Nonlocal dispersion in media with continuously evolving scales of heterogeneity
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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.
- Afrken, G., 1985,Mathematical Methods for Physicists, 3rd edn., Academic Press, San Diego, CA.
- Boone, J. P. and Yip, S. 1980,Molecular Hydrodynamics, McGraw-Hill, New York.
- Cushman, J. H., 1991, On diffusion in fractal porous media,Water Resourc. Res. 27, 643–644.
- Dieulin, A., Matheron, G. and de Marsily, G. 1981a, Growth of the dispersion coefficient with the mean travelled distance in porous media,Sci. Total Environ.,21, 319–328.
- Dieulin, A., Matheron, G., de Marsily, G. and Beaudoin, B., 1981b, Time dependence of an ‘equivalent dispersion coefficient’ for transport in porous media, in A. Verruijt and F. B. J. Barends (eds.),Proc. Euromech 143, Delft 1981, Balkema, Rotterdam, The Netherlands, pp. 199–202.
- Kinzelback, W. and Uffink, G. 1991. The random walk method and extensions in groundwater modelling, in J. Bear and M. Y. Corapcioglu (eds.),Transport Processes in Porous Media, Kluwer Academic Publishers, The Netherlands, pp. 761–787.
- Scheibe, T. and Cole, C., 1993, Non-Gaussian particle tracking: application to scaling of transport processes in heterogeneous porous media, unpublished manuscript, submitted toWater Resour. Res.
- Schiedegger, A. E., 1958, The random-walk model with autocorrelation of flow through porous media,Can. J. Phys. 36, 649–658.
- Van Hove, L., 1957, Non-Markovian many-body kinetics from perturbation technique,Physica,23 441–444.
- Zwanzig, R., 1960, Ensemble method in the theory of irreversibility,J. Chem. Phys. 33, 1338–1341.
- Zwanzig, R. W., 1961, Statistical Mechanics of Irreversibility, in W. E. Brittin, B. W. Downs, and J. Downs (eds.),Lectures in Theoretical Physics, Vol. III, Interscience, New York, pp. 106–141.
- Zwanzig, R. W., 1964, Incoherent inelastic neutron scattering and self-diffusion,Physical Review 133(1A) A50-A51.
- Nonlocal dispersion in media with continuously evolving scales of heterogeneity
Transport in Porous Media
Volume 13, Issue 1 , pp 123-138
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- Nonlocal dispersion
- Lagrangian dynamics
- memory function
- heterogeneous porous media
- statistical mechanics
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