Pore-scale study on solute dispersion in the aqueous phase within unsaturated porous media

Solute dispersion in the aqueous phase within unsaturated porous media has critical implications to various natural and engineered systems, such as nutrient and contaminant transport in the vadose zone. This work developed pore-scale lattice Boltzmann (LB) modeling to simulate water-air multiphase flow and solute transport in the aqueous phase, which unraveled the role of the water saturation and Peclet (Pe) number on solute dispersivity in unsaturated three-dimensional porous media. The Pe number and water saturation influenced the solute concentration profile along the longitudinal direction in a coupled manner. Under a low Pe number, the solute concentration profile approximately followed the classic Gaussian distribution regardless of the water saturation. Under a high Pe number, the solute concentration profile became skewed and the role of the water saturation was noticeable. Under a moderate water saturation, a significant portion of the solute particles were trapped at the trailing edge, leading to the non-Fickian transport behavior. In contrast, with a high water saturation, the enhanced water connectivity in the pore space mitigated the trapping of solute particles at the trailing edge, leading to the classic Fickian dispersion. This study also showed the non-monotonic dependence of longitudinal dispersivity on the water saturation, which was caused by a competing process between pore water connectivity and flow field heterogeneity. The pore-scale simulation confirmed that the dispersivity is not a constant but depends on the Pe number nonlinearly. Therefore, there is a complicated coupling between the dispersivity, water saturation, and Pe number for multiphase flows in porous media. This study developed a six-parameter empirical model to account for the role of the water saturation and Pe number on the longitudinal dispersivity in unsaturated flows. This empirical model can be used to predict the solute dispersion coefficient in unsaturated porous media, which is critical to large-scale contaminant transport modeling.