Special Session 108: New Developments in porous media

Diffusion in Random Networks

Duan Z Zhang
Los Alamos National Laboratory
USA
Co-Author(s):    Juan C. Padrino
Abstract:
We study mass diffusion in an ensemble of random networks consisting of junction pockets connected by tortuous microchannels. Inside the channels, the mass diffusion is governed by the one-dimensional diffusion equation. Using the ensemble averaging technique to derive an averaged equation for these processes, we find that the average concentration evolution is governed by an integro-differential equation. In the case of diffusion in a semi-infinite domain, this equation predicts that for an early time compared to the characteristic time of channel diffusion, there is a similarity variable $xt^{-1/4}$ for the average concentration in these inhomogeneous media, instead of the traditional $xt^{-1/2}$ in a homogeneous medium, where $x$ is the distance from the boundary, and $t$ is the time. This early time similarity is a result of the time required to establish the linear concentration profile inside the channels and can be explained by the random walk theory. Work sponsored by LANL LDRD project 20140002DR.