Effect of solute concentration on sorption of polyaromatic hydrocarbons in soil: uptake rates

The effect of solute concentration on sorption kinetics may be a factor in determining bioavailability and transport of organic pollutants in soils and sediments, but there is conflict in the literature over whether sorption is concentration-dependent. Sorption of phenanthrene and pyrene to seven soils ranging in organic carbon (OC) content from 0.18 to 43.9% was studied. Careful analysis revealed that experimentally the normalized rate of approach to equilibrium for compounds exhibiting a concave-down (with respect to the solute concentration axis) nonlinear isotherm increases with concentration. However, the effect is rather small and is most apparent when the fraction of total solute finally taken up by the solid (F) is low. The explanation is rooted in the nonlinearity of the isotherm and the finite-bath condition of the experiment and can be expressed in terms of two opposing effects. On the one hand, the apparent diffusivity of a (concave-down) nonlinearly sorbing compound within particles increases with concentration because its affinity for the solid phase decreases with increasing concentration. On the other hand, rates in finite-bath reactors carried out at the same liquid/solid ratio will suffer from a batch process temporal bias called the "shrinking gradient" effect. It is an artifact of the methodology and is due to gradient driving forces that slow the sorption rate as F declines. In nonlinear cases F declines as concentration increases. The shrinking gradient effect vanishes as the liquid/solid ratio approaches infinity. Although this effect is self-correcting when an appropriate nonlinear diffusion model is applied, consensus about such models has not yet been achieved. To provide bounds for the shrinking gradient effect in finite-bath systems semiempirically, two models that give lower and upper bounds of the characteristic sorption time tau in the limit of infinite bath have been employed: (a) a wetting front model, which assumes sorption is rate-limited by molecular migration, and (b) a fast diffusion model, which assumes a mass-transfer resistance at the sorption site. The results are consistent with an intrinsic positive concentration dependence of sorption kinetics.