ANALYTICAL EXPRESSION FOR SOIL-WATER DIFFUSIVITY DERIVED FROM HORIZONTAL INFILTRATION EXPERIMENTS

A technique is developed that utilizes a rational function theta = (A1 + A3-lambda)/(1 + A2-lambda) 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, theta is water content (L3 L-3), lambda is the Boltzmann variable, and A1, A2, and A3 are constants. The Boltzmann variable, lambda, 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 inhibition. 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.