Sorptivity and macroscopic capillary length relationships

The relationship of sorptivity S and macroscopic capillary length λc 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 = λc(θwct ‐ θdry)(Kwct ‐ Kdry)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 = D0 exp (Bθ) and for D = D0(θb ‐ θ)−2. We now extend the investigation to four additional cases, two for which S and λc 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.