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Sorptivity and macroscopic capillary length relationships
Author(s) -
Warrick A. W.,
Broadbridge P.
Publication year - 1992
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr02599
Subject(s) - sorptivity , hydraulic conductivity , ponding , mathematics , capillary action , thermal diffusivity , exponential function , thermodynamics , mathematical analysis , soil science , hydrology (agriculture) , geotechnical engineering , geometry , physics , soil water , geology , ecology , compressive strength , drainage , biology
The relationship of sorptivity S and macroscopic capillary length λ c is explored. Sorptivity is the proportionality constant between cumulative intake, expressed as a length, and the square root of time for sorption into an unsaturated soil. The capillary length is defined as the integral of the unsaturated hydraulic conductivity with respect to matric potential normalized by the difference between the conductivity at the two limits of integration. The approximation b = λ c (θ wct ‐ θ dry )( K wct ‐ K dry ) S −2 was found previously to have bounds of 0.5 and π/4, with 0.55 as a good overall approximation. Those results were for two diffusivity functions, an exponential D = D 0 exp ( B θ) and for D = D 0 (θ b ‐ θ) −2 . We now extend the investigation to four additional cases, two for which S and λ c are analytical and two described by the empirical hydraulic functions of Brooks and Corey (1964) and by van Genuchten (1980). The representative value b = 0.55 was found to be generally correct. For those functions with a finite D value at the wettest value, a refinement from the 0.55 value is offered. The results are believed of value for future parameter estimation problems, including two previous applications related to time of ponding and disk infiltrometers.