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The effect of hydrodynamic dispersion on reactive flows in porous media

Published online by Cambridge University Press:  28 November 2001

J. CHADAM ,
P. ORTOLEVA ,
Y. QIN  and
R. STAMICAR
J. CHADAM
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PN, USA
P. ORTOLEVA
Affiliation:
Departments of Chemistry and Geology, Indiana University, IN, USA
Y. QIN
Affiliation:
Algorithmics Incorporated, Toronto, Canada
R. STAMICAR
Affiliation:
Department of Mathematics, McMaster University, University of Pittsburgh, USA
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Abstract

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 12 , Issue 5 , October 2001 , pp. 557 - 569
Copyright
2001 Cambridge University Press

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