Modeling single sorbent systems

Christl and Kretzschmar (2001) studied the interaction of copper with fulvic acid and hematite, and the results were compared with model calculations based on the linear additivity assumption. The sorption data for the ion-single sorbent systems were modeled with a basic Stem model (BSM) (Section 12.2.2) for hematite and the NICA-Donnan model for fulvic acid. In the second step, pH-dependent sorption of Cu and fulvic acid in systems containing Cu, hematite, and fulvic acid was investigated in batch sorption experiments. Comparison of the experimental data with model calculations shows that Cu sorption in binary hematite-fulvic acid systems is systematically underestimated by up to 30% by using the linear additivity assumption, as shown in Figure 14.4. 

The equilibrium sorption isotherms are one of the most important data to understand the mechanism of the sorption. They describe the ratio between the quantity of sorbate retained by the sorbent and that remaining in the solution at the constant temperature at equilibrium and are important from both theoretical and practical points of view. The parameters obtained from the isotherm models provide important information not only about the sorption mechanisms but also about the surface properties and affinities of the sorbent. The best known adsorption models in the linearized form for the single-solute systems are ... 

Nonequilibrium sorption due to mass-transfer limitations (including slow external or internal diffusion) and sorption to two different sorbents have been incorporated into a single ADE to evaluate the conditions under which mass-transfer processes may be important [206]. Simulations with this model, using mass-transfer parameters estimated from empirical correlations, reveal nonequilibrium conditions (i.e., mass-transfer limitations) when groundwater velocities increase (such as those that might occur in a funnel-and-gate system). 

Real systems can be expected to correspond to some intermediate case between the extremes. The rate laws that must be expected, either for the migration of a pure sorbate or for the exchange of one sorbate against another one, can best be derived from a more detailed consideration of the model of sorption on interstitial single sites. The intermediate case between a lattice of single sites and a macroporus sorbent will be covered as we consider how the rate laws will be modified if several types of sites exist in the solid, a situation that has been shown to prevail in zeolites. Diffusion in the solid will be considered first, subsequently how it couples with the rate of transfer at the phase boundary. 

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