Analytical solutions for one-dimensional contaminant ion transport through electro-kinetic barriers

Abstract

To prevent contaminant ions from spreading over the adjacent environment, it is of great interest to consider using electro-kinetic barriers to counteract contaminant transport through the combined effects of electro-osmosis and electro-migration. In this study, considering the bottom surface as a Cauchy boundary or a Drichlet boundary condition, two analytical solutions are proposed to predict the contaminant ion transport in the electro-kinetic barrier. Analytical solutions are verified against experimental data and numerical solutions from the previous literature. Subsequently, the proposed analytical solutions are used to investigate the effects of average applied voltage gradient, barrier thickness, diffusion coefficient, retardation factor and electro-osmotic conductivity on the transport of contaminant through the electro-kinetic barrier. The results show that the steady state base contaminant concentration decreases with the increase in average voltage gradient and barrier thickness. Additionally, the logarithm of the final stable base contaminant concentration changes linearly with the average applied voltage gradient and barrier thickness. For the contaminants with a high diffusion coefficient, a larger average voltage gradient should be applied to improve the electro-kinetic effects. Clayey soils with high sorption capacity and relatively high electro-osmotic conductivity are the suggested material choice for constructing compacted soil liners within the electro-kinetic barrier, due to distinct advantages in contaminant migration prevention. Finally, a dimensionless factor is introduced to uniformly describe influences on the base relative concentration, and it can be used as an important parameter for the design of an electro-kinetic barrier.