Macroscopic and microscopic capillary length and time scales from field infiltration

Estimates of characteristic times to approach steady state flow in multidimensional infiltration in the landscape depend on the magnitude and character of the capillary length scale λc and the associated capillary time scale tc. Here we derive relationships between λc and tc and readily measured field properties sorptivity S and hydraulic conductivity K or S at two supply heads. We explore the relations between λc and tc and other macroscopic and microscopic length, potential, and time scales. In addition, we show that the microscopic characteristic length λm associated with λc gives physically plausible estimates of flow-weighted mean pore dimensions. We contrast values of λc, tc, and λm for undisturbed field soils with those of repacked materials for water supply potentials close to zero. Large λm for the undisturbed surface soils are attributed to preferential flow. Data from here and elsewhere reveal no apparent trend of λc with soil texture, with most λc of the order of 100 mm. We suggest that the characteristic size of devices used to determine hydraulic properties of field soils should be greater than or equal to λc for representative measurements. The geometric mean time of approach to steady state flow when water is supplied at potentials near or greater than zero is found to be 1.7 hours. This value together with published results suggest that the time of approach to steady state flow from multidimensional cavities is of the order of 1 hour for many field situations.

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