  The simultaneous presence of liquid and gas in porous media increases flow
heterogeneity compared to saturated flows. However, so far the impact of
saturation on flow statistics and transport dynamics remained unclear. Here, we
develop a theoretical framework that captures the impact of flow reorganization
on the statistics of pore-scale fluid velocities, due to the presence of gas in
the pore space, which leads to the development of a highly-structured flow
field. Preferential flow is distributed spatially through the denoted backbone
and flow recirculation occurs in dead-end regions branching from it. This
induces a marked change in the scaling of the velocity PDF compared to the
saturated case, and a sharp transition to strongly anomalous transport. We
develop a transport model based on the continuous time random walk theory that
successfully predicts advective transport dynamics for all saturation degrees.
Our results provide a new modelling framework linking phase heterogeneity to
flow heterogeneity and to transport in unsaturated media.
