Properties of exact and approximate traveling wave solutions for transport with nonlinear and nonequilibrium sorption

Water Resources Research

Volumn 33, Issue 5, 1997, Pages 1139-1147

  Simon, Werner ^a   Reichert, Peter ^a   Hinz, Christoph ^b  

^a SWISS FEDERAL INSTITUTE OF AQUATIC SCIENCE AND TECHNOLOGY   (Switzerland)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ADSORPTION ISOTHERMS; DIFFERENTIAL EQUATIONS; ISOTHERMS; PIECEWISE LINEAR TECHNIQUES; POROUS MATERIALS; SORPTION; WAVE EQUATIONS; WAVEFRONTS;

APPROXIMATION ERRORS; ISOTHERM PARAMETERS; MOVING COORDINATE SYSTEM; NON-EQUILIBRIUM SORPTION; SECOND-ORDER DIFFERENTIAL EQUATION; TRAVELING WAVE EQUATION; TRAVELING WAVE FRONTS; TRAVELING WAVE SOLUTION;

NONLINEAR EQUATIONS;

AQUIFER; CONTAMINATION; GROUNDWATER; GROUNDWATER PROCESSES; POROUS MEDIUM; SORPTION; TRAVELLING WAVE;

EID: 0030663682     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/97WR00301     Document Type: Article

References (22)

1. Bolt, G., Movement of solutes in soil: Principles of adsorption/ exchange chromatography, in Soil Chemistry B, Physico-Chemical Models, edited by G. Bolt, pp. 285-348, Elsevier, New York, 1982.
2. Bosma, W., and S. van der Zee, Analytical approximation for nonlinear adsorbing solute transport and first-order degradation, Transp. Porous Media, 11, 33-43, 1993.
3. Brusseau, M., P. Rao, R. Jessup, and J. Davidson, Flow interruption: A method for investigating sorption nonequilibrium, J. Contam. Hydrol., 4, 233-240, 1989.
4. Charbeneau, R., Groundwater contaminant transport with adsorption and ion exchange chemistry: Method of characteristics for the case without dispersion, Water Resour. Res., 17(3), 705-713, 1981.
5. Godfrey, K., and J. DiStefano, Identifiability of model parameters, in Identification and System Parameter Estimation 1985 - Proceedings of the Seventh IFAC/IFORS Symposium, vol. 1, edited by H. Barker and P. Young, Pergamon, pp. 89-114, Tarrytown, N. Y., 1985.
6. Godfrey, K., and J. DiStefano, Identifiability of model parameters, in Identifiability of Parametric Models, edited by E. Walter, Pergamon, pp. 1-20, Tarrytown, N. Y., 1987.
7. Helfferich, F., Theory of multicomponent chromatography: A state of the art report, J. Chromatog., 373, 45-60, 1986.
8. Helfferich, F., and G. Klein, Multicomponent Chromatography, Marcel Dekker, New York, 1970.
9. Lighthill, J., Waves in Fluids, Cambridge Univ. Press, New York, 1978.
10. Reichert, P., AQUASIM - A tool for simulation and data analysis of aquatic systems, Water Sci. Technol., 30(2), 21-30, 1994.
11. Reichert, P., Design techniques of a computer program for the identification of processes and the simulation of water quality in aquatic systems, Environ. Software, 10(3), 199-210, 1995.
12. Rhee, H.-K., and N. Amundson, A study of the shock layer in nonequilibrium exchange systems, Chem. Eng. Sci., 27, 199-211, 1972.
13. Rhee, H.-K., and N. Amundson, Shock layer in two solute chromatography: Effect of axial dispersion and mass transfer, Chem. Eng. Sci., 29, 2049-2060, 1974.
14. Rhee, H.-K., B. Bodin, and N. Amundson, A study of the shock layer in equilibrium exchange systems, Chem. Eng. Sci., 26, 1571-1580, 1971.
15. Rhee, H.-K., R. Aris, and N. Amundson, First-Order Partial Differential Equations, vol. II, Theory and Application of Hyperbolic Systems of Quasilinear Equations, Prentice Hall, Englewood Cliffs, N. J., 1989.
16. Schweich, D., M. Sardin, and M. Jauzein, Properties of concentration waves in presence of nonlinear sorption, precipitation/dissolution, and homogeneous reactions, 1, Fundamentals, Water Resour. Res., 29(3), 723-733, 1993a.
17. Schweich, D., M. Sardin, and M. Jauzein, Properties of concentration waves in presence of nonlinear sorption, precipitation/dissolution, and homogeneous reactions, 2, Illustrative examples, Water Resour. Res., 29(3), 735-741, 1993b.
18. Smoller, J., Shock Waves and Reaction-Diffusion-Equations, Springer-Verlag, New York, 1983.
19. van der Zee, S., Analytical traveling wave solutions for transport with nonlinear and nonequilibrium adsorption, Water Resour. Res., 26(10), 2563-2578, 1990.
20. van Duijn, C., and P. Knabner, Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange, 1, Transp. Porous Media, 8, 167-194, 1992a.
21. van Duijn, C., and P. Knabner, Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange, 2, Transp. Porous Media, 8, 199-225, 1992b.
22. Whitham, G. B., Linear and Nonlinear Waves, John Wiley, New York, 1974.