Hydrodynamic dispersion in a hierarchical network with a power-law distribution of conductances

Dispersion is studied on a two-dimensional hierarchical pore network with a power-law distribution of conductances, i.e., P(g)similar to g(mu-1), with g is an element of(0,1), and mu is the disorderliness parameter (mu>0). A procedure for computing tracer dispersion transport on hierarchical networks was developed. The results show that the effective diffusion coefficient of the network scales similarly as conduction on the same lattice. This means that the disorder length scales for conduction and diffusion processes are the same, and can be predicted from percolation theory. The dispersivity, xi=D-parallel to/U, was found to diverge rapidly as mu -> 0. The result is in agreement with the model developed by Bouchaud and Georges (C.R. Acad. Sci. (Paris) 307 1431, 1988). A limiting value of mu approximate to 0.45 was found, below which the convection-dispersion equation is no longer valid.