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The effect of order on dispersion in porous media

Published online by Cambridge University Press:  26 April 2006

Donald L. Koch ,
Raymond G. Cox ,
Howard Brenner  and
John F. Brady
Donald L. Koch
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853
Raymond G. Cox
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, 3480 University Street, Montreal, Quebec H3A 2A7, Canada
Howard Brenner
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
John F. Brady
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125
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Abstract

The effect of spatial periodicity in grain structure on the average transport properties resulting from flow through porous media are derived from the basic conservation equations. At high Péclet number, the mechanical dispersion that is induced by the stochastic fluid velocity field in disordered media and is independent of the molecular diffusivity is absent in periodic media where the velocity field is deterministic. Instead, the fluid motion enhances diffusion by an amount proportional to U2l2/D when the bulk flow is in certain directions (of which there are an infinite number), and to D otherwise. The non-mechanical dispersion mechanisms associated with the zero velocity of the fixed grains is qualitatively similar in ordered and disordered media.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 173 - 188
Copyright
© 1989 Cambridge University Press

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