Inclusion of Asymptotic Effects of Diffusion on Dispersion by Advection

Previously we developed accurate predictions of full solute time arrival distributions, W(t), by advective transport through disordered porous media. This treatment of W(t) combined critical path analysis, cluster statistics of percolation theory and percolation scaling of tortuosity. Effects of diffusion on the dispersion coefficient, D, are included now as a function of Peclet number, Pe, in generating relative probabilities that particles can remain on paths of a given time. Known scaling of D on Pe is generated for 1<Pe<100, while experiemntal scaling of dispersivity on system size is generated for large Pe values. This success was unexpected given the asymptotic treatment of diffusion. Research was supported by NSF-EAR 0810186 and 0911482