Time-dependency of naphthalene sorption in soil: Simple rate-, diffusion-, and isotherm-parameter-based models

Sorption mechanisms and kinetics govern contaminant fate and bioavailability in soil to a great extent. In this study, temporal development of naphthalene sorption was measured on four soils and showed continuously increasing sorption with time. Two mechanistically based analytical models were fitted to the sorption kinetics data: (i) a Two-Rate Sorption Kinetics model (TRSK) and (ii) an Intraparticle Diffusion model (ID) with an initial sorption capacity, X-i. Both models described measured data well, with the TRSK model providing the best fit (lowest root mean square error). Although the two models are mathematically different, the parameters describing the slow sorption rate in the two models (in ID the effective diffusion coefficient, D-a/l(2), and in TRSK the slow rate coefficient, r(s)) exhibited comparable values. Both D-a/l(2) and r(s) showed a minor concentration dependency. Sorption isotherms measured at different time scales were described well by the Freundlich equation and showed that the Freundlich coefficient, K'(F), increased with time. The Freundlich exponent, n'(a), decreased at short sorption times (t < 4 days) but was reasonably constant at longer sorption times (t > 4 days). An empirical, two-term K'(F)(t) model, used together with a constant value of the Freundlich exponent, n'a (defined as n'a measured at t > 4 days), gave good predictions of the measured sorption at different time scales and represented a simple alternative to the ID and TRSK models. Calculating the naphthalene retardation factor as a function of time, R(t), using the two-term K'(F)(t) model implied that sorption non-linearity is highly important when evaluating both short- and longer-term naphthalene mobility in soil and will often overshadow the effects of sorption time-dependency.