Retardation due to adsorption may be an important factor in the fate and transport of contaminants in porous media. Reversible adsorption is generally described by isotherm functions giving the relationship between the concentrations in dissolved and in adsorbed phases. Several authors defined such parametric functions, the most widely used being the linear, the Freundlich and the Langmuir isotherms, which are also implemented in many solute transport simulation software. Some substances however exhibit a multi-step adsorption isotherm, mostly for organic compounds or organic adsorbents, as indicated by a few papers.
The isotherm function defined by Czinkota et al. (2002) introduces a limit concentration above which new adsorption mechanism starts to takes place. By summing up simple nonlinear isotherms in which the limit concentrations are set, isotherms including several steps may be described. One important feature of these multi-step isotherm is that their first derivative is not a monotonic function, hence the retardation factor may have several peaks if plotted against the solute concentration.
The effect of multi-step isotherm have been studied numerically with a modified version of the MT3DMS software. For this reason a general sorption isotherm (GSI) package have been developed which extends the functionality of the reaction (RCT) package with the ability to define arbitrary isotherms.
Adsorption described by multi-step isotherm may develop a specific concentration distribution during advective transport. As the retardation factor may have several peaks, the position of which is determined by the limit concentrations, several solute concentration fronts may develop, forming a step-wise concentration distribution.
The most evident parameters affecting the concentration distribution are the limit concentrations as they determine the “height” of the plateaus. Concentrations higher than the limit are characterized by sharply increased retardation which will delay their propagation. Other relations may be described depending on the type of isotherm function being used to describe the multi-step isotherm. When using Langmuir parameters, the propagation of concentration fronts seems to be determined by the adsorption capacity and the Langmuir constant.
The concentration distribution developed by multi-step isotherm may be altered by other transport processes like dispersion/diffusion or reactions. Their effect is to be expected as usual. The diffusion may be increased by the high concentration gradient along the concentration fronts.
The research was carried out within the GINOP-2.3.2-15-2016- 00031 “Innovative solutions for sustainable groundwater resource management” project of the Faculty of Earth Science and Engineering of the University of Miskolc in the framework of the Széchenyi 2020 Plan, funded by the European Union, co-financed by the European Structural and Investment Funds.
Czinkota, I., Földényi, R., Lengyel, Zs., Marton, A. (2002): Adsorption of propisochlor of soils and components equation for multi-step isotherms. Chemosphere, 48, 725-731