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General Criteria for the Validity of the Buckingham‐Darcy Flow Law
Author(s) -
Sposito Garrison
Publication year - 1980
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1980.03615995004400060006x
Subject(s) - mathematics , momentum (technical analysis) , flow (mathematics) , isotropy , darcy's law , statistical physics , physics , classical mechanics , mechanics , geotechnical engineering , geology , quantum mechanics , finance , porous medium , porosity , economics
A detailed, first‐principles study is undertaken on the exact equation of linear momentum balance for water in an unsaturated soil. First, it is shown that an approximate momentum balance equation, presented originally by Raats and Klute, can be used to demonstrate unequivocably that the flow of water through a rigid, homogeneous, isotropic, unsaturated soil will obey the Buckingham‐Darcy law within 10 −12 to 10 −5 sec after a gradient in the total potential of soil water has been applied. Next, an exact equation of motion for the Fourier component of the water mass flux density vector is derived using standard methods in nonequilibrium statistical mechanics. This exact equation is employed to deduce the general physical criteria required for the Raats‐Klute equation to be an accurate expression. The results of the investigation lead to the conclusion that the Raats‐Klute equation will be accurate if: (i) the water mass density and mass flux density vector constitute a complete set of strongly coupled, macroscopic dynamical variables; and (ii) the time scale over which these two variables change significantly is much longer than that over which any other dynamical quantities vary. If these two conditions are met, then, according to statistical mechanics, the flow of water through unsaturated soil will be described accurately over all macroscopic time intervals by the Buckingham‐Darcy law.