Pore-scale shear distributions in unsaturated porous media and their role in transport and mixing

Understanding the probability distributions of flow velocities in heterogeneous porous media is crucial for the study of transport phenomena, as velocity variability controls residence times and dispersion phenomena. However, our knowledge of velocity distributions and their relation to medium structure remains incomplete, especially under partially-saturated conditions, where phase heterogeneity plays a key role in determining the flow structure. In addition, the distributions of shear (the spatial rate of change of velocity transverse to the flow) are essential for understanding the impact of flow on mixing processes, because they represent a key control on solute plume deformation and its interplay with diffusion. Yet, these distributions are far less explored, particularly at the pore scale and under unsaturated conditions. This gap limits our ability to predict the impact of microscopic dynamics on macroscopic plume structure.

In this work, we focus on pore-scale velocity and shear distributions in unsaturated systems. Velocity fields are obtained through numerical simulations based on experimental data for the structure of the medium and fluid-phase distributions. The media are quasi-two-dimensional, with cylindrical pillars of variable radii and different correlation structures, and the flow conditions are such that the spatial phase distributions are time-independent. We characterize velocity and shear distributions and use this information to parameterize Continuous Time Random Walk (CTRW) models to predict solute transport and mixing.