On the physical meaning of retardation factor and velocity of a nonlinearly sorbing solute

This study investigated the variation of retardation factor and velocity of a lithium (a nonlinearly sorbing solute) plume in relation to the variation of lithium concentration in the plume by using field-measured breakthrough curves (BTCs). A concentration-dependent/time-dependent retardation factor (Rc) and a cell-averaged retardation factor image (please see for definitions) of the lithium plume were derived from the BTCs. The concentration-dependent retardation factor, Rc, is initially large at low concentration of the lithium plume, and it drops steadily with the increasing concentration to a minimum value at the highest concentration of the plume. After the peak concentration has passed away, Rc increases gradually with the decreasing concentration of the plume. The cell-averaged retardation factor, image is close to a section of the concentration-dependent retardation factor, which is obtained at the few highest concentrations in a BTC. image varies widely, especially at the low concentrations of the lithium plume, with the distribution coefficient K of lithium and exponent n of the Freundlich isotherm for lithium adsorption. Considerable variations in image are also observed between the BTCs at different depths in a monitoring well. A single average retardation factor defined for a monitoring well is thus confounded with the variation of concentrations in the BTCs at different depths. The instantaneous velocity of the lithium plume, called the retarded velocity/local velocity (please see for definitions), changes with the concentration of the plume in an opposite way from the retardation factor. The retarded velocity is, of necessity, always lower than the constant velocity of the groundwater flow in the aquifer. A cell-averaged velocity of the lithium plume, derived from the cell-averaged retardation factor, is an average velocity of the plume at any point on the travel path for the entire breakthrough time of the plume. This velocity provides little information about the transport processes of lithium in the aquifer.