Two-dimensional transport of inorganic contaminants through electro-kinetic barriers in a layered system: A semi-analytical method.

As a novel active pollution containment technology, the electro-kinetic barrier (EKB) has considerable potential for controlling the migration of inorganic contaminant ions into adjacent soil and groundwater environments. To address the non-uniform spatial distribution of contaminant sources in layered subsurface systems and the limitations of conventional one-dimensional models in describing two-dimensional plume spreading and EKB containment performance, this study develops a two-dimensional semi-analytical model for contaminant transport with a non-uniform contaminant source boundary. The model incorporates electro-osmosis, electro-migration, and coupled advection-dispersion-adsorption processes. A semi-analytical solution in the Laplace domain is derived using Laplace and finite cosine transforms combined with the transfer matrix method, and the time-domain solution is obtained through Talbot numerical inversion. The model is validated against an existing one-dimensional analytical solution, laboratory soil column test data, and COMSOL numerical simulation results. The effects of model dimensionality, contaminant source spatial distribution, and key design parameters on contaminant transport behavior in the triple-layer system are further investigated. The results show that existing one-dimensional models overestimate contaminant migration distance and plume centerline concentration while underestimating the lateral contamination extent. Compared with a fixed-concentration inlet boundary, a non-uniformly distributed contaminant source delays breakthrough time, indicating that existing design methods may be overly conservative. Based on these findings, this study proposes an optimization scheme for the coordinated design of voltage gradient and EKB thickness, providing a practical tool for the design and parameter optimization of EKBs in engineering applications.