Soil water diffusivity as explicity dependent on both time and water content
Guerrini, I.A. | Swartzendruber, D.
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, theta, that is, D = D(theta,t). With product-form separation of variables introduced at two stages of the solution process, there emerges the new variable lambda 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) = t(n) with exponent n as a positive constant, thus yielding lambda = 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(theta,t) = 2nE(theta)t(2n-1), where E(theta) is a diffusivity-like function of theta alone.
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