Simultaneous diffusion of isotopes from a radioactive series in homogeneous and isotropic solids

The simultaneous diffusion of the members of a radioactive series is analyzed. The diffusion equations consider both the radioactive production and decay of each of the series members, including the effect of radioactive recoil for alpha decays. Hydrodynamic coupling between the several isotope fluxes is not considered. The diffusion equations are solved in spherical coordinates for general initial and Dirichlet boundary conditions. The obtained solutions are applied in an example of the influence of diffusion and alpha recoil on the disequilibrium between the five initial isotopes of the uranium series