Radon diffusion

In addition to the assumptions of initial conditions, the validity of U-Pb methodology relies on closed system behavior of U, Pb and intermediate nuclides in the decay chain. Concordance between the two U-series decay chains is most likely to be compromised by Rn loss because Rn is the only gas in the decay chains and has a high diffusivity. Radon-222 in the decay chain has a half life of 3.8 days. This is much longer than the half-life of Rn (3.96 s) in the decay chain. Therefore, partial loss of Rn will give rise to an apparent age younger than the true age, whereas the 207p /235p ... 

The dimensionless group Pep is essentially the ratio of the rate of convective transport to the rate of diffusive transport. Similarly, Nr describes the relative importance of radioactive decay to convective flow as a method of removing radon from the soil pores. In the case of Pep >>1/ diffusion can be neglected and the first term in equation (1) drops out. If in addition Nr >>1, then radioactive decay can be neglected as a removal term. If Pep 1, then diffusive radon migration dominates, and the second term in equation (1) can be neglected. 

There are two main sources of Rn to the ocean (1) the decay of sediment-bound "Ra and (2) decay of dissolved "Ra in a water column. Radon can enter the sediment porewater through alpha recoil during decay events. Since radon is chemically inert, it readily diffuses from bottom sediments into overlying waters. The diffusion of radon from sediments to the water column gives rise to the disequilibrium (excess Rn) observed in near-bottom waters. Radon is also continuously being produced in the water column through the decay of dissolved or particulate "Ra. 

Loss of radon in the ocean occurs typically through radioactive decay (producing four short-lived daughters before decaying to °Pb) or loss to the atmosphere at the air-sea interface. Loss of radon owing to turbulence or diffusion at the air-sea interface leads to a depletion of radon with respect to "Ra, allowing for studies on gas exchange at this interface. ... 

Radon is a noble gas and is therefore not readily ionized or chemically reactive. Its properties in terrestrial material will be controlled by its solubility in melt and fluid as well as its diffusion coefficients. Compared with the lighter noble gases, Rn diffuses more slowly and has a lower solubility in water. It will also more readily adsorb onto surface that the lighter rare gases. It can, however be lost by degassing in magmatic systems (Condomines et al. 2003). More information about the behavior of Rn can be found in Ivanovich and Harmon (1992). 

Gauthier P-J, Condomines M, Hammouda T (1999) An experimental investigation of radon diffusion in an anhydrous andesitic melt at atmospheric pressure Implications for radon degassing from empting magmas. Geochim Cosmochim Acta 63 645-656... 

Morawska L, Philhps CR (1992) Dependence of the radon emanation coefficient on radium distribution and internal stractnre of the mineral. Geochim Cosmochim Acta 57 1783-1797 Neretnieks I (1980) Diffusion in the rock matrix an important factor in radionuclide retardation J Geophys Res 88 4379-4397... 

Radon can also enter buildings when there are no pressure differences. Place a drop of food coloring in a glass of water eventually, the coloring will spread out (diffuse) and color the water— even without stirring. Radon will do the same thing—spread from an area of higher concentration to an area of lower concentration until the concentrations are equal. Radon movement in this way is called diffusion-driven transport. 

Membranes of plastics and rubbers that are used to control liquid water penetration and water vapor diffusion are effective in controlling air movement as well. If they can be adequately sealed at the joints and penetrations and installed intact, then they could also provide a mechanical barrier to radon entry. 

Polyethylene-based membranes are manufactured for use in hazardous waste landfills, lagoons, and similar applications. Two of these products have been tested to determine their effectiveness as barriers against radon diffusion. (In most cases, diffusive flow is considered of little or no significance as a mechanism of radon entry compared with convective flow). A 20-mil high-density polyethylene tested 99.9% effective in blocking radon diffusion under neutral pressure conditions. A 30-mil low-density polyethylene tested 98% effective in blocking radon diffusion under neutral pressure conditions. 

Another available product has two faces of aluminum foil over a core of glass scrim webbing it is coated with asphalt. The membrane is 0.012 in. thick. This material has not been tested as a barrier against diffusive flow of radon, but its performance should be similar to that of other foil-faced products. Seams are sealed with aluminum tape. 

Knutson, E.O., A.C. George, L. Hinchliffe, and R. Sextro, Single Screen and Screen Diffusion Battery Method for Measuring Radon Progeny Size Distributions, 1-500 nm, presented to the 1985 Annual Meeting of the American Association for Aerosol Research,... 

Figure 1. Schematic illustration of factors influencing the production and migration of radon in soils and into buildings. Geochemical processes affect the radium concentration in the soil. The emanating fraction is principally dependent upon soil moisture (1 0) and the size distribution of the soil grains (d). Diffusion of radon through the soil is affected primarily by soil porosity ( ) and moisture content, while convective flow of radon-bearing soil gas depends mainly upon the air permeability (k) of the soil and the pressure gradient (VP) established by the building.

A general transport equation describing the rate of change of the radon activity concentration in the pore space results from combining the effects of diffusion and convection ... 

Thamer, B.J., Nielson, K.K., and Felthauser, K., The Effects of Moisture on Radon Emanation Including the Effects on Diffusion, Report BuMines 0FR 184-82, PB83-136358, U.S. Dept, of Commerce,... 

From equation (1) it can be seen that application of the diffusion theory leads to the conclusion that the rate of attachment of radon progeny atoms to aerosol particles is directly proportional to the diameter of the aerosol particles. 

When the radius of an aerosol particle, r, is of the order of the mean free path, i, of gas molecules, neither the diffusion nor the kinetic theory can be considered to be strictly valid. Arendt and Kallman (1926), Lassen and Rau (1960) and Fuchs (1964) have derived attachment theories for the transition region, r, which, for very small particles, reduce to the gas kinetic theory, and, for large particles, reduce to the classical diffusion theory. The underlying assumptions of the hybrid theories are summarized by Van Pelt (1971) as follows 1. the diffusion theory applies to the transport of unattached radon progeny across an imaginary sphere of radius r + i centred on the aerosol particle and 2. kinetic theory predicts the attachment of radon progeny to the particle based on a uniform concentration of radon atoms corresponding to the concentration at a radius of r + L... 

If it is accepted that the hybrid theory is the most complete theory for attachment of radon progeny to aerosols, the magnitude of the error involved in using exclusively either the kinetic or the diffusion theory can be seen from Figs. 3-7 and Table III. 

Unattached fractions of RaA (at t = °°) for two mine aerosols and for a typical room aerosol are shown in Table III. It is usually assumed that the attachment of radon progeny to aerosols of CMD < 0.1 ym follows the kinetic theory. In Table III it is apparent that the hybrid and kinetic theories predict similar unattached fractions for monodisperse aerosols. However, for more polydisperse aerosols, the kinetic theory predicts lower unattached fractions than the diffusion theory and thus the diffusion theory is the more appropriate theory to use. It is also evident that the kinetic-diffusion approximation predicts unattached fractions similar to those predicted by the hybrid theory in all cases. 

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

During the transport in the chamber, radon atoms decay to form RaA atoms. The RaA atoms except those diffused to the wall of the chamber are collected on the exit filter. The sample collected on the exit filter is removed and counted. The present method is able to simultaneously measure radon and thoron concentrations by alpha spectroscopic technique (Ikebe et al., 1979). 

At the time of the NBS review (Collfe et al., 1981) in 1981 no one had applied the results of time-dependent diffusion theory to the accumulation closed-can method. Therefore neither the review nor the earlier contemporary state-of-the-art papers (e.g. Jonassen, 1983) could describe properly or quantify the influence from radon... 

In order to simplify the situation, we assume that our porous sample under investigation covers the bottom of an open straight-walled can and fills it to a height d (Figure 1). Such a sample will exhibit the same areal exhalation rate as a free semi-infinite sample of thickness 2d, as long as the walls and the bottom of the can are impermeable and non-absorbant for radon. A one-dimensional analysis of the diffusion of radon from the sample is perfectly adequate under these conditions. To idealize the conditions a bit further we assume that diffusion is the only transport mechanism of radon out from the sample, and that this diffusive transport is governed by Fick s first law. Fick s law applied to a porous medium says that the areal exhalation rate is proportional to the (radon) concentration gradient in the pores at the sample-air interface... 

In order to answer the former question, how long does it take to change from the free to final steady-state exhalation, we must again consult detailed diffusion theory. It can be shown (Samuels-son, 1984) that the reshaping of the radon depth-concentration gradient is characterized by an exponential sum of the form... 

Figure 7. Radon concentration growth in the outer volume during the first fifteen hours after closure. The exhalation can is radon-tight (y= 1). The exhalation material is dry sand mixed with 11 % ground uranium ore by weight. The diffusion length, L, is 1.4 m, the sample thickness, d, is 26 cm and the outer volume height, h, is 4.0 cm. Other parameters of the sample are as follows porosity 0.47, radium concentration 1180 Bq kg, emanation fraction 0.33, bulk density 1710 kg m 3 (experiment + theory).

O outer volume radon concentration as predicted by time-dependent diffusion theory... 

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