Anomalous diffusion models to characterize the migration of heavy metals in heterogeneous media

The study on the problems of heavy metal pollution is a key focus in current research of soil management. The migration of heavy metals in soil was simulated using the fractional advection–dispersion equation (FADE) and the Hausdorff fractal derivative advection–dispersion equation (HADE) models in the soil column experiment. The results show that the concentrations simulated by the FADE and HADE models have good consistency with the measured concentrations. Compared with the traditional advection–dispersion equation (ADE) and HADE models, the FADE model has good simulation results for the front end (initial part of the outflow concentration curve) and the back end (tail part of the outflow concentration curve) of the breakthrough curves (BTCs), indicating that the FADE model can well simulate the migration characteristics of heavy metal pollutants in heterogeneous media.