Unsaturated seepage flow from a horizontal boundary
Introduction. A knowledge of the time-depth history of infiltration from rainfall or irrigation water into a permeable soil is useful for soil-moisture and ground-water studies and in the analysis of the movement and dispersal of dissolved or suspended materials such as nutrients or pollutants. If these materials are subject to adsorption by soil, the concentration profiles which develop are influenced by the amount and timedistribution of water application. Since the physical system leads to a rather special form of nonlinear transport equation, its properties are reviewed briefly. (a) Since the soil is generally unsaturated in the infiltration zone, flow is induced by capillarity as well as gravity, and the system exhibits strongly nonlinear properties. Comprehensive reviews [1,2] discuss the literature on this problem. (b) Capillarity is subject to hysteresis effects, so that at each point in the porous medium, the relationship between capillary pressure and soil moisture is dependent upon previous history. A convenient mathematical description of the hysteresis phenomenon in porous materials does not exist at present [3, 4], (c) Usually the principal boundary condition—the availability of water at the soil surface expressed as a flux—exhibits time dependence, and may be a variable with 'stochastic' properties. Only in the case of either ponding or zero input can a steady surface condition be expected to prevail. (d) In unsaturated flow, some water may be 'bound', e.g. by adsorption or by entrapment in dead-end pores [5]. If the amount of bound water depends nonlinearly upon the total water present in unit volume, there will be some influence upon the flow characteristics. (e) Variation of permeability with depth may be important, and can become extreme in certain hydrophobic ('water-repellent') surface conditions. It is then possible for the wetting front to become unstable [6] and complicated three-dimensional flows can develop. (f) Infiltration of water into an air-filled porous medium leads to a two-phase flow problem [7], The buildup of pressure due to entrapped air reduces the rate of infiltration, and instability such as that discussed in (e) can again occur. Some indications of 'fingering', suggestive of instability, have been observed [8], Several authors [1, 9, 10] have examined the problem of infiltration into a uniform porous medium when the moisture content at the surface is suddenly increased, e.g. by flooding, so that the boundary moisture condition has a step-function time dependence. Effects of capillary hysteresis were not considered by these authors, since the problem