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Analytical Expression for Soil Water Diffusivity Derived from Horizontal Infiltration Experiments

Dep. of Soil and Water Science, 429 Shantz 38, Univ. of Arizona, Tucson, AZ 85721

*Corresponding author.

ABSTRACT

A technique is developed that utilizes a rational function = (A₁ + A₃)/(1 + A₂) to fit water content (or other liquid) profiles resulting from horizontal infiltration as used in the Bruce-Klute method for determining soil water diffusivity. In the above function, is water content (L³ L^–3), is the Boltzmann variable, and A₁, A₂, and A₃ are constants. The Boltzmann variable, , is equal to xt^-0.5, where x is the distance from the inlet of a horizontal soil column and t is time from the commencement of liquid imbibition. The function is easily fit to experimental data by either linear or nonlinear regression techniques and leads to analytical expressions for sorptivity and soil water diffusivity without further numerical approximation or fitting. If boundary conditions are specified, only one of the three coefficients is left to be determined. The rational function provided excellent approximations to liquid distribution for water and alcohol horizontal infiltration experiments in this study and is adequate for representation of experimental data of several other researchers. An example is included to illustrate that the approach is also applicable to determination of diffusivity for the hot-air method.

Journal no. 7166 of the Arizona Agric. Exp. Stn. Support in part by Western Regional Project W-155.

Received for publication December 11, 1989.

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