Heavy Metals Transport in Soil With Exponential Decay Source

Abstract

Heavy metal pollution is a global environmental concern due to its extreme hazards and complicated challenges in removing it from soil. The behavior of heavy metal migration in soil can be aptly depicted using a mathematical model, specifically the advection-diffusion equation (ADE). This research considers the scenario where a pollutant is injected in an exponentially decaying manner within a fixed time interval 0 < t ≤ t0, and ceases at t > t0. The solutions are obtained by taking Laplace transform, and the propagation behavior of the pollutant for various exponential decay coefficients are studied. The results show that for 0 < t ≤ t0, heavy metal concentrations experience an initial rapid rise during injection, peaking at the boundary, followed by dispersion to surrounding areas. Upon injection cessation, a minor concentration rebound occurs due to residual effects, followed by gradual attenuation. The results provide insight for environmental management and pollution control strategies.