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.
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References
J. H. Cushman Introduction toDynamics of Fluids in Porous Media, J. H. Cushman, ed. (Academic, London, 1990).
M. Avellaneda and A. J. Majda,Commun. Math. Phys. 131:381 (1990).
H. Brenner,Phil. Trans. R. Soc. Lond. A 297:80 (1980).
J. Glimm and D. H. Sharp,J. Stat. Phys. 62(1/2): 415 (1991).
C. C. Mei and J.-L. Auriault,Proc. R. Soc. Lond. A 426:391 (1989).
S. P. Neuman,Water Resource Res. 29:633 (1993).
S. Whitaker,J. Am. Inst. Chem. Eng. 3(13):420 (1967).
J. Glimm, W. B. Lindquist, F. Pereira, and Q. Zhang,Transport Porous Media 13(1):97 (1993).
S. W. Wheatcraff and J. H. Cushman, U. S. National Report to International Union Geodesy and Geophysics, 1987–1990,Rev. Geophys. 1991:263.
D. A. McQuarrie,Statistical Mechanics (Harper and Row, 1976).
R. W. Zwanzig,Phys. Rev. 133(1A):A50 (1964).
J. P. Boone and S. Yip,Molecular Hydrodynamics (McGraw-Hill, New York, 1980).
B. J. Berne and R. Pecora,Dynamic Light Scattering (Wiley, New York, 1976).
J. H. Cushman and T. R. Ginn,Transport Porous Media 13(1):123 (1993).
J. H. Cushman and T. R. Ginn,Water Resources Res. 29(10):3513 (1993).
J. H. Cushman,Water Resources Res. 27(4):643 (1991).
F. W. Deng, J. H. Cushman, and J. W. Delleur,Water Resources Res. 29(9):3241 (1993).
G. Dagan,J. Fluid Mech. 145:151 (1984).
Z. J. Kabala and G. Sposito,Water Resources Res. 27(3):341 (1991).
J. Bear,Dynamics of Fluids in Porous Media (Elsevier, 1972).
S. E. Serrano,Water Resources Res. 28(7):1801 (1992).
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Cushman, J.H., Hu, X. & Ginn, T.R. Nonequilibrium statistical mechanics of preasymptotic dispersion. J Stat Phys 75, 859–878 (1994). https://doi.org/10.1007/BF02186747
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DOI: https://doi.org/10.1007/BF02186747