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Diffusion and dispersion in porous media
Author(s) -
Whitaker Stephen
Publication year - 1967
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690130308
Subject(s) - laminar flow , tortuosity , dispersion (optics) , porous medium , diffusion , partial differential equation , dispersion relation , mechanics , flow (mathematics) , differential equation , compressibility , diffusion equation , anisotropy , mathematical analysis , physics , mathematics , chemistry , thermodynamics , porosity , optics , economy , organic chemistry , economics , service (business)
The dispersion equation for a single, nonreacting, nonadsorbing species is derived for incompressible, laminar flow in anisotropic porous media. Direct integration of the appropriate differential equations gives rise to a dispersion vector ψ i and a tortuosity vector τ i , both of which must be evaluated experimentally. For the dispersion vector, this is conveniently done by representing ψ i in terms of the velocity and gradients of the velocity and concentration. The experimental determination of τ i is not straightforward except for the case of pure diffusion. The analysis yields a result which contains all the features of previously presented dispersion equations without making any assumptions as to the nature of the flow, that is, bypassing, cell mixing, etc., except that it be laminar. Attacking the dispersion problem in terms of the differential diffusion equation provides a rational basis for the correlation of experimental data and illustrates the connection between the microscopic and macroscopic equations.