Analytical Solution for Two-Dimensional Reactive Contaminant Transport under a Neumann Flux Boundary: Adsorption, Release Mode, and Landfill Leakage Application

This study aims to derive an analytical solution for two-dimensional transport of reactive contaminants under a Neumann flux boundary, incorporating linear first-order kinetic adsorption. The research gap is that this combination of processes has not been addressed in existing closed-form models. The novelty lies in the Neumann-based analytical formulation, which enables quantitative assessment of release mode, adsorption/retardation, source geometry, and decay. For instantaneous release, contaminant concentrations initially increase and then decrease with time due to the combined effects of advection, dispersion, and decay; for exponentially decaying release, concentrations initially increase but subsequently decrease as source strength diminishes. A decrease in the retardation factor increases peak concentration under both release modes, whereas the adsorption coefficient exhibits the opposite trend. A larger source length extends the transport distance of heavy metals but does not increase peak concentration. Quantitative sensitivity analysis identifies the retardation factor as the dominant control (sensitivity index -0.979; a ± 20% change alters peak concentration by ± 19.6%), while decay and source width have negligible influence. Compared with an equivalent Dirichlet solution, the Neumann formulation predicts a 22% lower peak concentration, an 18% farther peak location, and up to 28% lower near-field concentration.