Tracer distribution coefficient

The rate of sorption of copper to suspended particles was determined for samples collected at the discharge area of a coastal power station (5). Steady-state conditions of sorption were approached within 10 hr after spiking with ionic copper using Cu as a tracer. Distribution coefficients range from 11,000 to 52,000 and k values from 0.2 to 0.8 hr There was some evidence from the data that part of the copper was sorbed in a very short period (less than about 10 min), while the remainder was sorbed onto the particles at an exponential rate over the next 10 hr as steady-state conditions were approached. However, for present purposes, considering sorption on particles as a single compartment, the transfer of copper from labile forms to those sorbed on suspended particles is fairly well represented as a first-order process in which kis approximately equals 0.75 hr ... 

For a radionuclide to be an effective oceanic tracer, various criteria that link the tracer to a specihc process or element must be met. Foremost, the environmental behavior of the tracer must closely match that of the target constituent. Particle affinity, or the scavenging capability of a radionuclide to an organic or inorganic surface site i.e. distribution coefficient, Kf, is one such vital characteristic. The half-life of a tracer is another characteristic that must also coincide well with the timescale of interest. This section provides a brief review of the role of various surface sites in relation to chemical scavenging and tracer applications. 

Consider a fluid flowing steadily along a uniform pipe as depicted in Fig. 2.13 the fluid will be assumed to have a constant density so that the mean velocity u is constant. Let the fluid be carrying along the pipe a small amount of a tracer which has been injected at some point upstream as a pulse distributed uniformly over the cross-section the concentration C of the tracer is sufficiently small not to affect the density. Because the system is not in a steady state with respect to the tracer distribution, the concentration will vary with both z the position in the pipe and, at any fixed position, with time i.e. C is a function of both z and t but, at any given value of z and t, C is assumed to be uniform across that section of pipe. Consider a material balance on the tracer over an element of the pipe between z and (z + Sz), as shown in Fig. 2.13, in a time interval St. For convenience the pipe will be considered to have unit area of cross-section. The flux of tracer into and out of the element will be written in terms of the dispersion coefficient DL in accordance with equation 2.12. For completeness and for later application to reactors (see Section 2.3.7) the possibility of disappearance of the tracer by chemical reaction is also taken into account through a rate of reaction term 9L... 

From our tracer experiments, the distribution coefficient of Pu(IV) is directly proportional to [HDEHP]2 and is inversely proportional to [H+]2. The capacity experiments show that there are four molecules of HDEHP and one plutonium ion in a molecule of extracted compound. From this, we conclude that HDEHP is a dimer in the concentration range studied. The proposed extraction mechanism is as follows ... 

Mechanisms and yields of analytical procedures such as precipitation or coprecipitation that are essential for their apphcation can be elucidated. Furthermore, general analytical data can be obtained by apphcation of tracer techniques, for example distribution coefficients, stability constants and solubilities. 

The berkelium (IV) extraction coefficients have been determined by stripping solvents previously loaded with tetravalent cerium and berkelium in the presence of sodium bismuthate. Sodium bismuthate has been found to be an efficient oxidizing agent for trivalent cerium. Because of its small solubility it does not affect the distribution coefficients of tetravalent cerium. These two properties have been demonstrated by comparing the distribution coefficients of cerium (IV) measured by spectrophotometry with those of cerium oxidized by sodium bismuthate and measured by beta counting of the cerium isotope tracer. The data are summarized in Table I and indicate no real difference in the distribution coefficients of cerium obtained by these two methods when using trilaurylmethylammonium salts-carbon tetrachloride as solvent. 

In the example shown here, the distribution of active elements (Co, Mo) and that of the deposited metals (Ni, V) arc of particular interest. This profile shows a strong interaction between Co and Mo (the signals follow each other and run counter to that of Al, the tracer clement from the matrix). The metals arc distributed at the surface for vanadium and at the core for nickel. Distribution coefficients can be defined to characterise these profiles and facilitate comparison between catalysts. 

Here, the putative length scale represents some kind of mean displacement, or some Lagrangian decorrelation scale that is evidenced by a granularity in the tracer distribution (see Armi and Stommel, 1983 Jenkins, 1987 Joyce and Jenkins, 1993). The uf term is usually characterized as a turbulent diffusion coefficient k, because of its functional similarity to the molecular diffusion coefficient ... 

The distribution coefficients have been determined for Cm(III), Am(III), Cf(III), Pu(IV), Pu(VI), Np(IV), Np(VI), and U(VI) between 30 volume % DHDECMP in DIPB and various nitric acid concentrations. Results are shown in Figure 2. Tracers were taken to incipient dryness in concentrated nitric acid several times, then dissolved with the particular nitric acid concentration being studied. After setting the oxidation state, extractions were done using equal volumes of aqueous and organic phases. Contact times were 5 minutes at 23°C. Extractions were done in 10 mL tubes which were agitated with a mechanical wrist shaker. Each data point was obtained by a separate extraction. 

Table IV. Effects of Dissolved and Degraded DHDECMP Impurities and Oxidative Treatements of These Impurities on the Distribution Coefficient of Tracer Pr3+ Between Cation Resin and an Aqueous Solution of 9.7 x 10-4 M Eu(N03)3 " 0.5 M HNO3...

Let ca in cm-2 be the equilibrium number concentration of the tracer entities in the adsorption layer, and cg in cm-3 the concentration in the gaseous phase. Experimental studies have shown that a range of small ca values (in the sense of surface coverage much less than unity) always exists, over which the dimensional ratio of the concentrations fca, the distribution coefficient... 

Fig. 5-I. Concentration tracer distribution in a soil column for fourdifferent sinusoidally varying tracer loading conccniraiiou.s at (lie column inlet. Unsteady stale tracer distribution curves are shown for t - 1. 10, 20 and I Odd. while a quasi steady-state (nicer distribution curve is shown lor t = 100 d, where it is noted it is identical to the unsteady slate curve for t = 100 d. The retardation coefficient, ft = I, and the sinusoidal loading Imjiieiu y. I/2-I li for all figures.

Figure 5-3 shows the effect of the dispersion coefficient on the tracer distribution in a soil column. Of course, the figure shows a 10-fold increase in dispersion coefficient quickly dampens out fluctuations in the concentration distribution curve leading to a near steady-state concentration profile for x > 200 cm. By con-... 

A quasi steady-state solution for the tracer distribution in a soilpolutnn has been developed for the inlet boundary concentration being a constant plus a Sinusoidal component. Then an unsteady state solution for tracer distribution a soil column was developed for the same inlet boundary condition as above. The unsteady-state tracer concentration distribution applies to the section of a soil column that still remembers the initial condition. The two solutions may be applicable to those planning experiments to measure parameters such as the dispersion coefficient from tracer tests. A sinusoidal loading of tracer at the inlet boundary may enable one to obtain repeated data traces at the column outlet as part of an extended experiment. Continued collection of tracer concentration vs. time data at the column outlet over a number of periods would enable one to collect data from repeated experiments, for each period of the sine wave would represent another experiment. This should enable one to obtain more replicates of data to improve statistical estimates of the dispersion coefficient than could be obtained by experimental methods that use a slug loading or a step change of concentration at the column inleL"... 

FIG. 9.2. Efficiency with which the tracer is carried for various values of the distribution coefficients D and X. (From Wahl and Bonner.)... 

Thin-layer methods are almost exclusively used for self-diffusion and tracer diffusion coefficient measurements a very thin layer of element is deposited on the surface (mass g per unit area), and the concentration distribution after diffusion is measured, whence... 

The computed distribution of the tracer concentration follows the Gaussian profile as shown in Figure 4. The length scale used for the tracer distribution is by which is larger than bo 5. It can be expressed as b = X bg j, where the spread coefficient X, > 1. 

Fig. 42. Volume distribution coefficient of the elements vs HCl concentration for Dowex 50 X 4 cation exchange resin. Tracer concentrations of the elements were used for the most part.

Fig. 46. The dependence of the distribution coefficients of several ions on zirconium phosphate on the aqueous HNO3 concentration. All adsorbates present in tracer amounts. Solutions of Pu(in) were 0.005 in sulphamic acid and 0.015 in Iwdrazine solutions of Pu(IV) 0.02 M in NaNOg and solutions of Pu02 0.02 M in KBrOs. ... 

Methods The measurements were carried out by batch equilibration, most by an isotope dilution technique. Samples of clay were pre-equilibrated several times with NaCl-CaCl2 solutions of fixed compositions, until successive equilibrations showed no change in concentration. To separate samples (separate because of he difficulty of discriminating between the gamma emission of Na and Ca radioisotopes) were added known amounts of Na and Ca tracers, and the solutions were allowed to equilibrate for 2-5 days. The solid was centrifuged down, and aliquots of the supernatant solutions were counted. By material balance, the fractions of the activity adsorbed were computed, and, from these, the distribution coefficients, D... 

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