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Concentration of radon, C/C0, vs. radius, r, within a sphere of water with radius rs = 3.6 cm. The interior of the sphere is surrounded by a spherical shell of water with a thickness 0.1 cm and a radon concentration C(r) = 0 at t = 0. The diffusion coefficient for radon in water is D = 1 x 10-5 cm2 s-1.
to be well mixed, but the concentration is decreasing exponentially with a half-time of 20 min. For simplicity, the volume of the lumen remains constant such that any material leaving the stomach is replaced with water that dilutes the radon.
The basic differential equations are unchanged. However, the interior surface of the stomach wall is driven by the function h(t) that is controlled by the concentration in the lumen. A solution can be obtained with Duhamel's theorem where the concentration in the wall is the convolution of the time derivative of a solution after a unit step function at t = 0 (Carslaw and Jaeger 1959).
The dimensions corresponding to the boundary conditions following an intake of 250 mL of water are as follows (see fig. B.2):