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Short-time asymptotics of hydrodynamic dispersion in porous media

Published online by Cambridge University Press:  17 September 2013

Tyler R. Brosten
Tyler R. Brosten*
Affiliation:
US Army Engineer Research and Development Center, Vicksburg, MS 39180, USA
*
†Email address for correspondence: [email protected]
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Abstract

We consider convection–diffusion transport of a passive scalar within porous media having a piecewise-smooth and reflecting pore–grain interface. The corresponding short-time expansion of molecular displacement time-correlation functions is determined for the generalized steady convection field. By interpreting the generalized short-time expansion of dispersion dynamics in the context of low-Reynolds-number flow through macroscopically homogeneous porous media, we demonstrate the connection between hydrodynamic permeability and short-time dynamics. The analytical short-time expansion is compared with numerical simulation data for steady low-Reynolds-number flow through a random close-pack array of mono-disperse spheres. The quadratic short-time expansion term of the dispersion coefficient closely predicts the numerical data for a mean displacement of at least 10 % of the sphere diameter for a Péclet number of 54.49.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 732 , 10 October 2013 , pp. 687 - 705
Creative Commons
This is a work of the U.S. Government and is not subject to copyright protection in the United States.
Copyright
©2013 Cambridge University Press.

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