Quantifying solute back-diffusion in heterogeneous dual-permeability systems: effects of flow velocity and matrix hydraulic conductivity using electrical resistivity monitoring

Groundwater contamination in heterogeneous aquifer systems containing high-permeability zones (analogous to fractures) and adjacent low-permeability zones (analogous to rock matrices) persists long after source removal due to back-diffusion, whereby contaminants stored in low-permeability zones gradually migrate back into high-permeability pathways. While this process critically controls contamination longevity and remediation effectiveness, the coupled influence of groundwater flow velocity and matrix hydraulic conductivity on back-diffusion remains poorly quantified. We conducted systematic laboratory experiments using sandbox models to simulate heterogeneous dual-permeability systems across four hydraulic conductivity levels and four flow velocities. Real-time electrical resistivity monitoring tracked sodium chloride tracer movement, enabling continuous, minimally-invasive characterization of back-diffusion dynamics. Results demonstrate strong inverse relationships between flow velocity and back-diffusion intensity: a 30% flow increase reduced contaminant release by 78% in high-conductivity systems. Matrix hydraulic conductivity exerted equally significant control, with high-conductivity materials accelerating contaminant exchange (reducing delay times by 65% and back-diffusion duration by 40%), while low-conductivity materials sustained release for over 4000 s. Dimensionless analysis using Péclet and Damköhler numbers demonstrated that all 16 experimental datasets collapse onto a single relationship, confirming the generalizability of the findings.These findings establish quantitative relationships between hydraulic properties and back-diffusion behavior, providing a predictive framework for assessing long-term contamination persistence and optimizing remediation strategies in heterogeneous aquifer systems.