A Temporally Relaxed Theory of Nonequilibrium Solute Transport in Porous Media With Spatial Dispersivity Involving Flexible Boundary

Groundwater is a vital drinking water source in tropical regions and supports many human activities. However, its pollution poses significant challenges. Researchers study pollutant behavior in porous media using advection–dispersion equations (ADEs), which account for Fickian and non-Fickian solute transport. This study presents a novel approach to solute transport in a medium with spatially variable dispersivity based on the temporally relaxed theory of Fick's Law. The methodology introduces two relaxation times accounting for solute particles' collisions and attachment, deriving a new ADE. The Darcy velocity is considered as a linear spatial function, and the dispersion coefficient is assumed to be proportional to the square of the velocity. Our findings indicate that the temporally relaxed theory can reproduce the solute transport behavior described by the existing two-stage models, equilibrium models in medium with constant and variable dispersivity. Additionally, the relaxation times significantly affect the temporal and spatial distribution of solute concentration and the remediation time. The effects depend on the input distribution, the position, and the heterogeneity parameter. The relaxation times possess similar properties to the transport parameters in the mobile-immobile and rate-limited sorption models. Time laggings can capture non-linear phenomena, including memory effects, nonequilibrium dynamics, multi-scale behavior, and anomalous transport, such as superdiffusion, subdiffusion, and long-tailed transport. This model can be applied to accurately predict transport parameters from soil column experiments and actual field conditions. This innovative approach provides a deeper insight into solute transport and its impact on groundwater contamination.