Numerical Investigations of the Deposition of Unattached ²¹⁸Po and ²¹²Pb from Natural Convection Enclosure Flow

We report numerical predictions of the deposition to enclosure surfaces of unattached ²¹⁸Po and ²¹²Pb, short-lived decay products of ²²²Rn and ²²⁰Rn, respectively. The simulations are conducted for square and rectangular two-dimensional enclosures under laminar natural convection flow with Grashof numbers in the range 7 × 10⁷ to 8 × 10¹⁰. The predictions are based upon a finite-difference natural-convection fluid-mechanics model that has been extended to simulate the behavior of indoor radon decay products. In the absence of airborne particles, the deposition velocity averaged over the enclosure surface was found to be in the range (2–4) × 10⁻⁴ m s⁻¹ for ²¹⁸Po and (1–3) × 10⁻⁴ m s⁻¹ for ²¹²Pb. In each simulation, the deposition rate varied by more than an order of magnitude around the surface of the enclosure with the largest rates occurring near corners. Attachment of decay products to airborne particles increased the deposition velocity; for example, attachment of ²¹⁸Po at a rate of 50 h⁻¹ increased the predicted average deposition velocity by 30–70% over values in the absence of attachment. The simulation results have significance for assessing the health risk associated with indoor exposure to ²²²Rn and ²²⁰Rn decay products and for investigating the more general problem of the interaction of air pollutants with indoor surfaces.