Tracer Concentration Distribution Research Articles

Horizontal mixing in lakes

Horizontal mixing in the upper hypolimnion of lakes far from the boundaries was studied in lake basins with surface areas between 5 and 220 km2 by observing the growth of the concentration distribution of the fluorescent dye sodium fluorescein (uranin). In each of the eight experiments, between 0.2 and 2 kg of uranin was instantaneously released into the lake in the appropriate depth (between 15 and 25 m) in such a way to keep the initial cloud size as small as possible. The horizontal extension of the cloud was repeatedly determined by integration of numerous vertical profiles. These surveys served to test theoretical models for horizontal mixing. The temporal development of the size and of the variances along the principal axes of the tracer concentration distribution was the main property considered here. The experiments cover a range of cloud sizes between 3 × 102 and 3 × 105 m2. None of them support the hypothesis that cloud size grows with elapsed time raised to the power of 3 as predicted by the inertial subrange turbulence model first applied to dispersion by Batchelor [1950]. The shear‐diffusion model of Carter and Okubo [1965] was found to provide a good description of the development of cloud size with time. This model also accounts for the fact that the tracer distributions were not radially symmetric. Effective horizontal diffusivities lie between 0.02 and 0.3 m2 s−1. Reevaluation of published data from experiments in Lake Ontario [e.g., Murthy, 1976] and in the ocean [e.g., Okubo, 1971] supports both the applicability of the shear‐diffusion model and the doubts raised against the appropriateness of the inertial subrange model for scales up to 1000 m.

Numerical simulations of the Arabian Sea using tracers as proxies for phytoplankton biomass

A set of numerical simulations were conducted to determine the potential interannual variation of phytoplankton biomass in the Arabian Sea. A four‐layer, reduced gravity model was forced with interannually varying, monthly mean winds for the years 1981 to 1990 and a seasonally varying, monthly mean climatological heat flux. Passive tracers, with fixed source and decay rates, were used as proxies for phytoplankton. The tracers were released in the second layer, and upwelling combined with interlayer mixing transported the tracers into the first (the top) layer of the model. In the top layer advection, diffusion and specified decay rate produced distributions of tracer concentration that we compare with coastal zone color scanner (CZCS) images. In addition to maps of tracer distribution, we constructed time series from areal averages of tracer concentration. The time series are particularly useful for analyzing the temporal variability of the tracer concentrations. There was substantial interannual variability in the results and a strong seasonal signal associated with the southwest monsoon. The years of maximal tracer concentration were 1990 and 1985. The first was associated with a decadal maximum in wind speed and the second with a large wind stress curl over the western Arabian Sea. The years with minimal tracer concentration were 1981 through 1983. We compare our results with published analyses of composited CZCS images during the southwest monsoon in 1981 and 1982. We find general agreement between our results and the CZCS images during the peak of the southwest monsoon; however, we find that during the early phase of the monsoon, when the winds are strengthening rapidly with time, the CZCS images are badly aliased by year to year changes in the time periods used to composite available satellite data.

Experimental study in a rotating channel on the similarity law of tracer concentration distribution in the turbulent Ekman boundary layer

Concentration disrribution of airborne pollutants released into the atmosphere by large and elevated industrial sources or extended urban areas generally depends on the dynamical and thermal structure of the whole depth of the atmospheric planetary boundary layer (PBL). In order to be able to get meaningful predictions of pollutant dispersion from simple dispersion formulae using surface parameters as input data (like the Gaussian one), it is necessary to establish some reliable relationships between these surface parameters and the whole PBL's vertical structure. This paper presents the results of laboratory experiments in rotating hydraulic channel, aimed at investigating the influence of the Earth rotation on the dispersion of tracers which spread in a near-neutral Ekman turbulent PBL and at expressing the change of u and v components of mean wind with height in terms of rotation and turbulence scales typical of the atmospheric PBL. The results provide some evidence that in a near-neutral PBL the profiles of dilution ratio, adimensionalized by means of friction velocity u ∗ = √ u′w′ and Coriolis parameter f = 2Ω sinϕ , as a function of an adimensional height zf χ u ∗ , where χ is the von Karman constant, can be described by a universal function for a given Rossby number of the flow. This result confirms the theoretical expectation put forth by Wippermann and Yordanov in their study on the prediction of concentration patterns in a rotating turbulent PBL.

Calculation of residence time distribution from tracer recycle experiments

This note develops a procedure that can be used to calculate the single pass residence time distribution in a reactor system, such as a landfill, operated with recycle, from pulse tracer studies. An equation relating the effluent tracer concentration and residence time distribution (“ E curve”) is derived, and a numerical technique to solve such an equation is presented and applied to data obtained from experiments on a laboratory-scale reactor. The significance of the procedure developed to biological reactors is discussed.

A Study of Tracer Distribution Parameter Estimation from Sparse Samples

Abstract How do design parameters such as the spacing of sampling stations affect the quality of information obtained from atmospheric dispersion experiments? In large-scale experiments such as the Cross-Appalachian Tracer Experiment (CAPTEX) and the Across North America Tracer Experiment (ANATEX), the average crosswind spacing between surface sampling stations Δy may be of the same order as, or greater than, the tracer cloud width parameter σy. For such sparse samplings, investigated are the errors in estimating five parameters of the crosswind distribution of tracer dosage or concentration: the crosswind integrated dosage (M); the centroid coordinate (ȳ); the lateral dispersion parameter (σy); the skewness (S); and the kurtosis (K). These are examined as functions of the ratio of σy to Δy, the nonuniformity of station spacing, and the location of ȳ relative to the nearest sampling station. Tracer experiments are simulated with the Gaussian distribution model, as well as a non-Gaussian model consisting o...

Elastic scattering, fluorescent scattering, and differential absorption airborne lidar observations of atmospheric tracers

Clear-air atmospheric motions can be visualized for evaluating atmospheric transport and diffusion parameters using tracer techniques in which a specific gas or particulate material is released into the atmosphere and the distribution of the tracers is evaluated by photographic or in situ sampling. However, photographic methods apply only to relatively dense tracer concentrations, and three-dimensional structure is difficult to evaluate. In situ sampling normally does not provide required spatial resolution over both horizontal and vertical directions; in addition, the platform supporting the in situ sensor may modify tracer concentration distributions. Lidar provides a method of mapping the three-dimensional distribution of tracer material released into the atmosphere with high spatial resolution from remote distances. A lidar operated from an airborne platform in a downward viewing direction can map tracer concentration distributions over long downwind distances and can also profile the earth's surface elevation so that atmospheric behavior in complex terrain can be effectively analyzed. This paper presents examples of airborne lidar used to observe the atmospheric distribution of tracer material by means of elastic scattering from smoke plumes generated within the near-surface mixed layer, fluorescent scattering from dye particles released above the mixed layer by means of a cropduster aircraft, and differential absorption lidar measurements of SF 6 tracer gas released at the surface level.

Dispersed-phase residence times and axial drop velocities in a multistage column contactor

The residence time of fluid elements in a control volume of any chemical process has a direct effect on the process efficiency. This effect is more important in liquid—liquid extraction where the residence time of the dispersed-phase droplets determines not only the extraction/reaction time but also the interfacial area of mass transfer. Dispersed-phase residence times and drop velocities were studied with operating conditions in a 127 mm diameter multistage contactor of pilot plant scale for the toluene—water physically equilibrated system. The two-point dynamic tracer technique was employed in combination with a laser photometric concentration technique. The tracer concentration distributions, measured at the entrance and exit of a single stage, and the simultaneously measured drop size distribution in the monitored stage were discretized appropriately to provide drop residence times and axial velocities in agitated dispersions. Results showed that the variance of the residence time distribution is proportional to the square of the mean residence time, suggesting that the dispersion model is not appropriate for the analysis of such flows. The obtained drop residence times or axial velocities can be directly applied in a comprehensive approach which considers the convective property of the droplets to predict the extraction performance of the contactor.

Investigations of round vertical turbulent buoyant jets

The axial and radial velocity components w and u, and the concentration c of a Rhodamine 6G dye were measured simultaneously in a turbulent buoyant jet, using laser-Doppler anemometry combined with a recently developed laser-induced-fluorescence concentration measurement technique. These non-intrusive techniques enable measurements in a region of plume motion where conventional probe-based techniques have had difficulties. The results of the study show that the asymptotic decay laws for velocity and concentration of a tracer transported by the flow are verified experimentally in both jets and plumes. The momentum and volume fluxes and the mean dilution factor are determined in dimensionless form as a function of the normalized distance from the flow source. Contradictory results from earlier experimental plume investigations concerning the decay laws of w and c and the plume width ratio bc/bw are discussed. The turbulence properties and the transition from momentum-driven jets to buoyancy-driven plumes are presented. The turbulence is found to scale with the mean flow as predicted by dimensional analysis and self-similarity. Buoyancy-produced turbulence is found to transport twice as much tracer as jet turbulence. Although velocity statistics in jets and plumes are found to be highly self-similar there is a strong disparity in the distribution of tracer concentration in the two flows. This occurs in the time-average mean flows as well as the r.m.s. turbulent quantities. Instantaneous concentration fluctuations are found to exceed time averages by as much as a factor of 3. The experimental results should provide a reasonable basis for validation of computer models of axisymmetric plumes.

Interpretation of tracer displacement during infiltration of river water to groundwater

The accidental release of a tritium pulse of about 500 Ci into a river in northern Switzerland allowed the measurement of travel times at a site where the river recharges a granular aquifer almost perpendicularly to the groundwater flow. A series of sampling wells had been previously installed in the aquifer. Most wells give access to shallow freshly infiltrated water. The infiltrated water flows along in the top layer of the aquifer, thus allowing for a one‐dimensional analysis of the spreading process from the river to the groundwater in the wells. The linear groundwater flow velocities calculated from the tritium responses at distances from the river of up to 500 m confirm the velocities determined from an earlier local‐scale uranine experiment at the same site. The scarce data used to describe tracer transport in the aquifer allowed for an assessment of dispersivity with the method of moments. A linearly scale‐dependent dispersivity is evaluated from the mode of increase of the temporal variance of the tracer concentration distribution. Some wells revealed bimodal responses; here the method of moments is applied in combination with a two‐layer model.

Transverse Mixing in Wide and Shallow River: Case Study

A method has been proposed for the computation of the transverse mixing coefficient in wide and shallow rivers. The study addresses the flow regime where vertical mixing has been completed. The method makes use of the second moments of the tracer concentration distribution and is very easy to apply. It can account for tracer loss by a first order process and for variability of stream cross sections. Field data from a portion of the upper Mississippi River were used for the computations. The values of the transverse mixing coefficient obtained agree well with results reported in the literature.

Liquid phase mixing in the gas-liquid jet reactor with liquid jet ejector.

The liquid-phase mixing pattern and dispersion coefficients were studied by the tracer concentration distribution at steady state and the impulse response method for the gas-liquid jet reactor with liquid jet ejector. The longitudinal liquid-phase mixing pattern was quite different between the spouting section and the calm section. In the spouting section, which was the lower region in the column, the liquid phase was regarded as almost completely mixed flow. By contrast, in the calm section, which was the upper region, the value of the dispersion coefficient was fairly smaller than that in bubble columns and back-mixing of the liquid phase was suppressed.

Axial dispersion in a segmented gas-liquid flow

Axial dispersion of a tracer in liquid flow segmented by gas bubbles is investigated by numerical calculations using a lumped parameter model. Slow mixing in the liquid segments is shown to be the major factor in determining the magnitude of axial dispersion, measured by the second central moment of the tracer concentration distribution. Experimental results obtained at a variety of tracer inputs substantiate the model predictions. Additionally, convolution and deconvolution of concentration profiles at the output are discussed. 22 refs.

Radiotracer evaluation of groundwater dispersion in a multi-layered aquifer

Groundwater flow near the Koeberg Nuclear Power Station was investigated by Stephenson in order to evaluate the extent of seawater intrusion around the foundations. In particular he studied the movement of the interface between fresh groundwater and seawater. For the purpose of such study it has been found necessary to determine the dispersion coefficient and confirm the velocity of fresh groundwater. This is carried out using 131 I as tracer. Measurement of time distributions of tracer concentration in a series of boreholes permits the development of a mathematical model which appears to describe quite satisfactorily groundwater flow as well as intermixing in several layers. Dispersion across the interface has been anticipated and the dispersion coefficients for each separate layer and for the whole aquifer are determined from a fit of the model to the experimental data.

Dispersion in annular climbing film flow

The dispersion of a tracer injected as a pulse into a climbing liquid film is investigated for a series of water and air flow rates, and for a number of different electrolyte tracers. It is found that at all flow rates the observed concentration distribution depends on the nature of the tracer. This observation is explained in terms of two effects: molecular diffusion in a viscous sub-layer and ion fractionation associated with droplet formation at the gas-liquid interface. The overall dispersive characteristics of the system are described in terms of a mathematical model assuming dispersed plug flow in both the film and entrained droplets with interchange between these phases. This model is fitted to experimental tracer concentration distributions using a non-linear least-squares regression procedure. The parameter values obtained from the fitting procedure are studied to determine trends with flow rates and tracer properties. Values for a film dispersion parameter, P f , are found to correlate significantly with the molecular diffusion coefficients of the tracers. Consistent values for an ion fractionation coefficient, k if , are also obtained.

DEPTH OF DISTURBANCE OF SAND IN SURF ZONES

A coring technique employed during wave action allowed accurate measurement of the depth of vertical mixing bm of fluorescent sand tracer grains within the surf zone of a gently sloping Pacific Ocean beach (beach slope tangent s = 0.012). The depth bm is the distance from the sediment surface to the lower limit of observed tracer grains within the inner portion of the core. Although this definition is only strictly applicable to a rectangular distribution of tracer concentration with depth, the bm results were quite similar to those using concentration-weighted depth averages of Crickmore (1967). For one winter regime experiment, vertical cross-sectional contour maps of tracer concentration normalized by the local core maximum were drawn with concentrations computed for each 0.4cm slice. Trends present are (1) in the onshore-offshore direction the maximum concentration is at the bed surface shorewards of the mid-surf position and 0.4 cm to 1.2 cm below the bed seaward of the mid-surf position, and (2) in the longshore direction (at the mid-surf position) the maximum concentration lies 0.4 cm to 1.6 cm below the bed surface. For spilling breaker heights Hb between 75 cm and 150 cm, histograms of bm were clearly different for spring/summer and fall/winter experiments: the mean and standard deviation (in parenthesis) are 0.5 cm (0.5 cm) and 1.1 cm (0.5 cm), respectively. These results are substantially less than both the 3.0 cm and the 20 cm to 40 cm disturbance depths per 100 cm of Hb reported by King (1951) and by Otvos (1965) and Williams (1970). The discrepancy with Otvos and Williams is due to the much different breaking process; in their experiments small breakers (Hb = 5 cm to 30 cm) plunged directly onto steep beach slopes (s = 0.1) causing large bm- The tracer grain's longer exposure to bottom stresses of passing surf bores may explain King's greater disturbance depths. Her sampling interval was one semi-diurnal tidal period T versus the span 0.02 T to 0.32 T in this study.

Transport Processes in the Two-Dimensional Near Wake

•TPESTS were conducted to characterize the two-dimensional JL recirculation zone downstream of circular cylinders and wedges, in the Reynolds number range 8 x 10 to 3 x 10. In this effort, a tracer material consisting of NO2 in a mixture of NO 2 — N204 was injected through holes in the bluff-body wall into the recirculation zone where tracer residence times and concentration distributions were determined using a fiberoptic probe. Vortex shedding and wake geometrical parameters were found from spark schlieren photographs taken with helium tracer injected into the zone. Measurements were taken at numerous approach flow velocities in the range 15 150 m/sec, at the three freestream densities of 0.41, 0.67, and 1.20 kg/m, and at several initial levels of turbulent intensity up to 11%. The data indicate that the vortex shedding phenomenon associated with two-dimensional bluff-bodies exerts a major influence on the transport of mass in the nearwake.

Nitrification and Denitrification during Miscible Displacement in Unsaturated Soil

AbstractNitrification and denitrification during the leaching of a pulse of NH4NO3 applied to the surface of soil columns are analyzed experimentally and theoretically. Experimentally, unsaturated soil columns of two lengths were leached steadily with a tracee solution containing NH4NO3 while the air‐filled portions of the columns were being flushed simultaneously with air. During these steady state conditions, a pulse of tracer solution containing either 15NH4+ or 15NO3‐ was leached through the columns. The words tracee and tracer signify that both solutions were chemically identical with the latter containing a greater proportion of 15N. Steady‐state tracee concentration distributions within the columns as well as the transient tracer concentration distributions in the effluent were analyzed assuming first‐order kinetics. Values of both the rate coefficients and the concentration distributions stemming from the tracee and tracer measurements were in general agreement. The agreement between the measured and theoretical results are discussed in terms of soil water properties and the kinetics of microbial populations.

Motion of Single Particles in Alluvial Channels

Movements of single sand-size radioactive particles were followed in a laboratory alluvial channel. Two sizes of bed material were used with experimental conditions limited to the ripple and dune bed forms of the lower flow regime. It was found that the frequency distribution of the particle step lengths was represented very well by the gamma distribution, and the frequency distribution of the particle rest period was represented adequately by the exponential distribution. The mean step lengths related well to the stream power of the flow; however, the relation cannot be considered general because observations were limited to a single depth of flow. The mean rest period related well to the celerity of the bed forms. Tests of a one-dimensional stochastic model for sediment dispersion showed that the model predicted the mean distance traveled by the tracer particles but did not predict the rate of spreading of the tracer concentration distribution.

Anion exchange of metal complexes—XVIII: Sorption of metal ions from anhydrous, chloride-containing, methanol and ethanol

The distribution of tracer concentrations of rhenium(VII), copper(II), cadmium(II) and iron(III) between Dowex-1 anion exchanger and anhydrous methanol and ethanol solutions of hydrogen chloride and tetra methylammonium chloride has been studied. The effect of low (2 wt.%) concentrations of water on the distribution of copper(II) in ethanolic hydrogen chloride was shown to be small. The loading of copper(II) chloride at macro concentrations, with no excess chloride present, has also been measured for methanol, ethanol and acetone solutions. Some conclusions concerning the species formed in the resin and in the solutions could be reached.

On hydrodynamic mixing in a model of a porous medium with stagnant zones

Hydrodynamic mixing in a porous medium is considered with the help of a model containing a series of perfect mixers with stagnant zones. The relationship between this model and the usual diffusion one is studied. Both models are investigated by the device of injection of a delta-shaped tracer at the entrance to the system. For a large enough number of cells and a sufficiently large length of the porous medium, described by a diffusion model, the tracer concentration distribution at the exit as a function of time is shown to be normal in both cases. The effective coefficient of diffusion, or the dispersion, is found from a comparison of the parameters of these two distributions. At small rates of fluid exchange between the flowing and stagnant zones, the dispersion coefficient is very large. This imposes rigorous limitations on the length of the porous medium necessary for the establishment of a normal concentration distribution at the exit. If, during experimental determination of the dispersion coefficient, these conditions are not fulfilled, i.e. if the porous medium does not prove to be long enough the normal distribution at exit is not established. Then the curve is bell-shaped with a long, steady “tail”. Calculation shows, that the distribution can then be represented as the sum of two distribution: a normal distribution and an exponentially decaying one. The parameters of the porous medium can be determined from experimental results.