Dual‐mode modeling of competitive and concentration‐dependent sorption and desorption kinetics of polycyclic aromatic hydrocarbons in soils

A radial dual‐mode diffusion model is proposed for mass transfer of hydrophobic compounds in soil organic matter (SOM) that is able to predict competitive and concentration effects on sorption and desorption rates. On the basis of dual‐mode sorption theory for glassy polymers the model assumes a population of specific adsorption sites (“holes”) interspersed uniformly in the dissolution (partition) domain of SOM. It further assumes Fickian diffusion in the dissolution domain and immobilization in the holes, with microscopic local equilibrium between the two domains. The model is solved numerically (Crank‐Nicolson implicit method). Using parameters from single‐solute equilibrium and kinetic experiments, the model adequately predicts batch transient sorption and desorption of phenanthrene (primary solute) as a function of pyrene (cosolute) concentration, and batch transient sorption of phenanthrene as a function of its own concentration, in two soils. The model shows that phenanthrene sorption approaches equilibrium faster with increasing cosolute or self‐concentration owing to the concentration dependence of the apparent diffusivity, as predicted by a simple hole‐plugging mechanism (i.e., fewer and fewer holes are available). Simulations show the effect to be greatest under infinite bath uptake conditions. Under finite bath conditions this positive effect on rate may be opposed by a batch process temporal bias present when the water:soil ratio is kept constant in a series of experiments. The bias is due to gradient driving force effects that slow the rate as a result of the decrease in percent of solute finally taken up by the solid as cosolute or concentration increases.