Application of a Lumped, Nonlinear Kinetics Model to Metal Sorption on Humic Substances

Abstract

Abstract Exposure assessment models are needed to predict the sorption behavior of metal ions with humic substances. To address this need, a lumped parameter nonlinear kinetics model based on the Langmuir‐Hinshelwood kinetic model— dC/dt = k 1 C /(1 + k 0 C )—is introduced and evaluated. The model was applied to a mixture of seven metal ions— Cr(III), Pb(II), Cu(II), Cd(II), Co(II), Ag(I), and Li(I)—reacted with three individual humic substances. The lumped parameter model employs a dimensional analysis technique (i.e., uses dimensionless parameters), Laplace transforms, gamma functions, and gamma distributions to produce analytical solutions for the kinetic equation of metal ion sorption to humic substances. During the initial reaction period, the most reactive species—Cr(III) and Pb(II)—dominated the lump parameter value, and the mixture behaved like a first‐order reaction. At longer periods, the lump followed a second‐order decay if there were less reactive species involved. The lumped parameter model provides valuable information about the overall kinetics behavior of metal ion mixtures with humic substances and could serve as a simulation tool to investigate the transport of metal ions in and out of landfill sites and the transport/retardation of metals in contaminated soils and aquifers.