New solutions for solute transport in a finite column with distance-dependent dispersivities and time-dependent solute sources

Dispersivity is widely accepted to be scale-dependent. Numerous studies have been published for solute transport in porous media with distance-dependent dispersivities in infinite or semi-infinite domains which set the effluent boundaries to be infinitely far away. However, discussion of finite domains is often overlooked. In this study, two new semi-analytical solutions for solute transport in a finite column are developed with linear-asymptotic (LAF solution) or exponential distance-dependent (EF solution) dispersivities and time-dependent sources. These two solutions are compared with the corresponding solutions for semi-infinite domains (LAI and EI solutions). Results show that breakthrough curves calculated by the LAF/EF solution change faster and possess higher peak values than those calculated by the LAI/EI solution, and the discrepancies increase with the growth rate of the dispersivity and the asymptotic dispersivity. At a specific time, the concentrations calculated by the LAF/EF and the LAI/EI solutions are the same close to the solute source. However, the concentrations calculated by the LAF/EF solution are higher than those calculated by the LAI/EI solution after a certain distance from the source. Such distances decrease with the growth rate of the dispersivity and the asymptotic dispersivity. The performances of the LAF, EF, LAI and EF solutions do not differ much when they are applied to interpret the laboratory column tests conducted in both homogeneous and heterogeneous soil columns.