Sharp Transition to Strongly Anomalous Transport in Unsaturated Porous Media

The simultaneous presence of liquid and gas in porous media increases flow heterogeneity compared to saturated flows. However, the impact of saturation on flow and transport has so far remained unclear. The presence of gas in the pore space leads to flow reorganization. We develop a theoretical framework that captures the impact of that reorganization on pore-scale fluid velocities. Preferential flow is distributed spatially through a backbone, and flow recirculation occurs in flow dead-ends. We observe, and predict theoretically, that this previously identified flow structure induces a marked change in the scaling of the velocity probability density function compared to the saturated configuration and a sharp transition to strongly anomalous transport. We develop a transport model using the continuous time random walk theory that predicts advective transport dynamics for all saturation degrees. Our results provide a new modeling framework linking phase heterogeneity to flow heterogeneity in unsaturated porous media. Plain Language Summary The unsaturated zone, where water and air coexist in the pore space, extends between the soil surface and the groundwater level. Its pronounced structural heterogeneity induces complex flow patterns, which lead to rich solute transport behaviors. Inputs (precipitation) and outputs (evaporation and deep drainage) induce spatiotemporal variability in water saturation (i.e., fraction of the pore space occupied by water), which impacts flow, transport, and biochemical reactions. It has been observed that water-unsaturated conditions lead to a strong separation of flow in regions of high velocity, where most of the fluid is transported, and regions of low velocity. We identify the spatial distribution and size of the low-velocity regions as key control features on water flow and transport of dissolved chemical species, leading to transport behaviors that differ from those described by classical transport formulations. We use these findings to develop a theoretical framework that allows us to predict flow and advective transport under unsaturated conditions, based on parameters that describe the heterogeneity in phase distribution within the pore space and that are directly linked to the geometry of the system. These results represent a decisive step toward the prediction of fate and transport phenomena from structural properties in unsaturated porous media.