A temporally relaxed theory of physically or chemically non-equilibrium solute transport in heterogeneous porous media

Groundwater constitutes a critical component in providing fresh water for various human endeavors. Never-theless, its susceptibility to contamination by pollutants represents a significant challenge. A comprehensive understanding of the dynamics of solute transport in groundwater and soils is essential for predicting the spatial and temporal distribution of these contaminants. Presently, conventional models such as the mobile-immobile (MIM) model and the rate-limited sorption (RLS) model are widely employed to describe the non-Fickian behavior of solute transport. In this research, we present a novel approach to solute transport that is founded on the temporally relaxed theory of Fick's Law. Our methodology introduces two relaxation times to account for solute particle collisions and attachment, leading to the derivation of a new advection-dispersion equation. Our findings indicate that the relaxation times possess similar properties to the transport parameters in the MIM and RLS models, and our solution can be applied to accurately predict transport parameters from soil column experiments. Additionally, we discovered that the relaxation times are proportional to the magnitude of Peclet number. This innovative approach provides a deeper insight into solute transport and its impact on groundwater contamination.