The dispersion coefficient (D) and retardation factor (R) are key parameters in convection–dispersion equation (CDE). The boundary-layer theory provides a simple and convenient method to solve the CDE for a third-type boundary condition under steady water flow. However, the present boundary-layer solutions cannot accurately describe the solute concentration at higher average pore-water velocities for a long-period solute transport process. In this study, an improved exponential solution to the CDE was developed using boundary-layer theory with the assumption that the resident solute concentration in soil was an exponential function related to the position under steady water flow. The accuracies of three boundary-layer solutions (parabolic polynomial, cubic polynomial, and exponential) were evaluated by comparing with the exact solution in concentration predictions for a third-type boundary condition under steady water flow. The solute concentration distributions calculated from the three boundary-layer solutions were close to those from the exact solution. At higher average pore-water velocities, the exponential solution was better than the polynomial solutions in D and R estimations. Moreover, the feasibility of the three boundary-layer solutions was verified using a column experiment. This study provides an effective way for estimating D and R in laboratory or field studies.
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Vol. 97 • No. 2