DIVISION S-l—SOIL PHYSICS

Temperature Dependence of Soil Water Retention Curves1

J. W. HOPMANS AND J. H. DANE2

ABSTRACTEffects of entrapped air volume and surface tension of soil solution

are often regarded as the primary cause of temperature effects onthe water retention curve. A procedure was developed to determinesimultaneously the water characteristic curves and the volume ofentrapped air for a glass beads medium and a Norfolk sandy loam(Typic Paleudults) at two temperatures. The volume change of en-trapped air was determined from the change in volume of the freegas phase and the volume of water outflow from or inflow into apressure cell. The results indicate a decrease in entrapped air volumewith increasing temperature and suction. Surface tension values, cal-culated from capillary height measurements, showed the tempera-ture coefficient of surface tension of soil solution to be smaller inmagnitude than that of pure water. It was concluded that neitherchanges in entrapped air volume nor the temperature coefficient ofsurface tension of soil solution could account for the temperatureeffect on experimentally determined water characteristic curves ofthe two porous media.

Additional Index Words: temperature coefficient, surface tension,entrapped air, hysteresis, soil-water pressure.

Hopmans, J.W., and J.H. Dane. 1986. Temperature dependence ofsoil water retention curves. Soil Sci. Soc. Am. J. 50:562-567.

PHILIP AND DE VRIES (1957) were among the firstto present an equation that describes changes in

water retention curves with changing temperature.These changes, viz., an increase in soil-water pressurehead with increasing temperature and a decrease insoil-water pressure head with decreasing temperatureat a given soil-water content, were attributed solely tothe temperature dependence of surface tension ofwater. While modeling soil-water flow, Hopmans andDane (1985) showed that the influence of soil tem-perature on the soil's hydraulic properties could havea considerable effect on the soil-water distributionduring infiltration.

The change in soil-water pressure head with tem-perature at a given water content, however, cannot befully explained by the temperature effect on the sur-face tension of water (Wilkinson and Klute, 1962;Gardner, 1955; Haridasan and Jensen, 1972; Yong etal., 1969; Nimmo, 1983). A larger temperature coef-ficient of soil-water pressure head was suggested as aresult of (i) the presence of solutes in soil solution,which changes the temperatuure coefficient of surfacetension of water, and (ii) the presence of entrappedair. The latter is defined as the portion of the soil-airenclosed within the external soil-water menisci andseparated from the free air by these menisci.

Peck (1960) studied the influence of entrapped air1 Contribution from the Ala. Agric. Exp. Stn., Auburn Univ., Au-

burn AL 36849. AAES Journal no. 3-85820. Received 6 June 1985.- Graduate Research Assistant and Associate Professor of Soil

Physics, respectively, Dep. of Agronomy and Soils, Alabama Ag-ricultural Experiment Station, Auburn Univ., Auburn AL 36849.

on the temperature coefficient of soil-water pressurehead. In his analysis, however, Peck assumed that themolar volume of entrapped air was constant withchanging temperature and changing soil-water pres-sure head. Chahal (1964; 1965) modified Peck's anal-ysis to include the rate of change of entrapped air vol-ume. Chahal matched experimental and theoreticalwater characteristic curves by choosing proper valuesfor the entrapped air volume and its rate of change.

Quantitative analyses of entrapped air volume werepresented by DeBacker (1967) and Cary (1967).DeBacker measured the volume of entrapped air withan apparatus combining an air pycnometer to obtainthe volume of the free gas phase and a pressure cellfrom which the outflow and inflow volumes of waterwere measured. By difference, the change in volumeof entrapped air was calculated. A method similar tothe one employed by Cary (1967), who determined thevolume of free gas from pressure measurements be-fore and after relaxation of an initially pressurized soilsample, was used in this study. Gary's experiments,however, were done at only one temperature and theexperimental error was such that no absolute valuescould be assigned to the total entrapped air volume.

No studies have been reported indicating the effectof dissolved chemicals on the surface tension of thesoil solution as temperature changes. Surface tensionmay either increase or decrease, depending on whetherthe dissolved chemicals reside in the interior of thesolution or at the surface.

The objectives of this study were (i) to simultane-ously measure water characteristic curves and corre-sponding total entrapped air volumes during severalsorption-desorption cycles at two temperatures and fortwo porous media, and, subsequently, to determinethe influence of entrapped air on the temperature coef-ficient of soil-water pressure head, and (ii) to evaluatethe effect of temperature on the surface tension of soilsolution.

THEORYEntrapped Air Measurements

Consider two pressure-regulated vessels A and B at tem-perature T (Fig. la). Vessel A contains a porous mediumconsisting of a solid phase, water, free air (with pressure PA)and entrapped air, while vessel B contains free air at pres-sure PB.

Assuming that the free gas phase behaves ideally, theequations of state for each vessel can be described by theideal gas law

[1]PBVB = [2]

where P is pressure (N rrr2), V is volume (m3) of the freegas phase, n is the number of moles of free gas, R is theuniversal gas constant (J mol~' K~'), Tis temperature (K),

562

HOPMANS & DANE: TEMPERATURE DEPENDENCE OF SOIL WATER RETENTION CURVES 563

and the subscripts refer to vessels A and B. Upon openinga valve connecting the two vessels, an equilibrium gas pres-sure (Peq) will be attained such that

^eq(FA + FB

water

Av) = nB)RT [3]where Av denotes the change in entrapped air volume invessel A (Av = VA — vcci) due to the change in pressure fromPA to />„ (by definition Av <0 for PA >/>„). It is assumedin Eq. [3] that the number of moles of free gas remainsconstant, i.e., there is no exchange of gas between the en-trapped and free air phase. Substituting Eq. [1] and [2] intoEq. [3], and solving for FA, the volume of free air in vesselA, yields

FA = - P,eg _ Av eg[4]

Determination of Av requires knowledge of the entrappedair pressures, which can be calculated provided the radii ofthe entrapped air bubbles and the soil-water pressure areknown (Eq. [8]). As the size of these radii are unknown, Gary(1967) assumed Av to be zero, which simplifies Eq. [4] to

[5]

which overestimates the value of FA.Another approach would be to obtain an approximation

for Av by applying the ideal gas law to the entrapped aironly, resulting in

veq = vA(pA/peq) [6]where v and p denote the volume and pressure of entrappedair. It is very likely, however, that different sizes of en-trapped air bubbles coexist. Therefore, the pressure definedin Eq. [6] represents an average value. From Eq. [6] it fol-lows thatAV = VA - Veq = VA(1 -

= VA(AK, ~ />A)/Peq • [7]

For a system at hydraulic equilibrium, the entrapped airpressure (p) can be expressed as a function of the free airpressure (P) as follows (Peck, 1960):

p = P + pgh - 2a/r [8]where h is the soil-water pressure head, r the average radiusof curvature of the entrapped air bubbles (h <0 and r <0),and p, g, and a denote the soil-water density, the gravita-tional constant, and the surface tension of soil water, re-spectively. Therefore, it seems reasonable to assume that

Aq ~ PA = />«, - -PA - [9]Substituting Eq. [9] into Eq. [7] yields an expression for Av,which upon substitution into Eq. [4] results in

FA = V, PR- -— v.^eq

Assuming that Pcq/peci can be approximated by its averagevalue over the range of measurements, i.e., Peq/Peq/>«, = c, yields

FA = V, 4— CVA [H]

Equation [11] can be applied each time a known amountof water (AKW) has been released from vessel A (Fig. Ib), asduring the determination of a water retention curve. Thecorresponding change in free air volume (AKA) can then becalculated from

Fig. 1. Two interconnected vessels A (containing solid phase, water,free and entrapped air in water) and B (free air only), (a) beforerelease of water, (b) after release of water.

AFA = FA"-FA' = FB- P.eq

-/>.

- FR- P.

- VA) , [12]

where the superscripts I and II refer to two consecutive hy-draulic equilibrium situations in vessel A. As the total vol-ume of vessel A remains constant, AFA can also be deter-mined from

AFA = FA» - FA' = AFW - (VA» - VA') [13]where Fw = FJ - Fw". Equations [12] and [13] can besolved for VA", provided c and VA" are known. For a giveninitial free air volume FA', we can then also calculate thefree air volume after the release of water (FA"), as neededfor subsequent steps.

Temperature Effects on Soil-water Pressure HeadPhilip and de Vries (1957) defined the temperature coef-

ficient of soil-water pressure head asdh/dT = (h/ff) (da/dT) = yh [14]

where h denotes the soil-water pressure head (m), a is thesurface tension at the air-water interface (N m~'), and y isthe temperature coefficient of surface tension of water (K~').This definition has the inherent assumption that the changein soil-water pressure head with temperature is only due tothe change in surface tension of water. Temperature changes,however, will also change the volume of water and that ofentrapped air due to thermal expansion. The contributionof these volume changes to the temperature coefficient ofpressure head can be determined by first defining the ap-parent volumetric water content 6' (m3 m"3) as the sum ofthe volumetric water and entrapped air content, 8 and v,respectively, i.e.,

6' = e + v. [15]Equation [14] can then be expanded to include tempera-

ture effects on the apparent volumetric water content, ordh/dT = yh + (dh/de')(dO'/dT). [16]

The second term on the right-hand side can be rewritten as

^f!£= I"—+ —1~' I"—-J-^lldff dT [dh dh\ [dT dT\' l J

564 SOIL SCI. SOC. AM. J., VOL. 50, 1986

pressure

porous plate

constant temperatureincubator j

Fig. 2. Experimental set-up for determination of entrapped air vol-ume.

In Eq. [17], dd/dh is known as the water capacity functionand dB/dT = 06, ft being the thermal expansion coefficientof water.

To calculate the temperature coefficient of soil-water pres-sure head from Eq. [16] it is necessary to determine thewater characteristic curve and measure the changes of vol-umetric entrapped air content with changing pressure headand temperature.

MATERIALS AND METHODSProcedure of Entrapped Air Measurements

A diagram of the experimental setup for measure-ment of entrapped air volume is shown in Fig. 2, wherethe dashed lines indicate that portion of the systeminside a constant temperature incubator.

Measurements were carried out for a glass beads (62nm <d <88 fim) medium and a Norfolk sandy loam(Typic Paleudults), which was first passed through a2-mm sieve. Each of the porous materials was packedin a 0.45-L lucite pressure cell, having a porous ce-ramic plate at the bottom and an annular tensiometerin the middle. Prior to measurements related to theobjectives, both porous media were first stabilized bysubjecting them to several wetting and drying cycles.At the end of the last drainage cycle the media wereflushed with CO2 and subsequently saturated withdeaerated water containing traces of thymol and mer-curic chloride to prevent bacterial growth.

The soil-water pressure head was controlled by ap-plying air pressure, while water content changes weredetermined with a burette. The loop connector be-tween the burette and the cavity below the porousplate allowed removal of accumulated air, which dif-fused through the porous plate, by circulating the waterin the tygon tubing. The soil-water pressure and air

pressure were measured by the pressure transducersPTX1 and PTX2, respectively. Although in this study,water retention curves were determined using air pres-sure, it should be mentioned that several investigatorshave reported discrepancies between water retentioncurves determined by air pressure and suction (e.g.,Chahal and Yong, 1965).

Drying and wetting water retention curves for theglass beads were obtained by stepwise increasing ordecreasing the applied air pressure. During hydraulicequilibrium, as determined from a zero soil-waterpressure head reading (matric and pneumatic headcounter balanced each other) and the cessation of out-flow of water, measurements were obtained to deter-mine the volume of entrapped air. The first two cycles(a cycle is defined as a drying curve followed by awetting curve) were determined at 15°C, while thethird was obtained at 35°C. For the sandy loam theprocess was expedited by obtaining the wetting anddrying curves during continuous drainage or wetting,only to be interrupted for volumetric entrapped airmeasurements at given soil-water pressure head (ac-tually matric head) values. After three cycles at 35°Cand two cycles at 15°C, four additional cycles weredetermined, two at 35°C and two at 15°C.

Entrapped air volumes were determined at varioussoil-water pressure head values for each drying andwetting curve. Valves 3,4, and 5 were closed and anair pressure of PA = 12 kPa was applied to the pres-sure cell. The temperature of the air entering the cellthrough valve 1 was first equilibrated with the incu-bator temperature in volumetric flask C. Upon closingvalve 1, PA was monitored with PTX2. If PA remainedconstant (indicating that the cell was leak-free and thepore water was air-saturated), valve 3 to flask B (FB= 131.6 mL, PB = atmospheric pressure) was opened.The attained equilibrium gas phase pressure (Peq) wasmeasured with PTX2. Due to the decrease in pressurefrom PA to Peq, some of the air originally dissolved inthe soil water would escape, thereby slowly increasingPeq. As it was assumed in Eq. [3] that the moles of airpresent in the free gas phase remain constant, Peq mustbe recorded before this pressure increase occurs. How-ever, some increase in Peq can also be expected be-cause of retarded air flow through the tortuous path-ways of the porous medium. The equilibrium gas phasepressure will, therefore, not be attained instanta-neously.

Initially, the porous medium was at or near satu-ration. The entrapped air volume upon completingdetermination of the first drying and wetting curves(VA") was calculated from Eq. [13] by comparing thevolume of water outflow during desorption with thevolume of water inflow during the sorption cycle (AKA= 0 and VA' = 0). For this particular case, superscriptI refers to the beginning of the first drying curve andsuperscript II to the end of the first wetting curve. Theconstant c can be determined by substituting VA" intoEq. [12] and was found to be 0.84 for the glass beadsmedium and 0.53 for the sandy loam soil. These val-ues for c show indeed that the pressure in the en-trapped air bubbles is greater than in the continuousor free air phase, which provides confidence in theproposed procedure and its measurements. Given thevalues for c and the entrapped air content at the end

HOPMANS & DANE: TEMPERATURE DEPENDENCE OF SOIL WATER RETENTION CURVES 565

2.5

glass beads———— 15°C———— 35°C

.40

Fig. 3. Water retention curves for glass beads. Curves 1 through 4:15°C, curves 5 through 6: 35°C.

of the first drying-wetting cycle, values for the en-trapped air volume at previous and subsequent pres-sure increments can be calculated from Eq. [12] and[13].

Surface Tension MeasurementsThe surface tensions of pure water and of the soil

solution phase of both porous media were indirectlydetermined at various temperatures by the capillaryheight method. A U-shaped tube, consisting of a widetube (i.d. = 7 mm) and a capillary tube (i.d. =* 0.36mm) was placed in a constant temperature chamber.The capillary height, denned as the difference betweenthe liquid menisci in the wide and the capillary tube,was measured with a cathetometer. Surface tensionvalues are related to capillary height by the Young andLaplace equation

= 2a/rc [18]where Ap is the difference in density between the liq-uid and the vapor-saturated air above the water me-niscus, g is the gravitational constant, hc the capillaryheight and rc the radius of curvature approximated bythe radius of the capillary tube. A constant value forrc was obtained by always adjusting the falling menis-cus in the capillary tube to the same position. Thus,differences in capillary height are linearly proportionalto differences in surface tension.

RESULTS AND DISCUSSIONEntrapped Air Effects

Retention data for the glass beads are shown in Fig.3 for 15 and 35°C. The corresponding experimentallydetermined entrapped air volumes are plotted in Fig.4. The entrapped air volume is expressed in milliliters,

-4

Fig. 4. Entrapped air volumes for glass beads. Curves 1 through 4:15°C, curves 5 through 6: 35°C.

each 4.5 mL representing a volumetric entrapped aircontent of 0.01. A significant increase in entrapped airis obvious at the end of the first desorption-sorptioncycle (curve 1 vs. 2, Fig. 4), which was attributed tothe increase in gas being trapped in discontinuouspockets or in water-blocked pores with increasing soil-water pressure head. The decrease of entrapped airduring desorption was attributed to the subsequentemptying of water-filled pores with decreasing soil-water pressure head. Consequently, pores that con-tained entrapped air will be connected to the contin-uous or free air phase. Similar results were obtainedfor the second desorption-sorption cycle (curves 3 and4, Fig. 4).

Following the determination of two loops at 15°C,one 0(/z)-cycle, with corresponding entrapped air vol-umes, was determined at 35°C (curves 5 and 6 in Fig.3 and 4). In accordance with the theory of Philip andde Vries (Eq. [14]) the soil-water pressure head valuesat 35°C were generally greater than those at 15°C.Because of the decrease in entrapped air with increas-ing temperature (Fig. 4, curves 4 and 6), soil-waterpressure head values approaching zero do not showthis behavior. The decrease in entrapped air volumewith an increase in temperature is in apparent con-tradiction with the concept that the entrapped air vol-ume should increase due to thermal expansion. Thisdecrease in entrapped air volume may have beencaused by an increase in pressure of the entrapped airbubbles, which results in an increased flow rate of airfrom entrapped regions to the free air. In addition, thevolume of water in the soil sample decreases with in-creasing temperature at constant soil-water pressurehead (Fig. 3, 5). Therefore, more opportunity may ex-ist for entrapped air to become continuous with thefree air.

Many more drying and wetting curves were deter-mined for the sandy loam soil than for the glass beads.The water retention data of the soil were thereforecombined to determine average drying and wettingcurves for both temperature regimes (Fig. 5). For each

566 SOIL SCI. SOC. AM. J., VOL. 50, 1986

2.5-

0.10 0.400.20 0.30

e,m3nr3

Fig. 5. Water retention curves for Norfolk sandy loam. Dashed lines:15°C, solid lines: 35°C.

loop the data were fitted by van Genuchten's (1978)closed-form analytical equation. The correspondingentrapped air volumes were also averaged for eachtemperature and for both drying and wetting regimes(Fig. 6). The entrapped air volume of the sandy loamsoil as a function of soil-water pressure head and tem-perature shows the same trends as for the glass beads.Entrapped air volumes generally decrease with de-creasing soil-water pressure head and with increasingtemperature.

The effect of temperature on the entrapped air vol-ume was further substantiated by determining en-trapped air volumes during changing temperatureswhile maintaining a constant soil-water pressure head(Table 1). The data for the sandy loam soil were ex-tracted from the available entrapped air volumes atzero pressure head (temperatures were changed at sat-uration). The entrapped air volumes were always lowerat the higher temperature.

The increase in soil-water pressure head at a givenwater content with increasing temperature (Fig. 3 and5) is in general agreement with the effect of temper-ature on surface tension of water (Eq. [14]). The ex-perimental drying curves at 15 and 35°C of the glassbeads are compared with the predicted curve at 35°Cfor a temperature coefficient of surface tension of waterof -0.0023 K"1 in Fig. 7. Although not quite the same,

2.0

1.5-

Ejf

1.0-

0.5-

Norfolk sandy loam35°C

000 .02 .04 .6e sav,m3rrr3

Fig. 6. Entrapped air volumes for Norfolk sandy loam. Dashed lines:15°C, solid lines: 35°C.

the predicted and experimental curves are fairly close.Previous investigators speculated that closer agree-ment could be obtained by considering the change inentrapped air volume with temperature, i.e., they as-sumed that the entrapped air volume would increasewith increasing temperature due to thermal expansion(Peck, 1960), i.e., dv/dT >0. As de/dh, and in mostcases also dv/dh are positive, the result of Eq. [17] isa positive number. Therefore, the temperature coef-ficient of soil-water pressure head in Eq. [16] wouldbe larger than if only temperature effects on surfacetension were considered (Eq. [14]). However, we mea-sured a decrease in entrapped air volume with increas-ing temperature, i.e., dv/dT <0. Hence, incorporatingthe entrapped air effect tends to increase the soil-waterpressure head less with increasing temperature thanexpected from surface tension considerations only (d6/dT is negligible over considered temperature range).It may even cause a decrease in soil-water pressurehead as shown for the higher soil water pressure headvalues (Fig. 3, curves 5 and 6).

Surface Tension EffectsDifferences between calculated and measured

changes in water retention curves with changing tem-peratures have also been attributed to surface tensionchanges of the soil solution being different from thoseof pure water. Values of y obtained by the capillaryheight method (Table 2) are compared with those ofpure water reported in Weast (1974). Agreement be-tween measured and calculated values of pure waterjustified the use of the capillary height method to de-termine temperature coefficients of the porous mediasolutions. The results indicate that the temperaturecoefficient (y) of both solutions is smaller in magni-tude than that of pure water (Table 2). Thus, the useof measured ^-values would cause an additional re-duction rather than an increase in the difference be-

HOPMANS & DANE: TEMPERATURE DEPENDENCE OF SOIL WATER RETENTION CURVES 567

Table 1. Effect of temperature (T) on entrapped air volume (v)at various constant soil-water pressure head values (h).

Glass beadsh

m-0.6dt-0.6d-1.2d-1.2d-2.4d-2.4d-0.6wJ-0.6w

T

°C3515153535151535

V

mL4.65.07.04.51.84.76.63.6

h

m000000

Sandy loamT

°C351515353515

V

mL31.633.023.122.014.815.8

t Drying cycle. t Wetting cycle.

Table 2. Temperature coefficient of surface tension (y)calculated from capillary height (he) measurements

for pure water and porous medium solutionsat various temperatures.

Tempeiature

°C

26.040.051.0

(N m-)0.07180.06960.0677

Pure water

Theoretical

do/dT

-0.00157-0.000173

Experimental

r

-0.002189-0.002482

Ac(m)

0.083100.081080.07894

dhc/dT

-0.000144-0.000194

r

-0.001733-0.002400

Porous medium solution

AC

Glass beads

dhc/dT y AC

Soil

dhc/dT r^j-O y.'™0*5 -0.000124 -0.001540 iM?!?H -0.000146 -0.001780

505 0%,m -°-00017° -°-°°2161 o:o?839 -°-°00175 -°-002074

tween water retention curves at different tempera-tures.

CONCLUSIONSNeither the presence of entrapped air nor the effect

of chemicals in the soil solution on surface tensioncould explain the magnitude of the measured tem-perature coefficient of soil-water pressure head.

In contradiction to what many investigators havespeculated, entrapped air volume decreased with in-creasing temperature. Incorporating the effect of tem-perature on entrapped air volume therefore reducedthe change in soil-water pressure head as compared tothe change based on surface tension effects only.

Comparison of capillary-height values for purewater, glass beads, and soil solution at various tem-peratures showed that the magnitude of the temper-ature coefficient of surface tension is less for both so-lutions than for pure water. Using the measuredtemperature coefficient of surface tension, rather thanthat of pure water, also produces a decrease in thepredicted temperature effect on the water retentioncurve.

The combined effects of entrapped air volume andsurface tension should, therefore, minimize the effectof temperature on the water retention curve. How-ever, like other studies, this study still showed a con-siderable temperature effect. The influence of adsorp-tive forces on the temperature coefficient of soil waterpressure head (Wilkinson and Klute, 1962) was thought

2.0

1.5

1.0

0.5

glass beads———15° C, experimental——— 35°C, experimental—*— 35°C, !£ = -0.0023 h

0.10 0.20 0.30 0.40e

Fig. 7. Experimentally determined drying and wetting curves forglass beads at 15°C (dashed lines), at 35°C (solid lines), andpredicted curve at 35 °C based on temperature correction on sur-face tension only.

to be negligible in this study, because water contentvalues were always >0.1. A complete explanation forthe discrepancy between measured and calculatedtemperature effects on water retention curves remainstherefore unknown.