From the assumptiox: that the microscopic behavior of the liquid in an unsaturated porous medium is controlled by the phYSlcallaws of surface tension and viscous flow, differential equations governing the macrosc:opic flow it; su~h a .medium ar: deduced. ~o sp~cial pore-shape assumptions are required, but one topolOgIcal approXImatlOn IS needed; I.e., that neither Isolated drops nor isolated bubbles occur. Several nonessential simplifying assumptions are used; i.e., that the macroscopic properties of the medium the character of the liquid, and the pressure of the gas are independent of position, time, and direction.' The macroscopic equations are obtained in a fully reduced form, permitting comparison between two mediaor between two flow systems-that differ only by scaling factors. A no:vel feature of this calculation is its prediction that the liquid-transmission and liquid-capacity proper~es of :m unsaturated me?ium will exhi~it hysteresis in their dependences upon tile liquid-gas pressure dlfferentlai, p. The properties of the medium depend upon the pressure history but are invariant to monotonic timescale distortions of that history. Such time-invariant functionals have been termed by the authors "hysteresis functions," symbolized by the subscript, H, e.g. FH(P). Although methods for measuring an~ ~escribin~ the char:,-cteristics of sl.'ecific "h~steresis functions" have not yet been developed, the general vabdlty of thiS analysIs can be studIed expenmentally bv testing predictions that are contained in the reduced variables. .

The hysteretic effects in the moisture characteristics and the hydraulic conductivity characteristics of two different glass‐bead media were measured while unsteady water flow was occurring. A gamma‐ray moisture sensor, a combination of pressure transducers and tensiometers, and a capillary‐tube flux meter were combined with a simple box‐like flow chamber for simultaneous measurement of (i) the degree of saturation, (ii) the water‐phase pressure, and (iii) the hydraulic conductivity. These quantities were recorded through out water‐pressure changes which traversed the main‐branch wetting and drying curves as well as the families of “rewet” and “redry” scanning loops. Large hysteresis was recorded in the relation of pressure to saturation or to conductivity. The relation of conductivity to saturation showed hysteresis which, though significantly larger than the experimental error, would for most practical purposes be negligible. The independent domain theory of hysteresis was used to check the relation between the “rewet” and “redry” families of moisture characteristics. By this test the theory was found to be very poorly suited to a description of these media. Two basic approximations of the theory were assumed to be responsible for this lack of applicability.

In the standard analysis of root water uptake, it is assumed there is a constant root membrane resistance in series with a soil resistance which is dependent upon the soil moisture diffusivity. The relation of root extraction rate to soil water content and to soil water potential predicted by this standard model was compared to the results of divided root experiments. The extraction rates predicted by the theory were as much as eight times larger than the measured values. A reasonable fit between theory and experiment could only be obtained by assuming in the theoretical calculations that the rooting density was 100 times smaller than that measured in the experiments. An alternative model emphasizing the possibility of a root‐soil contact effect was developed. It was assumed that as the soil dried, the surface area of the roots in contact with the soil decreased, which caused an increase in the root membrane resistance. By assuming that the effective root membrane permeability was simply proportional to the relative saturation of the soil, a much better fit to the data was obtained than by using the conventional theory.

A method has been developed for rapid, transient measurement of hysteretic soil‐moisture characteristics as a function of temperature. While a varying soil‐water pressure was imposed on a thin sample by means of flexible membranes held in firm contact with the soil, water content was measured by gamma‐ray attenuation, and matric potential was measured with tensiometers. The applied pressure was cycled through a program designed to obtain hysteretic θ(ψ) main and scanning curves. Isothermal characteristics were measured for 181‐µm glass beads, Plainfield (Typic Udipsamments) sand, and an undisturbed core of Plano (Typic Argiudolls) silt loam at several temperatures in the 4° to 50°C range. At each temperature the measurements included main drying and wetting curves covering the θ range from 0.30 to 0.05 m3 water/m3 for glass beads, 0.30 to 0.17 for sand, and 0.45 to 0.37 for silt loam. A model has been developed to quantify the temperature dependence as a function of θ. Combined with an isothermal hysteresis model of Mualem, this model requires only three characteristic functions to represent all hysteretic θ(ψ) curves for a given medium at all temperatures. Model calculations for the sand and silt loam data indicate that except near saturation, the temperature effect is greater than can be accounted for by the temperature dependence of the surface tension of pure water. The results rule out several possible explanations but they support the hypothesis that the concentration and effectiveness of dissolved surfactants increases with temperature.

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