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 onedimensional 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 integrodifferential equation. In the case of diffusion in a semiinfinite 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. 
