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Modelling heterogeneous phosphate sorption kinetics on iron oxyhydroxides and soil with a continuous distribution approach

Warrinnier, R., Goossens, T., Braun, S., Gustafsson, J. P., Smolders, E.
European journal of soil science 2018 v.69 no.3 pp. 475-487
adsorption, desorption, equations, ferrihydrite, frequency distribution, iron, iron oxyhydroxides, models, orthophosphates, soil, soil sampling
The kinetics of orthophosphate (PO₄) sorption in soil has far reaching consequences on its long‐term fate. Traditionally, a distinction is made between fast, reversible adsorption and slow fixation. The kinetics are commonly described by compartmental models (CMs) assuming kinetically distinct homogeneous pools (e.g. a rapid‐ and slow‐sorbing pool), with phenomenological equations or with complex diffusion‐based models. Alternatively, this process can be described by assuming frequency distributions of both adsorption and desorption rate constants and, thereby, enabling better description of experimental data with fewer adjustable parameters. Here, we developed such a rate constant distribution (RCD) model and compared it with CMs and other commonly used rate equations. Batch ³³PO₄ sorption was measured in agitated suspensions between 2 minutes and 20 days after spiking in 13 contrasting types of soil and two iron oxyhydroxides. Overall, the RCD model, with three adjustable parameters, describes the data better than the other models tested. The so‐called slow reactions, denoted as the factor change in soluble ³³PO₄ between 1 and 20 days after spiking, were described better by the RCD model and ranged from 1.0 (i.e. no change) to 6.9. The extent of slow reactions increased with the increase in the fraction of poorly crystalline iron in the soil (r = 0.69; P = 0.0088). Equilibrium was elusive up to 20 days for PO₄ sorption on ferrihydrite and on soil samples with a large fraction of poorly crystalline iron oxyhydroxides. The RCD model code is available as freeware from the first author. HIGHLIGHTS: A new rate constant distribution (RCD) model for PO₄ sorption kinetics was developed. The RCD model offers a simple approach to take surface heterogeneity into account. The RCD model fitted PO₄ sorption kinetics better than commonly used equations. Equilibrium was elusive for PO₄ sorption on ferrihydrite and soil with poorly crystalline iron.