Journal of Statistical Physics

, Volume 75, Issue 5–6, pp 859–878 | Cite as

Nonequilibrium statistical mechanics of preasymptotic dispersion

  • John H. Cushman
  • Xiaolong Hu
  • Timothy R. Ginn
Articles
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Accepted:

Abstract

Turbulent transport in bulk-phase fluids and transport in porous media with fractal character involve fluctuations on all space and time scales. Consequently one anticipates constitutive theories should be nonlocal in character and involve constitutive parameters with arbitrary wavevector and frequency dependence. We provide here a nonequilibrium statistical mechanical theory of transport which involves both diffusive and convective mixing (dispersion) at all scales. The theory is based on a generalization of classical approaches used in molecular hydrodynamics and on time-correlation functions defined in terms of nonequilibrium expectations. The resulting constitutive laws are nonlocal and constitutive parameters are wavevector and frequency dependent. All results reduce to their convolution-Fickian quasi-Fickian, or Fickian counterparts in the appropriate limits.

Key Words

Preasymptotic dispersion nonequilibrium porous medium heterogeneity 
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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • John H. Cushman
    • 1
  • Xiaolong Hu
    • 1
  • Timothy R. Ginn
    • 2
  1. 1.Purdue UniversityWest Lafayette
  2. 2.Pacific Northwest LaboratoryRichland

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