On the Measurement of ²¹⁸Po Diffusivity Using the Two-Filter Method

Determining the diffusion coefficient of ²¹⁸Po is an important application of the two-filter method (Thomas and LeClare, 1970, Hlth Phys.18, 113). Air containing a known concentration of ²²²Rn is drawn through a cylindrical tube with filters at both ends. The ²¹⁸Po activity on the downstream filter relative to the ²²²Rn concentration in air is interpreted to determine the diffusivity of ²¹⁸Po. Previously, the interpretation scheme was based on a theoretical analysis of ²¹⁸Po transport and production in a tube by Tan (1969, Int. J. Heat Mass Trans.12, 471), and Tan and Hsu (1970, Int. J. Heat Mass Trans.13, 1887). Their analysis did not account for radioactive decay of airborne ²¹⁸Po within the apparatus nor for the perturbation of the fluid flow caused by the flow resistance of the downstream filter. Also, simplified analytical air flow profiles were assumed in that analysis. In this paper, the two-filter method is re-analyzed numerically, by solving the continuity equation, the Navier-Stokes equations and the species conservation equation for a tube. Full account is taken of the effects of radioactive decay of ²¹⁸Po, and the flow resistance of the downstream filter. The results of the new analysis lead to a downward correction of reported diffusivities of ²¹⁸Po by about 10–20%.