Transport in Porous Media

, Volume 13, Issue 1, pp 123-138

First online:

Nonlocal dispersion in media with continuously evolving scales of heterogeneity

  • John H. CushmanAffiliated with1150 Lilly Hall, Purdue University
  • , T. R. GinnAffiliated withPacific Northwest Laboratory

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General nonlocal diffusive and dispersive transport theories are derived from molecular hydrodynamics and associated theories of statistical mechanical correlation functions, using the memory function formalism and the projection operator method. Expansion approximations of a spatially and temporally nonlocal convective-dispersive equation are introduced to derive linearized inverse solutions for transport coefficients. The development is focused on deriving relations between the frequency-and wave-vector-dependent dispersion tensor and measurable quantities. The resulting theory is applicable to porous media of fractal character.

Key words

Nonlocal dispersion Lagrangian dynamics memory function heterogeneous porous media statistical mechanics