Evaporation of an iodine sphere: hindered diffusion and Langmuir's conjecture

Here we examine Langmuir's conjecture (1918) regarding hindered diffusion in the context of the computation of a diffusion coefficient for iodine in air from experimental results. Using an expression that he derived for diffusion from a small sphere in an infinite nonabsorbing medium, Langmuir calculated a diffusion coefficient based on the measured (Morse, 1910) rate of mass loss from a small sphere of iodine sitting on the flat pan of a microbalance. He obtained a diffusion coefficient of 0.053 cm(2)/s under the experimental conditions but noted that due to the pan of the microbalance, diffusion in all directions was hindered, and that the actual diffusion coefficient was more likely closer to 0.07 cm(2)/s. To examine how the pan of the microbalance might have hindered the evaporation, we have considered a two-sphere model in which one sphere is evaporating. The other sphere is purely absorbing and comparatively large compared to the evaporating sphere so a flat surface can be approximated. For generality in future applications with arbitrary geometries, we solve the diffusion equation in the volume surrounding the spheres using Green's function to obtain the normalized evaporation rate of the sphere and compare it to that of an evaporating sphere surrounded by a large volume of air. In doing so, we have reinterpreted the experimental data, accounting for the hindered diffusion, obtaining a diffusion coefficient of 0.072 cm(2)/s, which supports Langmuir's conjecture.