Travelling waves during the transport of reactive solute in porous media: Combination of Langmuir and Freundlich isotherms

Van Duijn CJ, Knabner P, van der Zee SEATM (1993)

Publication Type: Journal article

Publication year: 1993

Journal

Advances in Water Resources Elsevier

Publisher: Elsevier

Book Volume: 16

Pages Range: 97-105

Journal Issue: 2

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_1993/1993_DuijnKnZee_TravlWaveDurTrspOfReactSoluteInPMCombOfLangFreundl

DOI: 10.1016/0309-1708(93)90001-V

Abstract

Recently, it has been shown that in the case of nonlinear solute adsorption the displacement may be in the form of a travelling wave. In this paper, we investigate whether a travelling wave type of behaviour can be expected when two different types of sorption sites can be distinguished with different isotherms and kinetics. Illustrations are given for cases where the overall isotherm comprises two contributions that follow the Langmuir and the Freundlich equations, respectively. Boundary conditions are chosen that ensure a decrease in concentration in the direction of flow. Depending on the value of the Freundlich power (p) the travelling wave may exist. For p ≤ 1, the travelling wave always exists, whereas for 1 < p ≤ 2 it depends on the values of the other adsorption parameters and whether a lower bound of the upstream concentration (at x = −∞) is exceeded. For p ≥ 2, the existence of the travelling wave requires that the upstream concentration does not exceed an (specified) upper bound. Besides illustrating some waves we show that two different rate functions that have the Freundlich isotherm as their limit for an infinite rate parameter result in qualitatively different travelling waves.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Centrum Wiskunde & Informatica (CWI) NL Netherlands (NL) Wageningen University & Research NL Netherlands (NL)

How to cite

APA:

Van Duijn, C.J., Knabner, P., & van der Zee, S.E.A.T.M. (1993). Travelling waves during the transport of reactive solute in porous media: Combination of Langmuir and Freundlich isotherms. Advances in Water Resources, 16(2), 97-105. https://dx.doi.org/10.1016/0309-1708(93)90001-V

MLA:

Van Duijn, C. J. (Hans), Peter Knabner, and Sjoerd E. A. T. M. van der Zee. "Travelling waves during the transport of reactive solute in porous media: Combination of Langmuir and Freundlich isotherms." Advances in Water Resources 16.2 (1993): 97-105.

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