Sorption and infiltration in heterogeneous media

Abstract

Problems of unsteady water transfer in unsaturated heterogeneous media are mathematically very complicated, and, in general, each problem for each medium requires its own ad hoc solution (e.g, by high speed computer). The approach is necessarily a piecemeal one and does not lead readily to generalizations. This paper reports a first attempt at an alternative method of attack, in which we identify and explore subclasses of problems that are amenable to quasi-analytical methods of analysis. The work deals, specifically, with problems of absorption and desorption in one-dimensional heterogeneous media. The extension to one-dimensional infiltration is also indicated. We consider 'scale-heterogeneous' media, i.e, media in which the internal geometry is everywhere geometrically similar but in which the characteristic internal length scale is free to vary spatially. The spatial variation of the hydraulic conductivity function and of the capillary potential function are thus connected. It is shown that, if the conductivity and potential functions are of certain simple forms (which are reasonable approximations to those found for soils, at least over certain ranges of potential), the flow equation, with potential as a variable, may be solved readily by established methods. The potential profiles preserve similarity, but the moisture profiles (which are found by a simple supplementary calculation) do not. Examples are given of absorption and desorption in five scale-heterogeneous media. The examples are for �0/�1 = 100 (absorption) and 0.01 (desorption), where �0 is the initial potential and �1 is the potential at which water is supplied to, or removed from, the surface. The solutions may be adapted very simply to apply to any other scale-heterogeneous medium of this class. They can also be extended readily to embrace other values of �0/�1, by reference to solutions in the literature, or by use of a rapid and accurate numerical method. Solutions of the corresponding one-dimensional infiltration problem may be found by similar means, use being made of quasi-analytical methods previously established in the analysis of infiltration in homogeneous media.