Reconciliation of expressions for the modified retardation factor and incorporation of non-linear contaminant sorption to the stationary phase

The retardation factor describes the average velocity of a sorbing contaminant in groundwater relative to the average velocity of groundwater. The modified retardation factor (R′ or R*) describes the average velocity of a sorbing contaminant relative to groundwater in the presence of a carrier that binds the contaminant and facilitates its transport. Dissolved organic matter and particulate colloids are examples of potential facilitating carriers. The modified retardation factor R′ concerns the case when sorption of the carrier itself to the stationary phase is negligible, whereas R* accounts for significant sorption of a facilitating carrier to the stationary phase, and so represents a magnitude less than R, but greater than R′. A well-cited expression for R* is shown to differ in form and behavior relative to a lesser known expression for R*, and the bounds of applicability of these expressions are examined. The lesser-known expression for R* is shown to be more broadly applicable in its ability to describe situations where carrier sorption to the stationary phase is significant, and even rivals or exceeds that of the contaminant. The well-known expression for R* is shown to be not applicable to situations involving significant sorption of the carrier. The derivation of the expression for R* presented in this paper is given by two separate methods used to develop the previously published expressions, in order to relate the presented and previously published expression to each other. The expression is extended to include non-linear contaminant sorption to the stationary phase, and predictions from this expression are compared to a set of experimental data.