Advective transport in the percolation backbone in two dimensions

We show that, in the case of advective transport on the percolation backbone, the relevant structure below the correlation length is an ensemble of tortuous paths, rather than the classical links-nodes-blobs system. These paths are embedded in the few largest blobs that dominate the structure of the backbone. We find numerically that the mean particle displacement differs from the prediction given by classical finite-size scaling arguments. We also show that because of the complex velocity distribution between the paths, the mean first-passage time of the particles cannot be inferred directly from the mean particle displacement.