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A non-local description of advection-diffusion with application to dispersion in porous media

Koch, Donald L. and Brady, John F. (1987) A non-local description of advection-diffusion with application to dispersion in porous media. Journal of Fluid Mechanics, 180 . pp. 387-403. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120626-123241319

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Abstract

When the lengthscales and timescales on which a transport process occur are not much larger than the scales of variations in the velocity field experienced by a tracer particle, a description of the transport in terms of a local, averaged macroscale version of Fick's law is not applicable. Here, a non-local transport theory is developed in which the average mass flux is not simply proportional to the average local concentration gradient, but is given by a convolution integral over space and time of the average concentration gradient times a spatial- and temporal-wavelength-dependent diffusivity. The non-local theory is applied to the transport of a passive tracer in the advective field that arises in the bulk fluid of a porous medium, and the complete residence-time distribution - space-time response to a unit source input - of the tracer is determined. It is also shown how the method of moments may be simply recovered as a special case of the non-local theory. While developed in the context of and applied to tracer dispersion in porous media, the non-local theory presented here is applicable to the general problem of determining the average transport behaviour in advection-diffusion-type systems in which spatial and temporal variations are occurring on scales comparable with the scale of interest.


Item Type:Article
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http://dx.doi.org/10.1017/S0022112087001861DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=393420&fulltextType=RA&fileId=S0022112087001861PublisherUNSPECIFIED
Additional Information:© 1987 Cambridge University Press. Received February 14 1986. Revised October 6 1986. Published online: 21 April 2006.
Record Number:CaltechAUTHORS:20120626-123241319
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120626-123241319
Official Citation: Donald L. Koch and John F. Brady (1987). A non-local description of advection-diffusion with application to dispersion in porous media. Journal of Fluid Mechanics, 180 , pp 387-403 doi:10.1017/S0022112087001861
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32097
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Jun 2012 22:12
Last Modified:26 Dec 2012 15:23

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