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Temperature effects on water absorption by three different porous materials.

Introduction

Effects of temperature on liquid water flow in porous materials are attributed to the temperature dependences of the kinematic viscosity and of the surface tension of water as tabulated in standard physical tables (e.g. Weast 1978). The former effect relates to viscous flow; surface tension affects the capillary potential. Frequently, however, experiments reveal behaviour requiring more complicated explanations. Nimmo and Miller (1986) reviewed reports of the temperature effect on the soil water content-water potential function and also measured these effects on glass beads and 2 different soils. They found that, except near saturation, temperature effects were greater than would be expected from the temperature dependence of the surface tension of pure water. They also observed that surfactant effects appeared to increase with temperature. Grant and Bachmann (2002), in a more recent survey of such experiments, also concluded that effects of temperature on the water potential are often several times greater than would be expected from the temperature dependence of the surface tension of pure water alone. They attributed effects to volume change of the water and of entrapped air, to interracial tension effects associated with solutes, and to the effect of temperature on contact angles.

Other papers (e.g. Constantz 1982; Stoffregen et al. 1997) also identify concerns where the response of steady liquid water flow to temperature change substantially exceeds effects that might simply be attributed to the temperature dependence of the kinematic viscosity of water. Hopmans and Dane (1986a), on the other hand, found temperature effects on steady flow to be generally consistent with the temperature dependence of the kinematic viscosity of water, although they also observed effects exceeding that of surface tension on the water potential characteristic. They discounted temperature affects due to entrapped air.

It is difficult to generalise, but it appears that the greatest difficulty arises in unsaturated porous materials where a temperature change occurs at 'static' equilibrium or during steady flow. These cases seem, qualitatively, to be consistent with the observations of Grant and Bachmann (2002). At the same time, some of these papers describe flow conditions and water content profiles that are very difficult to control. Stoffregen et al. (1997), for example, describe experiments where steady upwards flow in a column of soil was driven by a suction of 500cm [H.sub.2]O maintained through a plate in contact with the top of the column while a suction of 50cm [H.sub.2]O was maintained at its base. Constantz (1982) established upwards vertical flow by imposing an evaporative flux at the top hut similarly imposed a constant suction at the base of an unsaturated column of soil. Regrettably, neither of these authors describes their calculation of the hydraulic conductivity, the mean value of which must be an integral average of the conductivity--capillary potential function in a region of the column where the capillary potential gradient is very steep because of the gravity term (Smiles and Towner 1968). Few experiments involve unsteady flow. Gardner (1959) measured the temperature dependence of integral absorption behaviour; his data are ambiguous but they approximate expectation based on simple theory. Bachmann et al. (2002) measured the temperature dependence of water retention curves during outflow and absorption into some wettable and water repellant soils, but time dependence of the water retention curves (Smiles et al. 1971) may affect their data during drainage.

This note describes non-steady water flow experiments, conducted at 3 different constant temperatures during (a) absorption by initially relatively dry loam, (b) absorption of water by chromatography paper, and (c) desorption of saturated swelling clay. The analyses derive from that of Bruce and Klute (1956) and the experiments are simple enough to illustrate basic physical principles of flow in 3 physically different materials. They reveal behaviour that is simply related to the temperature dependence of the kinematic viscosity and the surface tension of pure water.

Theory

Refer to Table 1 for nomenclature used in this paper. Theory of equilibrium and flow of water in unsaturated soils treats flow as viscous and with the capillary potential related to the surface tension of water. Stoffregen et al. (1997) provide a useful summary. We presume that the horizontal flux, v, of water at temperature, T, is described by Darcy's law in the form

(1) v = -(([[mu].sub.293]/[[mu].sub.T]) [K.sub.293]([THETA]))([differential](([[sigma].sub.T]/[[sigma].sub.293]) [[psi].sub.293]

= -K([THETA])(([sigma]/[mu] / [([sigma]/mu]).sub.293])([differential][psi]/[differential]X)

We use 293 K as datum and T is the temperature at which measurements are made. Thus:

(i) [K.sub.293]([THETA]) is the hydraulic conductivity at 293K and ([[mu].sub.293]/[[mu].sub.T])x[K.sub.293]([THETA]) = [K.sub.T]([THETA]) is the hydraulic conductivity at temperature T, where [mu] the kinematic viscosity of water at the temperature identified by the subscript 293 or T. Equation 1 presumes that the permeability, ([[mu].sub.T]) x [K.sub.T]([THETA]), for viscous flow measured at any T is independent of T and the liquid and is a property only of the internal geometry of the medium (Terzaghi 1923; Childs 1969; Hopmans and Dane 1986b).

(ii) Similarly, [[psi].sub.293] is the suction at 293K and [[psi].sub.T] =([[sigma].sub.T]/([[sigma].sub.293]) x [[psi].sub.293] is the suction at T, while [sigma] is the surface tension of water at an air-water interface at each temperature (Philip and de Vries 1957).

In addition, [THETA] is the water content and X is distance. The dimensions of [THETA] and X (and consequently those of K([THETA])), which must be mutually consistent, differ depending on the nature of the experimental materials and are explained for each experimental set below.

Both [mu] and [sigma] are temperature-dependent properties of water and of the air-water interface (Weast 1978) and we presume that neither depend of [THETA] or X, so they might be grouped in the second equality of Eqn 1. Figure 1 shows how ([mu]/[sigma]) and [mu] of pure water vary with T over the temperature range of the experiments described here. The curves are normalised relative to the value of these variables at 293 K. The second graph is included to illustrate the relatively minor effect (in principle) of [sigma], which is much less temperature-sensitive than is [mu]. Temperature effects derive from the slopes of these graphs rather than their absolute values. The absolute value is subsumed in measurement of K([THETA]).

[FIGURE 1 OMITTED]

The water flow equation is derived (Richards 1931) by combining Eqn 1 with the 1-dimensional material balance equation for the water:

(2) [differential][THETA]/[differential]t = -[differential]v/[differential]X

in which t is time. The use the first equality on the right hand side of Eqn 1 yields, for non-hysteretic flow, the equation:

(3) [differential][THETA]/[differential]t = [differential]/[differential]X ([D.sub.T]([THETA]) [differential]([THETA])/[differential]X)

in which [D.sub.T]([THETA]) is a water diffusivity at temperature T defined (Childs and George 1948) by:

(4) [D.sub.T]([THETA]) = [K.sub.T]([THETA])) (d[[psi].sub.T]/d[THETA])

and where d[[psi].sub.T]/d[THETA] is the slope of the moisture characteristic measured at T.

Alternatively, combination of Eqn 2 with the second equality in Eqn 1 yields:

(5) [differential][THETA]/[differential]t = [differential]/[differential][X.sup.*] ([D.sub.293]([THETA]) [differential][THETA]/[differential][X.sup.*]) with

(6) [X.sup.*] = [([([mu]/[sigma]).sub.T]/[([mu]/[sigma]).sub.293]).sup.1/2] X and

(7) [D.sub.293]([THETA]) = [K.sub.293]([THETA])(d[[psi].sub.293]/d[THETA])

and where d[psi]/d[THETA] is the slope of the moisture characteristic at 293 K.

Each of our experiments involves initial and boundary conditions defined by:

(8) [THETA] = [[THETA].sub.i]; X or [X.sup.*] [greater than or equal to] 0; t = 0 [THETA] = [[THETA].sub.0]; X or [X.sup.*] = 0; t > 0

Introduction of the Boltzmann variable [LAMBDA] = X/[square root of t] to Eqn 3 and Eqn 8, or [[LAMBDA].sup.*] = [X.sup.*]/[square root of t] to Eqns 5 and 8, eliminates X and [X.sup.*] and t from these equations, which become:

(9) d/d[LAMBDA]([D.sub.T]([THETA])d[THETA]/d[LAMBDA]) + [LAMBDA]/2 d[THETA]/[LAMBDA] = 0

(10) d/d[[LAMBDA].sup.*]([D.sub.293]([THETA])d[THETA]/d[[LAMBDA].sup.*]) + [[LAMBDA].sup.*]/2 d[THETA]/d[[LAMBDA].sup.*] = 0

(11) [THETA] = [[THETA].sub.i]; [LAMBDA] or [[LAMBDA].sup.*] [right arrow] [infinity] [THETA] = [[THETA].sub.0]; [LAMBDA] ro [[LAMBDA].sup.*] = 0

Equations 9 and 11 imply that if flow is described by Eqn 3 and if Eqns 8 are realised then [THETA]([LAMBDA]) will be unique for each temperature T. On the other hand, Eqns 10 and 11 imply that if Eqns 5 and 8 are valid then [THETA]([[LAMBDA].sup.*]will be unique for all temperatures with data normalised with regard to flow conditions at 293 K in the range of temperatures for which viscous liquid flow occurs.

Materials and methods

Experiments consistent with Eqns 3, 5, and 8 were performed at constant temperatures of 277.5 [+ or -] 0.5 K, 293 [+ or -] 0.5 K, and 303-306 [+ or -] 0.5 K, and at each temperature, experiments were replicated and terminated at different times to test the Boltzmann scaling associated with the use of [LAMBDA] and [[LAMBDA].sup.*]. Three different porous materials were used.

Absorption of water by a non-swelling soil

These experiments were similar to those of Bruce and Klute (1956) as performed by Smiles et al. (1978). A uniform horizontal column of relatively dry soil absorbed saturated CaS[O.sub.4] solution from a source at a small constant negative potential. Properties of this soil are presented in Table 2. Gypsum was used to prevent dispersion of clay and consequent structure change.

The column was cut into short sections to terminate the experiment and the water content distribution was determined by oven drying each section. Care was taken to retain all the soil from each section. Experiments were performed at 3 different temperatures and they were repeated with different termination times within each temperature set. In these experiments, [THETA] is expressed as the water mass fraction (kg/kg) and A is the cumulative mass of soil per unit cross-section of the column (measured from the inflow end) per unit square root of time (kg/[m.sup.2].[s.sup.1/2]) (Smiles 2001). The water content profiles are graphed as ([THETA])([LAMBDA]) and [THETA]([[LAMBDA].sup.*]).

Absorption of water by chromatography paper

Chromatography paper is used by chemical engineers to determine simply the filterability of muds and slurries. These experiments were identical to those described by Smiles (1998). A horizontal strip of dry Whatman #17 chromatography paper absorbed distilled water from a reservoir at zero suction at one end of it. The strip of paper, which was ~1 mm thick, was cut into short sections with scissors and oven-dried after different elapsed times to test [THETA]([LAMBDA]) scaling at each temperature. [THETA]([[LAMBDA].sup.*]) profiles were also graphed. Chromatography paper increases in thickness as it wets (Smiles 1998), so the water content, [THETA], in this case is expressed as the amount of water per unit area of horizontal cross section of the paper (kg/[m.sup.2]), and A is the cumulative area of paper per unit width per unit square root of time (m/[s.sup.1/2]), measured from the end where the water was applied.

Desorption of water by a saturated clay paste

In these experiments, bentonite slurries with initial water contents of 12.2 kg water/kg clay mineral were filtered through a 0.45-[micro]m membrane under a sustained constant air pressure of 48 cm Hg. The filter membrane permits the water to escape easily but prevents passage of the clay. The water content profiles were obtained at appropriate elapsed times by serial sectioning and oven drying (Smiles and Rosenthal 1968). In these experiments, [THETA] is expressed as the mass of water per unit mass of clay and [LAMBDA] is the cumulative mass of clay per unit area measured away from the filter membrane, per square root of time.

Properties of the clay are presented in Table 3.

Experimental results

Absorption of water by non-swelling soil

Figure 2 shows [THETA]([LAMBDA]) profiles for the non-swelling soil at 278 K, 293 K, and 304 K, whereas Fig. 3 shows these data normalised to 293 K and graphed as [THETA]([[LAMBDA].sup.*]). Figure 2 shows, within acceptable experimental error (Smiles and Smith 2004), that the [THETA]([LAMBDA]) profiles for each temperature are unique despite the different times at which the columns were sectioned. That is, they preserve similarity in terms of A for each temperature. We therefore conclude that the basic flow equations are valid and the initial and boundary conditions are realised. These profiles reveal greater penetration of water as the temperature increases from 278 K to 304 K. They do not appear to reveal effects associated with temperature on [[THETA].sub.0].

[FIGURES 2-3 OMITTED]

Figure 3 shows that normalisation of the Fig. 2 data according to the temperature dependence of the kinematic viscosity and the surface tension of pure water at 293 K reduces the [THETA]([LAMBDA]) profiles to a single curve that corresponds with those for the experiments performed at 293 K.

Within acceptable experimental error, there is no reason to invoke effects other than surface tension and viscosity of pure water to deal with temperature dependence in these datasets. Saturated gypsum was used in these experiments to minimise structural change during absorption and this invading solution displaced soil water of field composition shown in the saturation extract data presented in Table 2. Smiles and Smith (2004) illustrate the magnitude of the chemical changes associated with dispersion and chemical reaction for this soil and show that this is, chemically, a relatively 'dirty' system with the soil close to the inflow surface dominated by a saturated gypsum solution and that near and beyond the piston front in equilibrium with [K.sup.+] and [Ca.sup.2+] with [Cl.sup.-] and N[O.sub.3.sup.-] the dominant anions. Analytical detail for this system, where gypsum displaces the ions initially present, is available from the author.

Absorption of water by chromatography paper

Figures 4 and 5 show [THETA]([LAMBDA]) and [THETA]([[LAMBDA].sup.*]) profiles for the chromatography paper at 278 K and 304 K. These figures also show that absorption of water was more rapid at the higher than the lower temperatures. Similarity is again preserved in [THETA]([LAMBDA]) for each temperature (Fig. 4) and in [THETA]([[LAMBDA].sup.*]) (Fig. 5) when flow is normalised according to a temperature of 293 K. This normalised profile corresponds to that measured at 293 K (see Smiles 1998). The 293 K data were not included here to avoid cluttering the figures. Thus, the flow equation again appears appropriate, the initial and boundary conditions are realized, and the surface tension and viscosity of pure water are sufficient to describe the observed temperature dependence of absorption of distilled water by chemically 'clean' chromatography paper. As with the soil, there appears to be no evidence of a temperature effect on [[THETA].sub.0].

[FIGURES 4-5 OMITTED]

Desorption of water by a saturated clay paste

Figure 6 shows desorption [THETA]([LAMBDA]) profiles for saturated bentonite subject to constant filtration pressure at 277 K and 306 K. Again, similarity is preserved so we presume that the flow equation is valid and the initial and boundary conditions are realised. The colder material loses water more slowly than does the warmer one. In the case of the desorbing clay, however, the system remained water-saturated throughout (the volume change equals the volume of water that escapes) and we do not expect surface tension effects associated with air-water interfaces to be observed. Figure 7, therefore, shows the data of Fig. 6 simply scaled according to the viscosity ratio (Terzaghi 1923) and graphed as [THETA]([[LAMBDA].sup.**]) where:

[FIGURES 6-7 OMITTED]

(12) [[LAMBDA].sup.**]/[LAMBDA] = [square root of ([[mu].sub.T]/[[mu].sub.293 K)]

Figure 7 also includes data derived from experiments performed at 293 K, which, to reduce 'clutter', were not graphed in Fig. 6. Evidently, simple scaling according to the temperature dependence of the kinematic viscosity of pure water again effectively eliminates differences between datasets generated at different temperatures in these clay systems.

Discussion

The effect of temperature on water relations in soil is generally measured during conditions of static equilibrium or steady flow. Effects of temperature change on [THETA], [psi], or v are then measured and related variously to temperature effects on viscosity, surface tension, volume change of entrapped air, or other effects due, for example, to surfactants. It is difficult, however, to impose and sustain steady, unsaturated vertical flow in soils, so the experiments tend to be complicated and their interpretation often ambiguous (e.g. Constantz 1982; Stoffregen et al. 1997).

Here, we explored cases of unsteady flow during sorption to or from sources at constant potential that are well understood analytically and are relatively easy to perform. These experiments have the advantages that (i) application of water using suction plates to achieve unsaturated conditions can be avoided and (ii) scaling in distance divided by the square root of time, at any temperature, encourages our belief that the flow equation is valid and the boundary conditions are realised. A disadvantage of sorption experiments, when compared with steady flow ones, is that the space-like coordinate scales according to the square root of the viscosity and surface tension ratios so that these experiments are less sensitive to changes in this ratio than are those involving direct measurements of hydraulic conductivity. Nevertheless, the relatively large effects ascribed to viscosity and surface tension described in some other papers should be evident if they are important.

Absorption or desorption experiments were conducted on 3 dissimilar materials at constant temperatures of ~277 K, 293 K and 304 K. For each material and temperature, the water content profiles were measured at different elapsed times and the space-like variable A = [Xt.sup.-1/2] was used to 'test' the validity of basic flow laws that lead to Eqn 3 and the initial and boundary conditions (Eqns 8).

This note does not review all possible effects in this complicated issue and other extensive surveys are cited. It is useful, however, to summarise key points that emerge in relation to these 3 materials. They are qualified by experimental error revealed in the scatter of data as well as by the scale, duration and temperature range of the experiments. Nevertheless, for each material:

(1) Water content profiles, [THETA]([LAMBDA]), for each temperature preserved similarity but differed between temperatures. This implies that Eqn 3 is valid and that the conditions of Eqn 8 are realised for all temperatures and materials.

(2) These [THETA]([LAMBDA]) profiles were consolidated for the soil and for the chromatography paper when graphed as [THETA]([[LAMBDA].sup.*]), where [[LAMBDA].sup.*] scales A according to [[LAMBDA].sup.*] = A x [([([mu]/[sigma]).sub.T]/[([mu]/[sigma]).sub.293]).sup.1/2]. They correspond, within experimental limits, with profiles measured at 293 K, as they should if the approach is valid. The consolidation using [[LAMBDA].sup.*] implies that the temperature dependence of the transient flow in these experiments is simply related to the temperature dependence of !a and [sigma] of pure water. Desorbing clay behaved similarly (Figs 6 and 7). There are no air-water interfaces in the clay, however, and flow there appears to be affected only by the temperature dependence of the kinematic viscosity of pure water. This conclusion is weak, however, because of the relatively trivial contribution, in principle, of [sigma] (see Fig. 1).

(3) There is no evidence that structured water at the water/clay interface, if it exists, affects the temperature dependence of flow, because the desorption data of the bentonite (which has a great specific surface) reveals no unusual effects (Smiles et al. 1985).

These experiments do not resolve effects of solutes and their concentration on the temperature dependence of either [mu] or [sigma], however. This is because theory and observations of dispersion and chemical reaction during these sorts of experiments lead us to expect solution concentration profiles that are themselves self-similar in [LAMBDA] and [[LAMBDA].sup.*]. Semi-quantitatively, this means that the soil solution between the piston front (the apparent interface between the absorbed solution and that initially present) and the wetting front is well described by the saturation extract data of Table 2. The soil solution between the piston front and X = 0 approaches the constitution of the solution being absorbed (Smiles and Smith 2004). Thus, solute dependence of ([mu]/[sigma]) will, itself, scale. Furthermore, within the solute concentration ranges observed here, [differential][([mu]/[sigma]).sub.T]/[differential]T curves for most aqueous solutions appear, practically, to be identical (cf. data for pure water with that for sea water in Sverdrup et al 1942), so water content profiles will continue to preserve similarity and la and cy effects will be buried in [D.sub.293]([THETA]) calculated from [THETA]([[LAMBDA].sup.*]) using the method of Bruce and Klute (1956). They will be revealed only if [mu] and [sigma] are independently measured on the pore water. Similarly, solutes may affect the soil water contact angles but appear not to affect their temperature dependence.

We did not measure [THETA]([psi]) for the unsaturated soil and chromatography paper. Data of Smiles et al. (1985) for the bentonite showed no significant effect, however. This is consistent with the observation that there can be few meniscuses in this system, but it also eliminates, for this system, effects on [psi] that might arise because of peculiar effects at clay/water interfaces. Those data were based on experiments where [THETA]([psi]) was measured at constant temperature and were similar to experiments described by Nimmo and Miller (1986) for unsaturated soils. We cannot comment on Nimmo and Miller's observations of 'gain factors' as great as 8 (the gain factor measured the degree to which measured suction exceeds that predicted simply from the temperature dependence of the surface tension). Gardner (1955) and Taylor and Stewart (1960) held [THETA] constant and measured [psi] as temperature was varied. Their experiments also revealed effects that were substantially greater than would be expected from considerations of the temperature effects on [sigma] alone. It remains noteworthy that values of [[THETA].sub.i] in these experiments appeared independent of temperature. This, however, is also weak evidence in view of observations of Nimmo and Miller (1986) mentioned above.

In summary, temperature effects on transient flow in each of these materials appear to be well described by the temperature dependence of the kinematic viscosity and the surface tension of pure water. No temperature change was imposed during flow in any experiment, but intuitively, the most likely origins of enhanced effects when the temperature is changed during flow must reside in (transient?) effects of temperature on the volume of entrapped air in unsaturated soils (but see Hopmans and Dane 1986a). Hysteresis in the soil moisture characteristic alone might result in relatively large changes in capillary potential associated with relatively small changes and directions of change in water content. These effects will be material characteristics that can be defined only by measurement. Effects on hydraulic conductivity might then arise because K([THETA]) scales as the square of the effective radius of the water conducting elements (Miller and Miller 1956), but again, the way water redistributes as isolated air-filled pores shrink and swell will be a material characteristic that will not permit generalisation in terms of the surface tension of air/water interfaces.

Acknowledgments

Some of these experiments were necessary to define flow properties in soils heavily irrigated with piggery effluent. Australian Pork Ltd supported this aspect of the work.

References

Bachmann J, Horton R, Grant SA, van der Ploeg RR (2002) Temperature dependence of soil water retention curves of wettable and water repellent soils Soil Science Society of America Journal 66, 44-52.

Bruce RR, Klute A (1956) The measurement of soil diffusivity. Proceedings of the Soil Science Society of America 20, 458-462.

Childs EC (1969) 'The physical basis for soil water phenomena.' pp. 164-165. (John Wiley: London)

Childs EC, George N (1948) Interaction of water and porous materials. Soil geometry and soil-water equilibria. Discussions of the Faraday Society 3, 78-85. doi: 10.1039/df9480300078

Constantz J (1982) Temperature dependence of unsaturated hydraulic conductivity of two soils. Soil Science Society of America Journal 46, 466-470.

Gardner R (1955) Relation of temperature to moisture tension of soil. Soil Science 79, 257-265.

Gardner WR (1959) Diffusivity of soil water during sorption as affected by temperature. Soil Science Society of America Proceedings 23, 406-407.

Grant SA, Bachmann J (2002) Effect of temperature on capillary pressure. In 'Contributions to environmental mechanics: a tribute to John Philip'. Geophysical Monographs Series. (Eds PAC Raats, DE Smiles, AW Warrick) pp. 199-212. (American Geophysical Union: Washington, DC)

Hopmans JW, Dane JH (1986a) Temperature dependence of soil hydraulic properties. Soil Science Society of America Journal 50, 4-9.

Hopmans JW, Dane JH (1986b) Temperature dependence of soil hydraulic properties Soil Science Society of America Journal 50, 4-9.

Miller EE, Miller RD (1956) Physical theory for capillary flow phenomena. Journal of Applied Physics 27, 324-332. doi: 10.1063/1.1722370

Nimmo JR, Miller EE (1986) Isothermal moisture vs potential characteristics of soils. Soil Science Society of America Journal 50, 1105-1113.

Philip JR, de Vries DA (1957) Moisture movement in porous materials under temperature gradients. Transactions American Geophysical Union 38, 222-232.

Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics 1, 318-333. doi: 10.1063/1.1745010

Smiles DE (1998) Water flow in filter paper and capillary suction time. Chemical Engineering Science 53, 2211-2218. doi: 10.1016/S00092509(98)00061-X

Smiles DE (2001) Chemical reaction and Co-60 retardation in unsteady unsaturated soil water flow: the effect of clay content. Australian Journal of Soil Research 39, 1059-1075. doi: 10.1071/ SR00067

Smiles DE, Barnes CJ, Gardner WR (1985) Water relations of saturated bentonite--some effects of salt concentration and temperature. Soil Science Society of America Journal 49, 66-69.

Smiles DE, Philip JR, Knight JH, Elrick DE (1978) Hydrodynamic dispersion during absorption of water by soil. Soil Science Society of America Journal 42, 229-234.

Smiles DE, Rosenthal MJ (1968) The movement of water in swelling materials. Australian Journal of Soil Research 6, 237-248. doi: 10.1071/SR9680237

Smiles DE, Smith CJ (2004) Absorption of artificial piggery effluent by soil: A laboratory study. Australian Journal of Soil Research 42, 1-15. doi: 10.1071/SR03048

Smiles DE, Towner GD (1968) The steady state measurement of the hydraulic conductivity-moisture content relationship in soils. Water Resources Research 4, 1029-1030.

Smiles DE, Vachaud G, Vauclin M (1971) A test of the uniqueness of the soil moisture characteristic during non-hysteretic, horizontal flow of water in a rigid soil. Soil Science Society of America Journal 35, 534-539.

Stoffregen H, Wessolek G, Renger M, Plagge R (1997) Effect of temperature on hydraulic conductivity. In 'Proceedings of the International Workshop on Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media'. (Eds MTh van Genuchten, FJ Leij, L Wu) pp. 497-506. (University of California: Riverside, CA)

Sverdrup HU, Johnson MW, Fleming RH (1942) 'The oceans. Their physics, chemistry and general biology.' (Prentice Hall: Englewood Cliffs, NJ)

Taylor SA, Stewart GL (1960) Some thermodynamic properties of soil water. Soil Science Society of America Proceedings 24, 243-247.

Terzaghi K (1923) Die Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf der Hydrodynamischen Spannungserscheinungen. Akademie der Wissenschaften in Wein, Sitzungberichte, Mathematisch-Naturewissenschaftliche Klasse Part IIa, 132, 3-4, 125-138.

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Manuscript received 13 August 2004, accepted 27 January 2005

D. E. Smiles

CSIRO Land and Water, PO Box 1666, Canberra, ACT 2601 Australia. Email: david.smiles@csiro.au
Table 1. Nomenclature

The physical dimensions and units of [THETA] and X depend on the
material and are defined for each in the text. Dimensions of
[K.sub.T]([THETA]) and [D.sub.T]([THETA]) then follow

Symbol Meaning

[THETA] Water content
[[THETA].sub.(i)] Initial water content
[[THETA].sub.(0)] Boundary water content
[LAMBDA] Boltzmann coordinate = X/[t.sup.1/2]
[LAMBDA].sup.*] Boltzmann coordinate scaled according to the
 temperature dependence of ([mu]/[tau])
[LAMBDA].sup.**] Boltzmann coordinate scaled according to the
 temperature dependence of [mu]
[K.sub.T]([THETA]) Hydraulic conductivity at temperature, T
[[PSI].sub.T] Suction at temperature, T
[[mu].sub.T] Kinematic viscosity of water at temperature, T
[[sigma].sub.T] Air/water surface tension at temperature, T
v Darcy flux of water
X Space-like material coordinate
t Time (s)
T Temperature (K)
[D.sub.T]([THETA]) Water diffusivity of material at temperature, T

Table 2. Soil properties

The soil was sampled from the top 0.10 m of a weakly structured,
sub-angular blocky fine sandy clay loam horizon of a Vertic mesotrophic
red dermosol. It is identified as CP338 and 339 in the CSIRO National
Soils Database (c/- david.jacquier@csiro.au)

 Particle size (%)

Clay Silt Fine sand Coarse sand
22 17 14 18

 Saturation extract

Water EC [Na.sup.+] [K.sup.+]
 content
0.27 g/g 0.2 0.3 0.3
 mS/cm [mmol.sub.c]/L [mmol.sub.c]/L

Water [Ca.sup.2+] [Mg.sup.2+]
 content
0.27 g/g 0.9 0.4
 [mmol.sub.c]/L [mmol.sub.c]/L

 Exchangeable cations

Units CEC [Na.sup.+] [K.sup.+]
[mmol.sub.c]/100 g 7.2 0.07 0.9

Units [Ca.sup.2+] [Mg.sup.2+]
[mmol.sub.c]/100 g 3.4 0.04

Table 3. The clay suspension

The clay was a Wyoming bentonite suspended in distilled water.
The major anion is S[O.sub.4].sup.2-], the cation concentrations in
a filtrate expressed at a pressure of 100 cm Hg

pH EC S[O.sub.4].sup.2-] [Na.sup.+]

8.3 1.93 mS/cm 13.6 [mmol.sub.c]/L 15 [mmol.sub.c]/L

pH [K.sup.+] [Ca.sup.2+] [Mg.sup.2+]

8.3 0.18 [mmol.sub.c]/L 0.19 [mmol.sub.c]/L 0.3 [mmol.sub.c]/L
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Date:Jul 1, 2005
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