Diffusion in a Sphere. These graphs show the results of diffusion in a spherical isotropic mineral grain as a function of a diffusion coefficient D (m2/s), radius of the sphere (a) in mm, and time (t) in years. The boundary conditions of the model are a sphere with a constant composition (C0) of the diffusing element at time = 0, and an environment that holds the surface of the sphere at a constant composition (C1) at all times. Move the "Time Slider" to see how the compsition of the sphere changes with time. The changes are shown both as a color change in the sphere as the concentration of the diffusing element increases, and also as a graph of the normalized concentrations (C-C2)/(C1-C2) as as function of the normalized radial position (r/a) in the sphere. You may change the radius of the sphere with the "Radius Slider." You may change the diffusion coefficient with the log D slider or by entering Arrhenius parameters for the diffusion coefficient. And you may change the starting compositions so that the concentration of the diffusing element is higher in the sphere.
This diffusion model is based on solutions of Fick's Second Law of Diffusion for a composition-independent diffusion coefficient and the boundary conditions listed above. The model uses equation's (6.18) and (6.21) from Crank (1975).
