, such as predation and competition. (c) 2006 Elsevier Ltd. All rights reserved.

Longitudinal distribution and lateral pattern of megalopal settlement and juvenile recruitment of Carcinus maenas (L.) (Brachyura, Portunidae) in the Mira River Estuary, Portugal

Settlement is a critical process in the life history of crabs, and thus affecting the abundance, distribution and structure of estuarine communities. The spatial pattern of settlement of megalopae of the shore crab Carcinus maenas along a longitudinal estuarine gradient (Mira River Estuary, Portugal) was examined, as well as its effects on the juvenile population. To measure megalopal settlement, four replicate collectors were deployed in six equally spaced stations along the estuarine axis. Juveniles were collected on the same locations with a quadrat randomly deployed on the substrate. To assess fine-scale megalopal settlement within a curved region of the estuary, replicate collectors were deployed on both margins along Moinho da Asneira curve. Megalopae settled differently along the six longitudinal points, with a tendency to attenuate their settlement upstream. Within the curved region, megalopae preferentially settled on the left margin collectors, probably due to the weaker velocity speeds felt on this margin. Concerning the overall juvenile density, there were significant differences among the stations distributed along the estuary, but they did no reflect a longitudinal dispersion attenuation pattern. Size-frequency distribution of the juvenile population showed that the average size is higher on the left margin. Recruits (carapace length between 1.0 mm and 3.4 mm) were more abundant on the upstream stations. Density of early juveniles (3.4 mm-6.5 mm) and juveniles (6.5 mm-10 mm) was more stable throughout the estuary axis than that of recruits. This distribution pattern may result from tidal excursion processes or mechanisms to avoid biotic interactions, such as predation and competition. (c) 2006 Elsevier Ltd. All rights reserved.

Effects of density differences on lateral mixing in open-channel flows

This study investigates lateral mixing of tracer fluids in turbulent open-channel flows when the tracer and ambient fluids have different densities. Longitudinal dispersion in flows with longitudinal density gradients is investigated also.

Lateral mixing was studied in a laboratory flume by introducing fluid tracers at the ambient flow velocity continuously and uniformly across a fraction of the flume width and over the entire depth of the ambient flow. Fluid samples were taken to obtain concentration distributions in cross-sections at various distances, x, downstream from the tracer source. The data were used to calculate variances of the lateral distributions of the depth-averaged concentration. When there was a difference in density between the tracer and the ambient fluids, lateral mixing close to the source was enhanced by density-induced secondary flows; however, far downstream where the density gradients were small, lateral mixing rates were independent of the initial density difference. A dimensional analysis of the problem and the data show that the normalized variance is a function of only three dimensionless numbers, which represent: (1) the x-coordinate, (2) the source width, and (3) the buoyancy flux from the source.

A simplified set of equations of motion for a fluid with a horizontal density gradient was integrated to give an expression for the density-induced velocity distribution. The dispersion coefficient due to this velocity distribution was also obtained. Using this dispersion coefficient in an analysis for predicting lateral mixing rates in the experiments of this investigation gave only qualitative agreement with the data. However, predicted longitudinal salinity distributions in an idealized laboratory estuary agree well with published data.

DesaLink:solar powered desalination of brackish groundwater giving high output and high recovery

Desalination of groundwater is essential in many arid areas that are far from both seawater and fresh water resources. The ideal groundwater desalination system should operate using a sustainable energy source and provide high water output per land area and cost. To avoid discharging voluminous brine, it should also provide high recovery. To achieve these aims, we have designed DesaLink, a novel approach to linking the solar Rankine cycle to reverse osmosis (RO). To achieve high recovery without the need for multiple RO stages, DesaLink adopts a batch mode of operation. It is suited to use with a variety of solar thermal collectors including linear Fresnel reflectors (LFR). For example, using a LFR occupying 1,000m of land and providing steam at 200°C and 15.5 bar, DesaLink is predicted to provide 350m of fresh water per day at a recovery ratio of 0.7, when fed with brackish groundwater containing 5,000ppm of sodium chloride. Here, we report preliminary experiments to assess the feasibility of the concept. We study the effects of longitudinal dispersion, concentration polarisation and describe a pilot experiment to demonstrate the batch process using a materials testing machine. In addition, we demonstrate a prototype of DesaLink running from compressed air to simulate steam.

Desenvolvimento de magnetizador para tratamento magnético da água

Dissertação (mestrado)—Universidade de Brasília, Faculdade Gama, Programa de Pós-Graduação em Engenharia Biomédica, 2015.

Polarization relaxation, dielectric dispersion, and solvation dynamics in dense dipolar liquid

A unified treatment of polarization relaxation, dielectric dispersion and solvation dynamics in a dense, dipolar liquid is presented. It is shown that the information of solvent polarization relaxation that is obtained by macroscopic dielectric dispersion experiments is not sufficient to understand dynamics of solvation of a newly created ion or dipole. In solvation, a significant contribution comes from intermediate wave vector processes which depend critically on the short range (nearest‐neighbor) spatial and orientational order that are present in a dense, dipolar liquid. An analytic expression is obtained for the time dependent solvation energy that depends, in addition to the translational and rotational diffusion coefficients of the liquid, on the ratio of solute–solvent molecular sizes and on the microscopic structure of the polar liquid. Mean spherical approximation (MSA) theory is used to obtain numerical results for polarization relaxation, for wave vector and frequency dependent dielectric function and for time dependent solvation energy. We find that in the absence of translational contribution, the solvation of an ion is, in general, nonexponential. In this case, the short time decay is dominated by the longitudinal relaxation time but the long time decay is dominated by much slower large wave vector processes involving nearest‐neighbor molecules. The presence of a significant translational contribution drastically alters the decay behavior. Now, the long‐time behavior is given by the longitudinal relaxation time constant and the short time dynamics is controlled by the large wave vector processes. Thus, although the continuum model itself is conceptually wrong, a continuum model like result is recovered in the presence of a sizeable translational contribution. The continuum model result is also recovered in the limit of large solute to solvent size ratio. In the opposite limit of small solute size, the decay is markedly nonexponential (if the translational contribution is not very large) and a complete breakdown of the continuum model takes place. The significance of these results is discussed.

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory

In the present work, the effect of longitudinal magnetic field on wave dispersion characteristics of equivalent continuum structure (ECS) of single-walled carbon nanotubes (SWCNT) embedded in elastic medium is studied. The ECS is modelled as an Euler-Bernoulli beam. The chemical bonds between a SWCNT and the elastic medium are assumed to be formed. The elastic matrix is described by Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation. The governing equations of motion for the ECS of SWCNT under a longitudinal magnetic field are derived by considering the Lorentz magnetic force obtained from Maxwell's relations within the frame work of nonlocal elasticity theory. The wave propagation analysis is performed using spectral analysis. The results obtained show that the velocity of flexural waves in SWCNTs increases with the increase of longitudinal magnetic field exerted on it in the frequency range: 0-20 THz. The present analysis also shows that the flexural wave dispersion in the ECS of SWCNT obtained by local and nonlocal elasticity theories differ. It is found that the nonlocality reduces the wave velocity irrespective of the presence of the magnetic field and does not influences it in the higher frequency region. Further it is found that the presence of elastic matrix introduces the frequency band gap in flexural wave mode. The band gap in the flexural wave is found to independent of strength of the longitudinal magnetic field. (C) 2011 Elsevier Inc. All rights reserved.

Local stability of a gravitating filament: a dispersion relation

Filamentary structures are ubiquitous in astrophysics and are observed at various scales. On a cosmological scale, matter is usually distributed along filaments, and filaments are also typical features of the interstellar medium. Within a cosmic filament, matter can contract and form galaxies, whereas an interstellar gas filament can clump into a series of bead-like structures that can then turn into stars. To investigate the growth of such instabilities, we derive a local dispersion relation for an idealized self-gravitating filament and study some of its properties. Our idealized picture consists of an infinite self-gravitating and rotating cylinder with pressure and density related by a polytropic equation of state. We assume no specific density distribution, treat matter as a fluid, and use hydrodynamics to derive the linearized equations that govern the local perturbations. We obtain a dispersion relation for axisymmetric perturbations and study its properties in the (kR, kz) phase space, where kR and kz are the radial and longitudinal wavenumbers, respectively. While the boundary between the stable and unstable regimes is symmetrical in kR and kz and analogous to the Jeans criterion, the most unstable mode displays an asymmetry that could constrain the shape of the structures that form within the filament. Here the results are applied to a fiducial interstellar filament, but could be extended for other astrophysical systems, such as cosmological filaments and tidal tails.