Diffusivity of decay products

It is important to know the diffusivities of decay products, whether as ions, neutral atoms or molecules, or as cluster ions, in order to calculate deposition in the respiratory tract. One way of doing this is to measure deposition on the walls of a tube in laminar flow. 

The fraction deposited is related to the diffusivity by Gormley Kennedy s (1949) equation 

In these experiments, and those of Raabe (1968), the levels of airborne activity, and hence of ionisation in the chamber, were sufficient to ensure that decay products were neutralised, by collision with negative air ions, before entering the diffusion tube. 

Data from (Raghunath Kotrappa, 1979). RH = relative humidity. 

Porstendorfer Mercer (1979) did similar experiments with 220Rn-laden air at 106 to 109 Bq m-3. Their diffusion tube had a central electrode and deposition was measured with and without an electrical field. Collection on the charged electrode was more efficient in moist than in very dry air (relative humidity, RH 2%). In moist air, D was 6.8 x 10-6 m2 s 1 irrespective of whether the 212Pb was partially or wholly neutralised before deposition. In very dry air and low 220Rn concentrations, D was 4.7 x 10-6, and it was concluded that the charged component had D equal to 2.4 x 10-6 m2 s 1. Paradoxically, this would correspond to k = 1 x 10 4 m2 V-1 s 1, the mobility found by Jonassen Hayes (1972) for 222Rn decay products in moist air. In all Porstendorfer Mercer s experiments, the ageing time was very short. 

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Careful reviews by Raes (1985) and Raes et al. (1985) leave unanswered the question of the role of humidity, and of acid or organic vapours, in modifying the diffusivity of decay product ions. By comparison with the mobility in normal air of decay product and ordinary atmospheric small ions, the diffusivity of decay product small ions is probably 2 to 3 x 10-6 m2 s-1. For neutral atoms, or possibly oxide molecules, most measurements give D in the range 5 to 8 x 10-6 m2 s-1, except where radiolytic reaction products or reactive trace gases are present in sufficient concentration to form intermediate ions. 

Raghunath, B. and P. Kotrappa, Diffusion Coefficients of Decay Products of Radon and Thoron, J. Aerosol Sei. 10 133 (1979). 

Attachment of decay products to nuclei greatly affects the process of deposition, because the Brownian diffusivity of nuclei is typically about four orders of magnitude less than the molecular diffusivity of unattached decay products. The lifetime of decay products in air before deposition on surfaces is shorter if the air is clean than if it is dirty. 

Raghunath, B. Kotrappa, P. (1979) Diffusion coefficients of decay products of radon and thoron. Journal of Aerosol Science, 10,133-8. 

Activities were estimated on the basis of long time operation where saturation exists. The escape of fission products by recoil was estimated to be about 10 . This could be stopped by an exceedingly thin coating (. 1mm.). I am informed by Mr. Mulliken that recent work on the diffusion of flssion products in U metal at 600 °C (hotter than in the He plant) fails to disclose any mechanism for escape other than recoil. Of order 1/10 of the recoil activity will be transmitted through a permanent gas (1/20 activity in permanent gases and 1/20 resulting from their decay). Another 1/20 of the recoil activity will be volatile at the helium temperature of 400 C (largely Iodine). We may then expect 10" of the total activity to deposit on walls as soon as it can. 10 of the activity will deposit as soon as it can after the helium is cooled, and 10 will remain as a noble gas. 

The previously proposed uptake models were mathematical assumptions and had no physical or chemical basis. Millard and Hedges, on the other hand, considered the chemistry of bone-uranium interactions. With the D-A model, they proposed that U was diffusing into bone as uranyl complexes, and adsorbing to the large surface area presented by the bone mineral hydroxyapatite (Millard and Hedges 1996). Laboratory experiments showed a partition coefficient between uranyl and hydroxyapatite under oxic conditions of 10" -10, demonstrating U uptake in the U state without the need for reduction by protein decay products as proposed by Rae and Ivanovich (1986). 

Porstendorfer, J. and T.T. Mercer, Influence of Electric Charge and Humidity upon the Diffusion Coefficient of Radon Decay Products, Health Phvs. 37 191-199 (1979). 

We believe that the calculations presented here give a better understanding of the many factors that determine the behavior of radon decay products, and that they explain why such a large range of values is being found of diffusion coefficients of the unattached fraction, of equilibrium constants, plate out rates, etc. (see (1) for a review, (9) for experiments in steel rooms and (10), (11), (12) for field studies in domestic environments). 

Porstendorfer, J. and T. Mercer, Diffusion Coefficient of Radon Decay Products and their Attachment Rate to the Atmosphere Aerosol, in Natural Radiation Environment III. (T. F. Gesell and W. M. Lowder, eds.), CONF-780422, Vol. 1, pp. 281-293, National Technical Information Service, Springfield, Virginia (1980). 

He is present in natural gases with a concentration of MO-7 of that of 4He and 1(T6 of the helium in the atmosphere. The separation is very expensive. Hence 3He is instead obtained as by-product of tritium production in nuclear reactors. Tritium in fact produces, by beta decay (the half life is 12.26 years), 3He the separation of 3He is obtained through a diffusion process. 

Because °Ar is radiogenic, that is, it is continuously produced by the decay of °K, the situation is more complicated than the treatment above. Below we consider another simple case °Ar generation and isothermal diffusion. Suppose the production rate of °Ar is time-independent, corresponding to the slow decay assumption of Dodson (1973). This assumption is valid if the cooling timescale -tc is much shorter than the half-life of (1250 Myr), such as a Xc of less than 25 Myr. 

Another procedure is based on the measurement of the radioactive isotope radon-222 (half-life 3.8 days), the decay product of natural radium-226. At the bottom of lakes and oceans, radon diffuses from the sediment to the overlying water where it is transported upward by turbulence. Broecker (1965) was among the first to use the vertical profile of 222Rn in the deep sea to determine vertical turbulent diffusivity in the ocean. 

To evaluate fission product release in a reactor, it is necessary to supply the appropriate particle geometry, diffusion coefficients, and distribution coefficients. This is a formidable task. To approach this problem, postirradiation fission product release has been studied as a function of temperature. The results of these studies are complex and require considerable interpretation. The SLIDER code without a source term has proved to be of considerable value in this interpretation. Parametric studies have been made of the integrated release of fission products, initially wholly in the fueled region, as a function of the diffusion coefficients and the distribution coefficients. These studies have led to observations of critical features in describing integrated fission product releases. From experimental values associated with these critical features, it is possible to evaluate at least partially diffusion coefficients and distribution coefficients. These experimental values may then be put back into SLIDER with appropriate birth and decay rates to evaluate inreactor particle fission product releases. Figure 11 is a representation of SLIDER simulation of a simplified postirradiation fission product release experiment. Calculations have been made with the following pertinent input data ... 

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