An analytical solution to contaminant diffusion in semi-infinite clayey soils with piecewise linear adsorption

The adsorption of contaminants onto soil particles typically is nonlinear if the contaminant concentration is sufficiently high. A simplified piecewise linear adsorption isotherm consistent with experimental results is proposed as an approximation for nonlinear adsorption behavior. This approximation allows for the use of analytical solution to model solute diffusion of contaminants that exhibit nonlinear adsorption. A moving boundary is introduced to represent significant changes in the retardation factor of clay with an increase in solute concentration. The proposed analytical solutions were validated using experimental data presented in the literature. There is negligible difference between the results obtained by the proposed analytical solution and those obtained by the linear model when C_m/C₀ reached 0.5. The results also show that the model based on linear adsorption using the initial secant of the Freundlich isotherm leads to significantly lower estimated breakthrough time for the contaminant of interest than that obtained using the proposed model. The earlier breakthrough is due to an under-estimation of the amount of adsorption. The proposed method is relatively simple to apply and can be used for evaluating experimental results and verifying more complex numerical models.