Modified Fickian Model for Solute Uptake by Runoff

A one-dimensional Fickian diffusion model for entrainment of interstitial soil water by overland flow is modified to account for early non-Fickian mass transfer observed during laboratory runoff experiments. Modification involves specifying a time-dependent diffusion coefficient that decreases with time and asymptotically approaches the constant Fickian value with time. Results show that this asymptotic diffusion coefficient varies with the square of the quantity V*K, where V* is shear velocity and k is media permeability. Modifying the model entails the development of type curves for a range of convective time scales, or times of non-Fickian mass transfer. A graphical curvematching technique using dimensionless cumulative mass loss data provides a means of estimating the entrainment, or mass transfer, coefficient as a function of the convective time scale. This procedure shows that the entrainment coefficient varies linearly with V*k, Reasonable prediction of mass loss results using the asymptotic diffusion coefficients, an empirical relationship for the entrainment coefficient, and a convective time scale of 5 min as model input.