Analytical evaluation of steady-state solute distribution in through-diffusion and membrane behavior test under non-perfectly flushing boundary conditions

The through-diffusion and membrane behavior testing procedure using a closed-system apparatus has been widely used for concurrent measurement of diffusion and membrane efficiency coefficients of low-permeability clay-based barrier materials. However, the common assumption of perfectly flushing conditions at the specimen boundaries could induce errors in analyses of the diffusion coefficients and membrane efficiencies. In this study, an innovative pseudo three-dimensional (3D) analytical method was proposed to evaluate solute distribution along the boundary surfaces of the soil-porous disks system, considering the non-perfectly flushing conditions. The results were consistent with numerical models under two scenarios considering different inflow/outflow positions. The proposed model has been demonstrated to be an accurate and reliable method to estimate solute distributions along the boundaries. The calculated membrane efficiency coefficient and diffusion coefficient based on the proposed analytical method are more accurate, resulting in up to 50% less relative error than the traditional approach that adopts the arithmetic mean value of the influent and effluent concentrations. The retardation factor of the clay specimen also can be calculated with a revised cumulative mass approach. Finally, the simulated transient solute transport matched with experimental data from a multi-stage through-diffusion and membrane behavior test, validating the accuracy of the proposed method.