Fractional uptake

Table 9—Fractional uptake of radionuclides from water into rice grain...

Figure 7. The fractional approach to equilibrium (after 73). Fractional uptake = mass of solute sorbed at equilibrium/mass of solute added to system fractional approach to equilibrium = mass of solute sorbed at time r/mass of solute sorbed at time .

Based on a fractional uptake from the small intestine to blood (f- ) of 0.002. 

Of course, Equations la and lb can be reversed to consider fractional uptakes in an atmosphere that at equilibrium would lead to a concentration C0 throughout the particle. This amounts to only a change in initial conditions, and the fractional uptakes are given by F — 1 — C(t)/C0. This form of Equations la and lb is more useful in calculations of fission product fractionation during fallout formation as discussed later. 

Processes involving liquid surfaces are subject to Henry s law, which limits the fractional uptake of a gas phase species into a liquid. If the gas phase species is simple solvated, a physical Henry s law constraint holds. If the gas phase species reacts with a condensed phase substituent, an effective Henry s law H contraint holds [40,41], Henry s law constants relate the equilibrium concentration of a species in the gas phase to the concentration of the same species in the liquid phase. 

The annual dietary intake of Pu is several times greater than the intake by inhalation, but the fractional uptake from the gut is only about 5 x 10-4 (Simmonds et al., 1982), so dietary intake has not contributed greatly to the Pu burden in the general public. Simmonds et al. concluded that inhalation has contributed 96% of the total. 

The determination of 180 KIEs requires a sealed reaction vessel that keeps the dissolved 02 in solution during the progress of the reaction. The moles of 02 consumed can, therefore, be accurately quantified. At varying stages of reaction, the 02 is collected and the 180/160 at a given percent conversion is determined. The 180 KIE is calculated from Equation 9.2, where terms include R0 for the initial 180/ leO composition of the 02 (in the absence of reaction at 0% conversion) and // for the 180/160 corresponding to the fractional uptake of 02 at the conversion designated/. 

The model overestimated final liver chromium concentrations, but bone and kidney concentrations were well-predicted. This was not a completely independent test of the model s validity since data from this study were used to set parameters for fractional uptake of chromium into bone. 

The most widely used unsteady state method for determining diffusivities in porous solids involves measuring the rate of adsorption or desorption when the sample is subjected to a well defined change in the concentration or pressure of sorbate. The experimental methods differ mainly in the choice of the initial and boundary conditions and the means by which progress towards the new position of equilibrium is followed. The diffusivities are found by matching the experimental transient sorption curve to the solution of Fick s second law. Detailed presentations of the relevant formulae may be found in the literature [1, 2, 12, 15-17]. For spherical particles of radius R, for example, the fractional uptake after a pressure step obeys the relation... 

Earlier studies of intracrystalline diffusion in zeolites were carried out almost exclusively by direct measurement of sorption rates but the limitations imposed by the intrusion of heat transfer and extra-crystalline mass transfer resistances were not always fully recognized. As a result the reported diffu-sivities showed many obvious inconsistencies such as differences in diffusivity between adsorption and desorption measurements(l-3), diffusivities which vary with fractional uptake (4) and large discrepancies between the values measured in different laboratories for apparently similar systems. More recently other experimental techniques have been applied, including chromatography and NMR methods. The latter have proved especially useful and have allowed the microdynamic behaviour of a number of important systems to be elucidated in considerable detail. In this paper the advantages and limitations of some of the common experimental techniques are considered and the results of studies of diffusion in A, X and Y zeolites, which have been the subject of several detailed investigations, are briefly reviewed. 

Fisher, T. R., R. D. Doyle, and E. R. Peele. 1988b. "Size-fractionated uptake and regeneration of ammonium and phosphate in a tropical lake." Verhandlungen International Vereinigen Limnologie 23 637-641. 

Riegman, R., and Noordeloos, A. A. M. (1998). Size-fractionated uptake of nitrogenous nutrients and carbon by phytoplankton in the North Sea during summer 1994. Mar. Ecol. Prog. Ser. 173, 95—106. 

Figure 4 shows the adsorption dynamics of ethane in a 4.41 mm half length slab of Norit activated carbon at 30 °C, 1 atm. The results are shown as the fractional uptake versus time. The fractional uptake is defined as the uptake... 

This section analyzes the scaling properties of the uptake curve M t)/Moo on/across fractals in a single theoretical framework. The (fractional) uptake curve M t)/Moo is the ratio of the solute quantity entering the structure up to time t and the quantity entering at saturation (i.e. at t —> oo), i.e. 

It is interesting to compare eq. (15) with the results obtained on finitely ramified fractals by means of Green function renormalization [9-10]. It has been shown that the fractional uptake curve for a structure possessing fractal dimension dj, walk dimension d, and adsorbing from a reservoir at constant concentration c through an exchange manifold B (which represents the permeable boundary for treuisfer) possessing fractal dimension d scales as... 

Once the retention parameters were determined for each individual, the thyroid activity was estimated at time 24 h from the linear regression of the activity as a function of time. The uptake is thyroid burden at time 24 h divided by the decay corrected amount administered by the hospital. The average fractional uptake (0.16 0.01) of the thyroid has declined from the ICRP recommended value of 0.3. A one-sided r-test comparing the average fractional uptake with the ICRP value (assuming that it has a similar uncertainty to the uptake value determined in this work) gives a... 

The fractional uptake has decreased from the value recommended by the ICRP and is about 18%. 

In an attempt to confirm that changes in diffusion coefficient in well known systems are consistent with expected behavior, a series of PE s with varying density were investigated. As expected the fractional uptake of solvent decreased with increasing film density or crystallinity. However, surprisingly, the diffusion coefficient increased with increasing density or crystallinity (Figure 5). 

Fig. 7 Sorption uptake-rate curves ofbenzene in 50 mg of NaX (cf. [65]) at 440 K and 2.0 Torr. and denote adsorption and desorption processes, respectively. The continuous line is obtained from Eq. 26 with a fractional uptake of 0.6 and D = 4.9 x 10 m s" Note 1 Torr = 133.33 Pa...

Sorption uptake rate curves of ben ne in silicalite-1 (0 x) and HZSM-5 ( 0,+) at 395 K, 0.826 foir. (0>0) denote adsorption processes and (x,- ) denote desorption processes. Lines were calculated using the solution for diffusion in a sphere for silicalite and a cylinder for HZSM-5 from a well-stined solution of limited volume with fractional uptakes of 0.46 and 0.33, respectively (see eqn. (7)). 

Evaluating the above integral using eqs. (6.5-1) and (6.5-2), we obtain the following expression for the overall fractional uptake ... 

When the film resistance becomes negligible compared to the internal diffusional resistance, that is when Bi is very large, the fractional uptake given in eq.(9.2-33) will reduce to simpler form, tabulated in Table 9.2-3 for the three shapes of particle. 

Table 9.2-3 Fractional uptake for three particle geometries when Bi ->oo Shape Fractional uptake ...

These solutions for the fractional uptake listed in Table 9.2-3 are used often in the literature, when linear isotherm is valid. The fractional uptake versus non-dimensional time T is shown in Figure 9.2-5a for three different shapes of the particle for the case of infinite stirring in the surrounding (Bi -> oo). The computer code UPTAKEP.M written in MatLab is provided with this book to help the reader to obtain the fractional uptake versus time. As seen in Figure 9.2-5a, for the given R and Dapp the spherical particle has the fastest dynamics as it has the highest exterior surface area per unit volume. 

Figure 9.2-5a Plots of the fractional uptake versus x for slab, cylinder and sphere for Bi = oo...

Example 9.2 Determination of diffusivity from fractional uptake data... 

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