The diffusion of contaminant through an accretion disc

We calculate the manner in which a trace contaminant diffuses through an accretion disc. For a steady disc in which the ratio of diffusivity to viscosity, ζ, is taken to be constant through the disc and for which the surface density distribution is taken to be a power law $$(\Sigma \propto R^{-a})$$ we present analytic solutions to the time-dependent equations governing contaminant evolution. We calculate the amount of contaminant which can diffuse its way outwards against the bulk inward accretion flow and show that this is a sensitive function of a and ζ.