WIAS Preprint No. 24, (1992)

The modeling of reactive solute transport with sorption to mobile and immobile sorbents.


  • Knabner, Peter
  • Kögel-Knabner, I.
  • Totsche, K.U.

2010 Mathematics Subject Classification

  • 76S05 76R50


  • flow in porous media, adsorption, contaminant transport, mathematical modeling




This paper presents a mathematical model to describe the transport of reactive solutes with sorption to mobile and immobile sorbents. The mobile sorbent is considered to be reactive, too. The sorption processes mentioned are equilibrium and nonequilibrium processes. A transformation of the model in terms of total concentrations of solute and mobile sorbents is presented which simplifies the mathematical formulation. Effective isotherms, which describe the sorption to the immobile sorbent in the presence of a mobile sorbent and rate functions are introduced and their properties are discussed. The differences to existing approaches to model reactive solute transport are shown. Possible extensions are pointed out and the numerical approximation is sketched. The restrictions of the model as a consequence of the assumptions made on reactive solute transport are not due to mathematical reasons, but due to limitations of experimental information available.

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