Macroscopic behavior and random-walk particle tracking of kinetically sorbing solutes

Analytical expressions are derived for the zeroth, first, and second spatia l moments of sorbing solutes that follow a linear reversible kinetic mass t ransfer model. We determine phase-transition probabilities and closed-form expressions for the spatial moments of a plume in both the sorbed and aqueo us phases resulting from an arbitrary initial distribution of solute betwee n the phases. This allows for the evaluation of the effective velocity and dispersion coefficient for a homogeneous domain without resorting to numeri cal modeling. The equations for the spatial moments and the phase-transitio n probabilities are used for the development of a new random-walk particle- tracking method. The method is tested against three alternate formulations and is found to be computationally efficient without sacrificing accuracy. We apply the new random-walk method to investigate the possibility of a dou ble peak in the aqueous solute concentration resulting from kinetic sorptio n. The occurrence of a double peak is found to be dependent on the value of the Damkohler number, and the timing of its appearance is controlled by th e mass transfer rate and the retardation factor. Two ranges of the Damkohle r number leading to double peaking are identified. In the first range (Da(1 ) less than or equal to 1), double peaking occurs for all retardation facto rs, while in the second range (1 less than or equal to Da(1) less than or e qual to 3), this behavior is most significant for R > 12.