Measurement of the Total Suction of Soils by a Thermistor Psychrometer1

B. D. KAY AND PHILIP F. Low2

ABSTRACTA detailed description of a thermistor psychrometer is pre-

sented. The psychrometer depends on differential cooling dueto unequal evaporation rates of water droplets suspended frommatched thermistors which are located above the sample andreference. The resulting difference in resistance between thethermistors is measured by a Wheatstone bridge and referredto a calibration curve for the determination of the total suctionof the sample.

Results obtained by the psychrometer on a Brookston siltloam are shown to agree with those obtained by a pressureplate. However, results obtained by the psychrometer on apure clay-water system are shown to differ from those obtainedby a tensiometer. A possible reason for this difference is given.

Additional Key Words for Indexing: vapor pressure.

THEORETICALLY, the relative partial molar free energy ofsoil water, T—F°, may be calculated from measure-

ments of osmotic pressure, TT, of suction head, T, or of rela-tive vapor pressure, p/p°, in accordance with the equations:

F-F° = -VTT = -Mgr - RT In pip° [1]where 7 is the partial molar volume of the soil water, Mis the molecular weight of water, g is the gravitationalacceleration, R is the molar gas constant, and T is the tem-perature. However, values of ?r and T which can be usedin these equations are not easily obtained. For instance,although values of •* and T can always be measured withan osmometer and tensiometer, respectively,_they_ cannotbe used in equation [1] for the calculation of F— F° unlessthe membranes of these instruments are impermeable toall dissolved solutes and particulate matter. Conventionalmembranes do not exclude dissolved solutes. And recently,Banin, Davey and Low (1968) have reported that mem-brane pore size affects the measured tension in dilute claysuspensions, indicating that these membranes also do notexclude clay particles. Therefore, the measurement ofvapor pressures to be used in the ratio p/p° becomes ofprime importance.

Thermoelectric methods of determining vapor pressurehave differed in the kinds of temperature-sensitive elementsemployed, in the way in which water droplets are formedon these elements and in the way in which compensationis made for changes in ambient temperature.

Spanner (1951) and Richards and Ogata (1958) used

1 Journal Paper no. 3728, Purdue University Agr. Exp. Sta.,Lafayette, Ind. Contribution from the Department of Agron-omy. This research was supported by grants from the NationalAeronautics and Space Administration. Received Aug. 4, 1969.Approved Dec. 31, 1969.2 Graduate Assistant and Professor of Agronomy, respec-tively. The first-named author is now located in the Departmentof Soil Science, University of Guelph, Guelph, Ontario, Can.

thermocouples to measure the depression of temperatureof an evaporating water drop exposed to the vapor pressureof the sample. Spanner condensed the drop on the wetjunction by Peltier cooling, whereas Richards and Ogataplaced it on this junction manually.

Two methods have been used to compensate for changesin ambient temperature. In one, the temperature of thewet element (thermocouple or thermistor) is measuredprior to wetting. In the other, the reference element islocated near the wet element in the sample chamber. Whenthe ambient temperature and the temperature produced byevaporation are measured by the same element, the as-sumption is made that the temperature does not changein the time interval between the two measurements. Whenthe reference element is located near the wet element, theassumption is made that the two elements are at the sametemperature and have identical temperature-response char-acteristics. Unfortunately, the utility of the thermocouplepsychrometers introduced by Spanner and by Richards andOgata is diminished by the requirement that the tempera-ture be rigidly controlled.

Rawlins and Dalton (1967) have developed a thermo-couple psychrometer for in situ measurements. Peltier cool-ing is used to develop a wet junction. By imposing certainboundary conditions, these authors were able to diminishthe requirements for temperature control.

Brady et al., (1951) incorporated thermistors into atechnique for measuring vapor pressures that was intro-duced originally by Hill (1930) and Baldes (1934). Theyplaced a drop of solvent on one thermistor and a drop ofsolution on the other and measured the steady-state tem-perature difference between them. Both drops were ex-posed to solvent vapor; hence, the reference themistor wasthe one to which the drop of solvent was attached. Thistechnique has been employed by Mechrolab in their com-mercial Vapor Pressure Osmometer. (Mechrolab, Inc.,1062 Linda Vista Ave., Mountain View, Calif.) Unfortu-nately, it cannot be used to measure the vapor pressure ofa liquid in pastes or porous materials.

Recently, Mokady and Low (1968) modified the tech-nique of Brady et al., (1951) for the measurement of thevapor pressure of water in clay pastes. Their apparatusconsisted of matched thermistors that were located in sepa-rate compartments above the sample and reference. Whendrops of water were placed on the thermistors they evapo-rated at different rates and cooled the thermistors differen-tially. The result was an imbalance in the Wheatstonebridge of the measuring circuit. The degree of imbalancedepended on the difference in vapor pressure between thesample and the reference. Hence, the vapor pressure ofthe sample was determinable.

Mokady and Low (1968) did not discuss the details oftheir psychrometer because it was not the principal subjectof their paper and, at the time of publication, was stillunder investigation. Unfortunately, this investigation was

373

374 SOIL SCI. SOC. AMER. PROC., VOL. 34, 1970

not completed. Therefore, we assumed the responsibilityof continuing it. The result was the design and constructionof the psychrometer that is described in this paper.

INSTRUMENTAL DESIGN

The principal features of our psychrometer are (i) matchedthermistors used as the temperature sensitive elements; (ii) thereference thermistor and that subjected to evaporative coolinglocated close together; (iii) identical water drops placed onboth thermistors, and (iv) the thermistors located in separatecompartments.

The use of thermistors in lieu of thermocouples offers theadvantage of much greater temperature sensitivity. Also, whenthe thermistors are matched, errors arising from differentialthermal response are minimized. Locating them close togetherassures that they will be exposed to the same ambient tempera-ture. Since thermistors undergo Joule heating, placing identicalwater drops on both of them prevents any imbalance in theirdissipation of heat. However, it requires that they be locatedin separate compartments above water and the sample, respec-tively. Otherwise, differential cooling would not occur.

The design of the thermistor psychrometer is given in Fig. 1.The psychrometer consisted of four circular plates, A, B, Cand D, which were positioned with respect to one another withtwo guide pins, E, and held together with four Vi-in (.63 cm)bolts. The plates had a common diameter of 7.6-cm and thick-nesses of 0.62-, 0.6-, 1.65-, and 1.2-cm respectively. Teflongaskets were located between plates B and C, and C and D.The two sample chambers F and G were symmetrically locatedin plates C and D. They were 3-cm in diameter and, in plateD, were 0.5-cm deep.

Plate B was Plexiglas and acted as a mounting for the ther-mistors, H and /, whi!e providing a window for the samplechambers. The window faciliated placing the droplets on thethermistors. Plate A was stainless steel and was employed todistribute the pressure uniformly over plate B when the psy-chrometer was assembled and the four bolts tightened to pullthe plates together.

The thermistors were tightly fitted inside stainless-steel postswith bushings of Tygon tubing. Both ends of the posts werecapped off with epoxy glue. The stainless-steel posts were fittedinto the Plexiglas plate with rubber O-rings, insuring a vapor-tight seal. When the psychrometer was assembled, the thermis-tors were located 2-mm from, but on opposite sides of, the wallseparating the chambers and 3-mm above the sample and ref-erence, respectively. This proximity of the thermistors to eachother minimized the effects of changes in the ambient tempera-ture.

The thermistors were YSI 100K thermistors (Yellow SpringsInstrument Co., Box 279, Yellow Springs, Ohio, 45378.)

matched to within 1 % of each other and encased in a thin Tef-lon film. Preliminary tests with bead thermistors and glass-encased thermistors indicated these thermistors would adsorbwater to change the response characteristics of the thermistors.Teflon-coated thermistors were found to be stable after beingin a water-saturated atmosphere for about 10 days. The Teflonfilm was found to be thin enough to give adequate heat transferto the sensitive elements.

Thermistors are light sensitive (Farm and Bruckenstein,1968). As a consequence, the psychrometer must be in a darkcontainer; or a constant light intensity must be maintained dur-ing measurement if, as in our case, a water bath with a trans-parent top is employed.

Plates C and D were stainless steel and gave the psychrom-eter a high heat capacity. Samples were placed in the lowerparts of the sample chambers, i.e., the parts in plate D. Plate Ccontained the upper parts which acted as vapor spaces. Locatedin plate C and connected with these spaces were injection ports,/, capped with rubber septums in a manner commonly em-ployed in injection ports in gas chromatographs.

The thermistors H and / were connected into the electricalcircuit shown in Fig. 2. A potential of 0.5-v was maintainedacross the Wheatstone bridge by employing a potential divider,M, in conjunction with two 1.34-v Hg batteries in parallel.Muller and Stalten (1953) have reported that a constant poten-tial must be maintained to obtain reproducible results. ResistorN was wire-wound and had a resistance of 75K. Resistor P wasa Leeds and Northrup decade box (catalogue no. 4706). Theoff-balance emf of the bridge circuit was amplified with a Keith-ley Model 150A /^volt-ammeter, V, and recorded on a Leedsand Northrup (Type G) Speedomax recorder, R.

Stray electrical field effects were minimized by using elec-trically-shielded, copper7cored cable and housing the Wheat-stone bridge circuit and the microvolt-ammeter in a groundedFaraday cage. Thermal emf's were reduced by using Cd-Snsolder on all solder joints.

CALIBRATION

Calibration of the psychrometer was accomplished in thefollowing way. With the thermistors disconnected momentarily,the microvoltammeter was zeroed. Thereafter, the thermistorswere reconnected, 3.6-ml of water was pipetted into each sam-ple chamber (to make the water level coincident with the uppersurface of plate D), the components of the psychrometer wereassembled and 4-yu.liter droplets of water were placed on thethermistor tips. This was done by means of a 10-/Jiter syringewhich was injected into the sample chambers through the rub-ber septums of the injection ports. Then the assembled psy-chrometer was equilibrated in a water bath maintained at 24.5± .025C. After the equilibration period (about 1.5-hr) the bridgewas balanced by adjusting resistor P to give a null reading onthe 30-,uv scale of the microvolt-ammeter. The required resis-tance was referred to as R°.

Instrumental calibration was completed by replacing thewater in one sample chamber with standard NaCl solutions and,in each case, adjusting resistor P to balance the bridge. Therequired resistance was referred to as R'. The recorder wasused to indicate when equilibrium was attained. In addition, the

Side View Top ViewFig. 1—Diagram of the thermistor psychrometer. Fig. 2—The electrical circuit of the thermistor psychrometer.

KAY AND LOW: MEASUREMENT OF TOTAL SUCTION OF SOILS 375

recorder was calibrated to measure small values of off-balanceresistance since experiments showed a linear relation betweenoff-balance emf and off-balance resistance for small values ofthe off-balance resistance. The recorder range was adjusted sothat an off-balance resistance of 1 ohm displaced the recorderpen 2.5 scale divisions. Finally, R' — R° was plotted against saltconcentration to obtain a calibration curve.

OPERATIONThe procedure for operation was essentially the same as that

for calibration. First, the microvolt-ammeter was zeroed withthe thermistors disconnected. Next, the thermistors were con-nected, the chambers were filled to the upper surface of plateD with water, the psychrometer was assembled, 4-/Jiter drop-lets were placed on the thermistor tips and after thermal equi-librium had been obtained, the value of R° was determined.Then, the water in the appropriate sample chamber (i.e., theone that had previously contained the calibrating solutions) wasreplaced by the sample. In the case of a fluid sample, the neces-sary volume was pipetted into this chamber. In the case of apaste or granular sample, the chamber was filled to excess anda knife edge was employed to produce a smooth surface coin-cident with the top of plate D. After reassembling the psychrom-eter, 4-ju.liter droplets were again placed on the tips of the ther-mistors, thermal equilibrium was re-established in the waterbath, and R' was measured, as before. In placing the dropletson the tips of the thermistors, care was always taken to insurethat their volume was exactly 4-/Jiters. If the droplets differedin size, the precision of measurement was reduced. However,as long as the droplets were the same size, increasing theirvolume did not increase the sensitivity. Once the value of R'was obtained, the corresponding value of R' — R° was referredto the calibration curve to obtain the osmotic pressure.

RESULTS AND DISCUSSION

The calibration curve relating the resistance change(R'—R°) to salt concentration and osmotic pressure, ir,is given in Fig. 3. Values of TT were calculated from thecorresponding salt concentrations using data provided byRobinson and Stokes (1959). Evidently, a linear relation-ship exists between (R'-R°) and TT. Additional unpub-lished measurements indicate this linear relationship ismaintained to much higher values of TT than those recordedhere. This is in agreement with the theory and results ofFarm and Bruckenstein (1968).

Resistance changes were read to the nearest 0.2 ohm.On the basis of the calibration curve and replicated results

77 (otm)0.9 1.8 2.7 3.6

.03 .04 .05 .06 .07Concentration of NaCI (molal)

for standard salt solutions, the error in determination ofTT was found to be ±0.023 atm (corresponding to ±0.00003in p/p°), which was within the reading error. Values ofmaximum sensitivity for the thermocouple psychrometer,which were calculated from the data of Richards and Ogata(1958) and Campbell et al., (1966) appear to be about±0.01 atm.

In the present method, differential cooling of the thermis-tors is the result of a difference in vapor pressure betweenthe sample and the reference (pure water). Hence, thethermistor psychrometer could be calibrated in terms ofthe vapor pressure, p, or the relative vapor pressure p/p°.Instead, for convenience, we have chosen to calibrate itin terms of the osmotic pressure. But it is not conventionalto refer to the osmotic pressure of a soil. Therefore, for asoil or a consistent clay paste, we will adopt the terminol-ogy of Richards, Low, and Decker (1964) and call themeasured quantity the total suction. And we will use theatmosphere as the unit of measurement.

Total suctions measured with the thermistor psychrom-eter were compared with those measured by conventionaltechniques. For the first comparison, samples of Brookstonsilt loam were passed through a 2-mm sieve and wetted.Following this, they were dried by evaporation to differentwater contents, which were measured gravimetrically. Thentheir total suctions were determined, in duplicate, by meansof the thermistor psychrometer. The resulting desorptionmoisture characteristic curve is shown in Fig. 4. Alsoshown in this figure is a desorption moisture characteristiccurve for the same soil which was determined indepen-dently in Dr. Dan Wiersma's laboratory by means of apressure-plate apparatus fitted with a Visking membrane.

14

- 8

• Pressure-plate apparatus«Thermistor psychrometer

16

14

12

8 12 16 20Water Content (% oven-dry wt.)

24

IOI

I1

Fig. 3—Calibration curve for the thermistor psychrometer.

Fig. 4—Moisture characteristic curve for Brookston silt loamobtained by a pressure-plate apparatus (reported as suction)and by the thermistor psychrometer (reported as totalsuction).

376 SOIL SCI. SOC. AMER. PROC., VOL. 34, 1970

14

1.2

1.0

:o.s

"0.6

0.4

0.2

1.4

• Thermistor psychrometero Tensiometer - Visking membrane> Tensiometer - ceramic membrane

1.2

I.O

OS B3

-0.6 ^en

-0.4

0.2

O 5 IO 15 20 25 30Concentration of Na/Al-clay (g/IOOg paste)

Fig. 5—Moisture characteristic curve for Na/Al-clay obtainedby a tensiometer (reported as suction) and by the thermistorpsychrometer (reported as total suction).

Obviously, the agreement between the two curves is good.Evidently, the Brookston silt loam contained negligibleamounts of dissolved solutes because the contribution ofdissolved solutes is detected by the thermistor psychrometerbut not by the pressure-plate apparatus.

In the second comparison, Na/Al-bentonite, preparedin the manner of Davey and Low (1968), was mixed indifferent proportions with water. Then samples were takenfrom these mixtures for suction measurements with boththe thermistor psychrometer and a tensiometer. An ultra-fine ceramic membrane and a Visking membrane wereused alternately in the tensiometer. Measurements madewith the tensiometer were not replicated. However, allmeasurements made with the thermistor psychrometer wereduplicated except those at the highest clay concentration.The measurements made at this concentration gave rela-tively high results and so they were replicated three timesto confirm their validity. The resulting data are comparedin Fig. 5.

The average deviations in the results obtained with thethermistor psychrometer on the 7.7, 15, and 23.5% claypastes were 0.0, 0.050, and 0.035 atm, respectively. Thesedeviations are larger than those we, and Richards andOgata (1958), obtained with salt solutions. However, theyare smaller than those Klute and Richards (1962) obtainedwith Ca-montmorillonite. The latter authors also foundgreater deviations in their results when standard salt solu-tions were replaced by soils or clay pastes.

From Fig. 5 it is evident that the suctions measured bythe two instruments were the same at low clay concentra-tions. However, at relatively high clay concentrations, thesuctions measured by the thermistor psychrometer ex-ceeded those measured by the tensiometer. This discrep-ancy could have been due to the presence of dissolvedsolutes. The tensiometer, like the pressure-plate apparatus,does not detect their contribution. Therefore, a samplecontaining 10-g of clay per 100-g of suspension was cen-trifuged and the osmotic pressure of the supernatant was

determined with the thermistor psychrometer. A zero valueof (R'-R°) was obtained. Also, the electrical conductanceof the supernatant was measured. It was found to corre-spond to that of a 3.35 X 1Q-4 molal solution of NaCl.Such a solution has an osmotic pressure of 0.016 atm.Anion exclusion would tend to make the average free saltconcentration in the paste even less than that found in thesupernatant. Clearly, therefore, the contribution of dis-solved salt to the total suction was insignificant. This sug-gests, in keeping with the work of Banin, Davey, and Low(1968), that neither membrane employed in the tensiome-ter excluded clay particles entirely.

Clay particles existed in the Brookston silt loam. If weare to ascribe the relatively low suctions measured in theclay system by the tensiometer to permeation of the mem-branes by clay particles, then why didn't the clay particlesin the Brookston silt loam permeate the Visking membraneof the pressure-plate apparatus and produce the sameeffect? A possible explanation is that the clay particles inthe Brookston silt loam were in a different state of aggre-gation and were not free to permeate the membrane. Otherexplanations are not obvious at this time.