We simulate advective transport in bond percolation clusters at the critical point. We compute the histogram of flow speeds in each bond of the backbone and find the multifractal spectrum for two-dimensional lattices with linear dimension $L⩽2000$ and in three dimensions for $L⩽250$. We demonstrate that in the limit of large systems all the negative moments of the velocity distribution become ill-defined. However, to model transport, the velocity histogram should be weighted by the flux to obtain a well-defined mean travel time. Finally, we use continuous time random walk theory to demonstrate that anomalous transport is observed whose characteristics can be related to the multifractal properties of the system.

• Received 27 June 2006

DOI:https://doi.org/10.1103/PhysRevE.75.011124