Radon diffusivity calculations

Each serie of measurements consisted of two parallel samples with counting during and after sampling, one with the screen diffusion battery and the second as the reference sample, so that the fractional free radon daughters could be calculated. The radon daughters are collected on a membrane filter (filter diameter 25 mm, pore diameter 1.2 ym) and the decays of Po-218 and Po-214 are counted by means of alpha spectrometry with a surface barrier detector (area 300 mn ). 

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). 

Diffusion is the dominant mechanism of lung deposition for radon daughter aerosols. It is generally assumed that airflow is laminar in the smaller airways and that deposition in each airway generation can be calculated adequately (Chamberlain and Dyson, 1936 Ingham, 1975). However, there is no such consensus on the treatment of deposition in the upper bronchi. Some authors (Jacobi and Eisfeld, 1980 NCRP, 1984) have considered deposition to be enhanced by secondary flow, on the basis of experimental results (Martin and Jacobi, 1972). It has been shown that this assumption reduces the calculated dose from unattached radon daughters by a factor of two (James, 1985). 

Radon moves upwards in soil partly by molecular diffusion in soil gas and partly by bulk flow caused by changes in air pressure at the surface. The diffusion flux can be calculated, if it is assumed that the radioactivity, porosity and density of the soil are independent of depth and that lateral movement of radon can be neglected. 

The concentration of radon decreases with height, the gradient being determined by the vertical diffusivity of the atmosphere. Jacobi Andre (1963) calculated the gradient by solving numerically the equation... 

The calculated size distribution of newly attached decay products is shown as curve C in Fig. 1.9. The activity median diameter is 0.16 /zm. With passage of time, the distribution would be shifted to larger particle sizes, as coagulation proceeds. George (1972) used diffusion batteries to measure the size distribution of nuclei carrying radon decay products and found activity median diameters (AMD) averaging 0.18,0.11, and 0.30 /um in a city basement, fifth floor room, and rural outside air, respectively. 

These authors used the global average piston velocity determined by Broecker and Peng (391 by the radon deficit method, 2.8 m/day. The Othmer-Thakar relationship was used to calculate the diffusivity of DMS, which has never been determined experimentally. Since the calculated diffusivity for DMS (1.2 x 10-5 cm2/s) is similar to that calculated for radon, the radon deficit piston velocity was assumed to apply to DMS without correction. The DMS concentrations used in this study were based on more than 600 surface ocean samples from a variety of environments. The global area weighted concentration used for the calculation was 102.4 ng S/l, resulting in a flux of 39 x 1012 g S/yr. 

We can attempt to apply the same type of model to the H2S data, however there are two additional unknown factors involved. First, we do not have a measurement of the sea surface concentrations of H2S. Second, the piston velocity of H2S is enhanced by a chemical enrichment factor which, in laboratory studies, increases the transfer rate over that expected for the unionized species alone. Balls and Liss (5Q) demonstrated that at seawater pH the HS- present in solution contributes significantly to the total transport of H S across the interface. Since the degree of enrichment is not known under field conditions, we have assumed (as an upper limit) that the transfer occurs as if all of the labile sulfide (including HS ana weakly complexed sulfide) was present as H2S. In this case, the piston velocity of H2S would be the same as that of Radon for a given wind velocity, with a small correction (a factor of 1.14) for the estimated diffusivity difference. If we then specify the piston velocity and OH concentration we could calculate the concentration of H2S in the surface waters. Using the input conditions from model run B from Figure 4a (OH = 5 x 106 molecules/cm3, Vd = 3.1 m/day) yields a sea surface sulfide concentration of approximately 0.1 nM. Figure S illustrates the diurnal profile of atmospheric H2S which results from these calculations. 

The second method is based on the amount of radon gas in the surface ocean. Radon gas is generated by the decay of Ra. The concentration of the parent Ra and its half-life allow calculation of the expected radon gas concentration in the surface water. The observed concentration is 70% of expected, so 30% of the radon must be transferred to the atmosphere during its mean lifetime of six days. Correcting for differences in the diffusivity of radon and CO2 allows an estimation of the transfer rate for CO2. The transfer rates given by the method and the radon method agree within 10%. 

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