Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media

We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, its role for evolution asymptotic behavior hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms that determine large scale particle motion, namely, smoothing intra-pore velocity contrasts, increase tortuosity paths, setting maximum time transitions. Based on these mechanisms, derive theory predicts anomalous normal dispersion based characteristic pore length, Eulerian distribution P\'eclet number.