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

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, θ that is, D = D (θ, t ). With product‐form separation of variables introduced at two stages of the solution process, there emerges the new variable λ 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 λ = 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 (θ, t ) = 2 nE (θ) t 2 n ‐1 , where E (θ) is a diffusivity‐like function of θ alone.