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Soil Water Diffusivity as Explicitly Dependent on Both Time and Water Content

Dep. de Fisica e Biofisica, UNESP, Botucatu, Sao Paulo State, Brazil

D. Swartzendruber^*

Dep. of Agronomy, Univ. of Nebraska, Lincoln, NE 68583

* Corresponding author.

ABSTRACT

Reliable experimental data do not always conform with customary soil-water flow theory for truly rigid porous media. The purpose of this study was to derive a mathematical description capable of accommodating such data. A new mathematical solution was obtained for the absorption of water by an unsaturated horizontal column of soil termed semirigid, but which does not swell in the ordinary sense of a change in bulk density. Nonetheless, the semirigid soil does undergo microlevel rearrangement of its particles, envisaged as introducing an auxiliary dependence on time t into the diffusivity D in addition to the usual dependence on the volumetric water content, that is, D = D(,t). With product-form separation of variables introduced at two stages of the solution process, there emerges the new variable equal to distance x divided by a new time function [Q(t)]^1/2. Subject to modest constraint, Q(t) may be selected to best describe the particular soil in question. Choosing [Q(t)]^1/2 = tⁿ with exponent n as a positive constant, thus yielding = xt^-n instead of the classical Boltzmann form xt^–1/2, the new solution was tested experimentally on a set of published data not conforming to customary flow theory for rigid media. The new solution provided a greatly improved description of these data, with exponent n = 0.46362 instead of 1/2 as for rigid media. The diffusivity function is D(,t) = 2nE()t^2n-1, where E() is a diffusivity-like function of alone.

Contribution from the Agricultural Research Division, Univ. of Nebraska, Lincoln; Journal Series Paper no. 9425; supported also by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, CNPq, Brazil.

Received for publication November 6, 1990.