hrakins jordan

7/30/2019 Hrakins Jordan

1/22

May, 1930 S U R F A C E T E N S I O N F R O M P U L L O N A R I N G 1751[CONTRIBUTIONRO M THE KENT CHEMICAL ABORATORYF THE UNIVERSITY F

CHICAGO]A METHOD FOR THE DETERMINATION OF SURFACE AND

INTERFACIAL TENSION FROM THE MAXIMUM PULL ON ARING

BY WILLIAM . HARKINSND HUBERT . JORDANRECEIVED ECEM BER, 1929 PUBLISHED AY , 1930

1. IntroductionAlthough many thousands of measurements have been made to deter-

mine the pull necessary to detach a ring from the surface of a liquid, it isa surprising fact that until three years ago there was no ri ng method forthe measurement of surface tension. Thus in (International CriticalTables, nine experimental methods for surface tension are listed but aring method is not included, since the procedure which had been desig-nated by this term,did not supply even one single measured value ofsurface tension of these tables.

The failure of the ring procedure was due to the fact tha t the theory hadnot been sufficiently developed to permit its use as a method of measure-ment, although an incomplete theory had been developed by Cantor,I,ohnstein,2 Lenard,3 Tichanowsky* and MacDougalL5

In 1926 Harkins, Young and Cheng,6 on the basis of the well-justifiedassumption that the capillary height method, properly applied, givescorrect values for the surface tensions of suitable liquids, showed how thering procedure could be used as a moderately accurate method for suchmeasurements. In the present paper the method is given a still higherdegree of accuracy (about 0.25%).

In a third paper from this Laboratory, Drs. B. B. Freud and HenriettaZollman Freud convert this into an absolute method, since by the use ofthe fundamental differential equation of Laplace they have been able tocalculate the shapes of the surfaces upheld by rings. It is of considerableinterest that their theoretical and our experimental procedure agree withinapproximately the limits of accuracy of either, that is, to about 0.25%)where the two have been compared.

Symbolsy = surface tension in dynes per centimetera =square root of th e capillary constant

Cantor, W i e d . Ann . , 47, 399 (1892).Lohnstein, Ann . P h y s i k , 2 5 , 815 (1908).Lenard, i b i d . , 74 , 395 (1924).Tichanowsky, P h y s i k . Z . , 25, 300 (1924); 26, 523 (1925).MacDougall, Science, [N. S.]62,290 (1925).

6 Harkins, Young and Cheng, i b i d . , 64, 33 (1926).


2/22

1752 WI LLI AM D. H A R K I N S A N D HUBERT F. ORDAN VOl. 52M =weight of liquid raised above the free surface of the liquid; M = maximumP = tota l pull on the ring in dynes = Mg; P =Mgp = P divided by 4xR; p =P / h RR = radius of the ring measured from the center of the ring to the center of the wirer =radius of the wireV = the volume of liquid raised above the free surface of the liquid, or M / ( D - )D = density of the liquidd = density of a ir saturated with vapor of the liquidS = shape of t he surfaceh = the pressure height or the vertical distance from the point in the meniscus

under the center of the ring to a point in the liquid where the pressure isequal to t ha t in the vapor a t the same level

In much of the earlier work the entirely false assumption was usedthat the maximum pull ( p ) per cm. on the ring is equal to the surfacetension of the liquid or

P = Mg =4xRp = 4xR-yin which P is the total maximum pull on the ring as determined by thebalance.

The results obtained by the use of this entirely incorrect equation varyfrom 30% too high to 30% too low, and even more. The high values arecommonly obtained for surface, and the low for interfacial, tensions.

Harkins, Young and Cheng considered tha t the size of the surfacesoutside and inside the ring is determined mostly by the size of the ring (R) ,and that it s shape is determined by the surface tension and density of theliquid, the radius of the ring ( R ) and of the wire (Y), and certain othervariables. In order to determine the form of the functional relationthey used the principle of similitude, which in this case indicates that theshape of each surface supported by the pull of the ring depends entirely,when a t rest, upon a few simple dimensionless variables. These are (1)the ratio ( K 3 / V ) f the cube of the radius of the ring to the volume of theliquid; (2 ) the ratio (R /Y ) f the radius of the circular ring to the radiusof the circular wire of which it is made, and (3) the ratio ( h3 /V) of the cubeof the pressure height to the volume of liquid which the ring supports.Thus, the shape S is given by

S =f (R3/V , / r, JtaV),orS = Qp(R/a,Rl r , h/a)

The surface tension is a function of the shape, and, therefore, of these samevariables, and i ts value is given by the equation

value of M

V =maximum volume

(1)

Since the volume upheld by the ring becomes a maxi-nim at a certaindefinite shape for which the value of h3/V is determined by the values ofR3/Vand R/r


3/22

May, 1930 SURFACE TENSION FROM PULL O N A R I N G 1753

The values of F may be determined experimentally by determiningthe true surface tensions of various liquids by the capillary height ordrop weight methods, and comparing with the values of p as shown in theabove equation.A number of values of F were determined experimentally by Harkins,Young and Cheng, and it was shown that if R /r is held constant byregu-lating the dimensions of the rings, F varies with R 3 / V along a smoothcurve, regardless of the values of R. However, this work was not suffi-ciently extensive or precise for general use with accurate data.

2 . Outline of ProcedureThe present work is a thorough investigation of the technique of the

ring method, and the accurate determination of the correction curveswhich were found in a preliminary way by Harkins, Young and Cheng.

The general method of procedure was to determine the surface tensionof water, of benzene and of bromobenzene by the capillary height method,and the values of p for these liquids by the use of sixteen different rings,with values of R between 0.4 and 1.8 cm., of r between 0.009 and 0.05 cm.and of R /r between 13.9 and 78.3. The quantities r/ p and R 3 / V werecalculated and plotted against each other, and the curves so obtained forthe various rings were corrected to even values of R l r . Thus curvesfor R/r equal to 30, 40, 50, GO and 80 were obtained. Interpolated curveswere also obtained for intermediate values of R l r .

The liquids water, benzene and bromobenzene were chosen for the stand-ardization for the following reasons: first, because their contact anglesagainst glass and against platinum also are zero, and their surface tensionsmay, therefore, be accurately determined by the capillary height method;and second, because they are easily purified and kept in the pure condition.While pure liquids were not required for the purposes of standardizationas long as the same sample of liquid was used throughout and its truesurface tension known, it was considered desirable to use pure liquids sothat the surface tension values may be compared with those obtained byothers.3 . Determination of the Surface Tension of Liquids by the Capillary

Height MethodThe surface tension of each liquid used in this investigation was de-termined by capillary height measurements made on very pure liquids.The method applied was similar to that of Richards and Coombs, Harkinsand Brown and Young and Gross. The apparatus was exactly that of the


4/22

1754 W I LL IA M D . H A R K I N S A N D H U B E R T F. JORDAN Vol. 52last-named investigators, except that a special stopcock (SI Fig. 1) wasinserted between the trap (T) and the large tube (L), to facilitate the dry-ing of the capillary. The average radius of the capillary, a 3-cm. sectionof a tube selected by Harkins, and Brown, and Davies, was 0.02557 cm.and of the large tube 1.805 cm. The mean diameter of this tube hadbeen determined by these investigators, but was recalibrated by us a t 26nI

Fig. 1.-Capillary heightapparatus.

levels by a determination of the capillary heightwith pure water a t 25', a t which temperatureits surface tension is 71.97 dynes per cm.

The observed heights were corrected by add-ing '/3 r t o correct for the volume of the smallmeniscus, and by adding 0.0018 cm. to correctfor the rise in the larger tube when water wasused. This latter correction was negligible withthe other liquids.

Six values for the surface tension of benzenea t 25' were obtained as follows: 28.19, 28.24,28.23, 28.24, 28.24, 28.23, with a mean value of28.22 dynes per cm. The density 25/4' was0.8733, and D - =0.87187 was used.

For bromobenzene the values are: 35.75,35.73,35.75, 35.73, 35.75,35.76,35.77,35.77, or a meanof 35.75, a t 25'. The density was 1.4887 (25/4'),and D - d was taken as 1.4875.

4. Apparatus for the Ring MethodTh e rings were made of platinum-iridium wire con-

taining 10% iridium to give the wire stiffness, with the ex-ception of rings 15 and 16. These contained no iridium,and proved to be unsatisfactory for practical purposes

It was found necessary to use wire of this alloy, as platinum wire bends too easily andrings made of it soon lose their shape through handling. Th e rings were constructed bybending the wire around a brass rod turned down to the exact inner diameter desired,an d welding the ends of th e wire together with a spot welder. This has to be done withextreme care or the wire will be flattened a t the spot of the weld. The stirrups werethen welded on to the top or side of the ring, and all protuberances and unevennessremoved with a fine file and emery paper. In four of th e rings, made with fine wire,silver solder was used instead of welding. The loop a t the top of the stirrup was made inth e form of an ellipse with the least possible radius of curvature a t the uppermost part,so th at the ring would always hang in the same position. All the rings with radii greaterthan 0.8 cm. were made with two stirrups whose planes were a t right angles to each other.

It was found th at the DuNoiiy tensiometer is too inaccurate for measurements ofthe high precision desired in the present investigation. Therefore, a chainomatic bal-ance, sensitive to 0.05 mg., was adapted for the work. Th e left pan was removed an d ahole three-eighths of an inch in diameter was bored in the base of the balance directlyunder it, through which an aluminum rod connected the ring with the beam of thebalance. The righ-hand pan was replaced by a very light aluminum pan, in order tha t


5/22

May, 1930 S URF ACE TENSION FROM PULL O N A R I N G 1755the momentum of the beam and pan might be reduced to a minimum. The pan restwas disconnected, as i t was found t o be troublesome in making measurements.

In order to prevent ripples in the surface of th e liquid, which might have beenformed by lowering the level of th e liquid or the containing vessel, a machine was de-vised to lower and raise the balance with great ease and smoothness. While such amachine is not essential to measurements by th e ring method, i t was deemed advisableto use it in this work in order to re-move the source of error mentionedabove. Th e machine is representeddiagrammatically in Fig. 2. I t consistsessentially of four heavy upright steelrods, which are screwed into a heavycast-iron base provided with levelingscrews. Fitted onto these rods are twoheavy bronze castings. Th e lower oneis fastened to th e rods, and supports the

'

set of gears which raise and lower theupper movable casting. T o the uppercasting are attached the balance plat- liorm and its counterweight. Frictionaleffects were reduced to a minimum bya delicate counterbalancing of weights Fig. 2.-Apparatus for determination of surfacethroughout. For example, th e balance tension by the ring method.is counterbalanced by the movableweight W '.by the weight JV,

These and the casting which supports them are, in turn, counterbalancedThis is connected to th e upper casting by a steel piano wire whichruns over a stationary pulley. The smoothness of operation

was also increased by reducing the bearing surface of th e mov-able casting to a minimum. The balance platform is providedwith two large oval-shaped openings, through which the rodconnecting the ring with the balance beam passes.

The flask used in the measurements is illustrated in Fig. 3 .The principle involved in the design is to provide a means ofoverflowing the surface to prevent surface contaminat ion. Th eflask was constructed by sealing a cup (C ) 7 . 5 cm. in diameterand 2 cm . high near the bottom of a two-liter flask, and by re-placing th e neck with a longer and wider one: Th e liquid isintroduced in the side-arm (A) and the excess withdrawnthiough ( B ) .

5 . Measurement of RingsSince the correction factor ( y / p or F ) is a function

of the variable K l r , it is necessary to have very ac-Fig. '.-'lank for the curate measurements of the radii of the wires of whichring method. the rings are made, as well as of the radii of the rings.

Th e diameters of the rings were measured b y a screw micrometer carrying a micro-scope with a magnification of t en diameters. One division on the screw head.corre-sponds to 0.0005 cm. The instrument had been originally calibrated by Dr. E. H. C.Davies, by comparison with a standardized invar scale by a series of 5000 measurements,and later checked by Mr . Frank Frese. I n order to make precise measurements i t isnecessary to illuminate t he ring from below, and the method was as follows. A reading


6/22

1756 W I L L IA M D . H A R K I N S A N D H U B E R T F. JORDAN Vol. 52glass about two and one-half inches in diameter was mounted in a hole in the top of abox, and within the box a t the principal focus of the lens was placed a 100-watt lamppainted black with the exception of a spot about a centimeter in diameter. This pro-vided for practical purposes a point source, with parallel light coming through the lens.Above the lens and about two inches away from it was placed the leveling table con-taining the ring. It may be leveled withleveling screws, or, with the leveling screws removed, may be attached t o a microscopeby removing the microscope platform. I n the top of the cylinder in the table wasmounted a transparent celluloid disk (D), roughened with emery paper. The diskhad two slits cut in i t a t right angles to each other (S) through which the stirrups were

This was constructed as is shown in Fig. 4.

, . passed, and on i t were scratched a series of con-centric circles (C) to aid in centering the ring.Measurements on the rings were made acrosstwelve evenly spaced diameters from the outeredge of the ring on one side to the inner edge onthe other. Readings were taken a t the pointwhere the cross-hair, which had been previously

- made perpendicular to the direction of travel,

Fig. 4.-Apparatus fo r measurement were made with a microscope, with a magnifica-tion of ten diameters and provided with a microm-eter eyepiece. This was calibrated by com-

parison with an invar scale standardized by the Bureau of Standards. One divisionon the micrometer screw head corresponds to 0,0001 cm. a t this magnification. Inthese measurements the leveling table wasattached to the microscope in place of themicroscope platform by means of a special adapter, and the illumination from belowwas used as in the previous measurements. I n place of the celluloid disk a piece of bondpaper was stretched over the top of the cylinder. I n order to make the ring appear veryblack and the edges sharp, a narrow strip of thin cardboard with a slit very slightly widerthan the diameter of the wire was slipped under the wire to cut down the extra light.This method gives excellent illumination, and precise measurements of the wire can bemade in this manner. Measurements a t twelve different, evenly spaced points on thering were made and the average of these was used. The values for the radii of the ringsand the radii of the wires are given in Table I.

of diameter of rings.

TABLERADIIO F RINGSNo. of No. ofring R r R / r ring R r

1 0.4143 0.01070 38.72 9 0.4678 0.016072 ,6065 .00903 67.17 10" 0.6366 .015703 ,5103 -.00973 52. 45 11 1.5245 .029464 ,8078 ,01877 43.04 12 1.8277 ,029865 1.0142 ,02001 50. 69 13 1.1806 ,040096 1.2185 ,02008 60 .6 8 14 0.7759 ,025787 1.2144 .02913 41.69 15 0.9421 .015858 0.6767 ,04875 13 .88 16 1.2603 ,01610a Ring number 10 was the ring furnished with a DuNoiiy Tensiometer.

R / r29.1140.5551.7561.2129.4530.8059.4478.28

6 . Measurement of Surface Tension by the Ring MethodThe difficulties involved in making precise measurements by the ring


7/22

May, 1930 SURFACE TENSION FROMPULL O N A RING 1757method are far more numerous than most investigators have assumed.Any rigorous theory of the ring method would require: (1) that thewire of the ring lie in one plane; (2 ) that the plane of the ring be hori-zontal; (3) that the vessel containing the liquid under investigationbe large enough so that any curvature of the free surface of the liquid wouldnot be great enough to affect the shape of the liquid raised by the ring;(4) tha t the surface of the liquid be free from wave motion; ( 5 ) tha t therebe no motion of the ring except an infinitesimally slow upward motion; (6)that there be no evaporation and consequent cooling of the surface; and(7) that the ring be round. These are requirements that are inherent inthe proper technique of the ring method, and must be approximated asnearly as possible. Of these sources of error, the last is probably the leastimportant.

The most important source of error arises from the ring not being hori-zontal. This was investigatedin a quantitative way by meas-uring the pull on the ring whentipped by various amounts.

2.0.6

2 1.2 1.5The stirrup was bent so thatthe plane of the ring was not 3 &$?1.0 gi

worizontal, and the difference I$-in height between the two sideswas measuredwith a cathetom- 0.4eter. From this the anglemade between the plane of thecalculated. Ring Number 12was used, and the data, whichare given in the table below, are illustrated in Fig. 5.

I0.5

1.0 2.0 3.0 4.0 5.0ring and the horizontal was d.Fig. 5.--Error du e t o tipping of ring.

TABLE1Angle , (I LIZ P AP Enor, %

0.00 0.00 84.05 0.00 0.001.10 1.21 83.61 0.44 0.521.62 2 62 83.20 0.85 1.012.10 4.42 82.73 1.32 1.67

DATAWIT H RING12

It is seen from the graph of the above data that for small angles suchas are liable to be encountered in practice, the error introduced is propor-tional to the square of the angle. Ap is, therefore, expressed by the equa-tionIn the present case the equation holds for angles not greater than 1.5degrees, and k has the value 0.36. From the graph it may be seen that

-Ap = ka 2


8/22

1753 W I L L IA M D . H A R K I N S AN D H U B E R T F. JORDAN Vol. 5 2for the error due to this source to be less than 0.1% the angle of tip mustbe less than 0.47 degree, and for an angle of 1 degree the error introducedis 0.43%.

The effect of the curvature of the meniscus and the size of the vesselwas studied by making measurements of water contained in crystallizingdishes of various sizes. The crystallizing dish was placed on a glassdesiccator triangle in a %liter beaker, and overflowed from the top, thusinsuring uniformly clean surfaces. T o prevent evaporation the top ofthe beaker was covered with a plate of glass in which a hole was bored.Measurements could not be made when the diameter of the dish was lessthan 7 cm., as the curvature of the meniscus was so great as to cause thering to cling to the side of the dish. The dataare given in Table 111.

Ring Number 12 was used.TABLE11

Diam. of dish, cm. 7 8 9 10 12P 83.96 84 03 84 08 84.05 84.06While this effect is not great for dishes more than 7 cm. in diameter in themeasurement of surface tension, it becomes of much greater importancein the measurement of interfacial tension.

The error caused by not having the wire all in the same plane cannot bemeasured quantitatively with any accuracy, but i t was observed that thiswas an important source of error.pull on the ring, and is one of the troublesome factors in measurementswith the larger rings made of fine wire. In straightening the wire a smallbrass plate was used in which a groove was cut. The ring was set on theplate with the portion of the ring to be straightened across the groove,and then tapped gently with a small brass rod rounded at the end. Whilethis method is not entirely satisfactory, it was the best of a number thatwere tried.

O B S E R V A T I O N S O N MENISCUSU R V A T U R E

This results in a consistently lower ,

7. Method of Measurement of Surface TensionThe method of measurement was as follows, The flask was cleaned with hot clean-

ing solution (10 cc. of saturated potassium dichromate solution and 990 cc. of concd.sulfuric acid) and the solution was allowed to stand in the flask for fifteen minutes.The flask was then rinsed thoroughly with conductivity water. In he case of measure-ments on liquids othei tha n water i t was also dried by circulation of air, previouslydried over sulfuric acid, and by gentle heating on the outside with a steam jet. Theflask was then filled with the liquid (already a t the temperature of the thermostat)to be measured and allowed to stand in the thermostat for three-quarters of an hourbefore measurements were made.

I t was suspended over a small gold plated brasstable, fitted with leveling screws and polished to a mirror finish on top. The table wasmade level by a small right angle level, and the ring was lowered to within a half milli-meter of the top of the table. By sighting between the top of the table and the ring in

The ring was leveled as follows.


9/22

May, 1930 SURFACE TENSION FROM PULL ON A R I N G 1759two mutually perpendicular directions, and by looking a t the ring and its mirror imagea t the same time, considerably less then 30' of t ilt could be determined. The stirrupof the ring was bent unt il the plane of the ring appeared to be perfectly horizontal.It was then cleaned by heating t o red heat in a flame. I n the case of three or four of t herings in which the stirrups were silver soldered to the ring, the ring was cleaned bydipping into warm cleaning solution, rinsing thoroughly in conductivity water, and dry-ing a t some distance above a gas flame.

The flask was then p ut in position under t he balance so tha t the plane of the innercup was as nearly horizontal as possible. The ring was then connected with the finealuminum rod from the left-hand stirrup of the balance beam by a jointed aluminumrod composed of links about two inches in length. On its end was a hook, the innercircumference of which was beveled to a knife edge to allow free motion of the stirruploop over it . An inverted Erlenmeyer flask with a hole about 1 cm. in diameter blownin the bottom was placed in the top of the measuring flask to prevent evaporation.

Th e weight of the ring suspended in air was determined and taken as the zero weight.The cup in the flask was overflowed with plenty of liquid to insure a clean surface, andenough liquid withdrawn through the side-arm (A ) (Fig. 3) to cause the liquid in thecup to become level instead of concave upward. With large rings the initial surface wasmade slightly convex upward, to such an extent that the outer part of the surface becomesplane when the ring is lifted to the height of detachment. The balance was lowered untilthe ring met the liquid, and then slowly raised while weights were added to determine theapproximate maximum pull. I n this procedure the addition of weights to the pan wasmade with the beam rest supporting the beam as in ordinary weighing, and during theaddition of weight by the chain the rest was lowered only enough to allow the pointerto swing three divisions in either direction. The final addi tion of weight and the raisingof the balance were so regulated as to keep the pointer always a t the scale zero. I ncheck determinations t he beam of the balance was raised and lowered again when thepull was about 10 mg. less than the maximum to insure its proper position, and the ad-ditional weight was added very slowly. When the maximum weight is reached, th ebalance pointer suddenly swings to the left and the liquid may or may not become de-tached from the ring, but any at tempt to raise the balance-to bring the pointer backto zero-causes detachment of the liquid. The maximum weight was taken as th eweight required to make the pointer suddenly move to the left, and which cannot becompensated by raising the balance without detachment of the liquid from the ring,

8. Experimental ResultsThe experimental results obtained by the ring method for water, ben-zene and bromobenzene are given in Tables IV , V and V I .

TABLEVWATER

Ringno . M P V R3/ V1 0.3446 64.89 0.3461 0.20552 ,5446 70 .05 ,5469 ,40793 ,4451 68.04 .4470 ,29734 ,7866 75. 96 ,7899 ,66735 1.0080 77.53 1.0123 1 03056 1.2196 78.08 1 2248 1.47717 1.2689 81.51 1.2743 1.40558 0.7374 85.00 0.7405 0.4185

Y/P1,10911.02741.05780.9475

,9283,9218. W O.8467


10/22

1760Ringno.

910111213141516

Ringno.12345678910111213141516

Ringno.12345678910111213141516

W I L L I A M D . H A R K I N S A N D H U B E R T P . JORDAN

M0.4123

,59501 60401.92391.28530.7741

,91781 2435

1M

0.1514.2273.1900.3283.4180,5037.5306,3243,1804,2515,6699.8029.EA65.3271.3768.5085

M0.1984,2939

.2462,4255,5419,6534,6924.4291.2358,3265.8729

1.04500.7179

,4269.4874.6583

TABLEV (Concluded)P V

68.75 0.414072.91 .597682.08 1.610882.11 1.932084.92 1.290777.84 0.777475.99 .921776.97 1.2488

TABLEBENZENE

P V28.51 0.173629.24 .260629.05 ,217931.70 ,376532.15 ,479332.25 ,577634.09 ,608437.39 .371930.09 ,206930.82 ,288434.28 ,768234.27 ,920736.11 ,626732.89 ,375131.20 ,432131.48 ,5831

TABLE IBROMOBENZENEP V

37.36 0.133337.80 ,197637.63 .165541.09 ,286141.68 ,364341.83 ,439344.48 .465549.47 ,288539.32 .158540.01 ,219544.67 .586844.60 .702547.44 .482642.93 .287040.36 .327740.75 .4426

RS/V0.2474

,43182.19963.16011.27490.6009

.90721.6030

R3/V0.4096.8561.60991 40002.17653.13202.94370.8333

,4949,8946

4.61226.63122.62561.24521.93523.4332

Ra/V0.53341.12900.80301 a 2 32.86354.11813 ,84741.07410.64611.17536.03808.69093.40961.62752.55174.5230

Vol. 52

?/P1.04680.9871

.8768,8765,8475.9246,9471I 9350

Y I P0.9902

.9655

.9718

.8905

.8781

.8754

.8281.7550

.9392

.9160

.8235

.8235

.7818

.8538

.9048

.8968

Y /P0.9569,9456

.9500,8700,8577.8M7.8037.7227.9092.8935.8003.8016,7536.8238,8858.8773


11/22

May, 1930 S U R F A C E T E N S I O N F R O M PULL O N A R I N G 1761In the treatment of the results above the first problem was to find the

variation of r/p with R lr when R 3 / V is kept constant a t various values,so that the values of r/p found experimentally could be converted intothose of the closest even value of R / r . While the values could have been

I i\2-

read from the r/p - R3/V plots of the values above, it was found thatin the case of the smaller rings the curvature of the plot was so great thatthis could not be done accurately. Other functions were then resorted to

Ring Waterno. R3 /V1 0.20552 ,40793 ,29734 .66735 1.03056 1.47717 1.40559 0.2474

10 ,431811 2.199612 3.160113 1.274914 0.600915 ,907216 1.6030

r i p1,11161.02221.05560,9408

,9268,9208,87851 0496

0.9859,8725,8744,8504,9216,9481.9368

TABLE I1EXPERIMENTALALUES

R3/ V Y IP0 5334 0.95691.1290 ,93560.8030 ,94591.8423 ,86002 8635 ,85574 1181 ,85323.8474 ,79670.6461 ,91221.1753 ,89206.0380 ,79538.6909 ,79893.4096 ,75701.6275 ,82882.5517 ,88694.523 ,8773

Bromobenzene BenzeneR3/V r / P0.4096 0.9932

,8561 .9555,6099 .9680

1.4000 .88102.1765 .87643.1320 .87422.9437 .82170.4949 .9412

,8946 .91454.6122 .81856.6312 .82112.6256 .78481.2452 .85411.9352 .go583.4332 .8989

R /r406050405060403040506030306080


12/22

1762 WILLL4M D. HARKI NS 4 N D HUBERT F . JORDAN Vol. 52in order to reduce this inaccuracy. The values for rings with R 3 / V between0 and 1.0 were determined by plotting V I R 3against yip, and the valuesfor rings with R3/Vvalues above 1.0 were determined by plotting log R 3 / Vagainst log y lp . In this way the curvature of the graphs was decreased toa minimum, and the accuracy greatly increased. When the resultingvalues of r / p are plotted against R l r , the series of curves shown in Fig. Gis obtained. The values of y l p were then corrected to those of the closestvalue of R l r . These values are 30, 40, 50, GO and 80. The correctedexperimental values are given in Table V I I .

The curves obtained by plotting the values above are shown in Fig. '7.Those obtained by plotting the values logarithmically are shown in Fig. S.It is seen that the curvature is greatly reduced by plotting the valuesin the latter way. By use of the r / p - R/r graphs, curves were also ob-tained for intermediate values of .R/r) rom which were read the values thatcompose the table mentioned in the following section.

9. Ring Method Correction (F) or the Shapes of the SurfacesIn order to avoid the necessity of plotting the corrected experimental

values for use in actual work, a table was constructed for a number ofintermediate values of R/r as well as the even values. The values of r / pgiven in the tables for R/r (except for too low values of R3/V) qual to 30,


13/22

Mav, 1930 SURFACE TENSION FROM PULL ON A R I N G 176340, 50, GO and 80 are considered accurate to 0.3% with a probable errorof less than 0.2%, while those for the intermediate values of R lr are con-

- .8 -0.4 0.0 0.4 0.8Log RSlV.Fig. 8.-Correction curves for r ing method.

sidered accurate to 0.4% with a probable error of less than 0.3%.values are given in Table VIII.

The

10. Weights of the Residual Drops on the R ingsThere has been a discussion concerning the importance of the drops of

liquid which adhere to the ring after it has been pulled out of the liquid.Klopsteg suggested that the zero weight should be taken a t the weightof the ring plus the weight of the drops of liquid which adhere to it, whileMacDougalP considers that such a correction is not justified. As aresult manufacturers have printed instructions that in the use of theirapparatus the intial reading be taken a t the weight of the ring in air plusthe weight of the adhering drops, and suggest tha t additional accuracy isacquired. Since, as may be seen from the experimental data presentedin this paper, most of the values for surface tension ( p ) obtained by the

TABLE IIIACORRECTIONACTORSOR EVENVALUES F R l r

v / p or F v / p or FR3;V R / r = 30 R/r = 40 RaV R / r = 30 R / r = 400.20 . . . 1.119 0.26 1.048 1.070

.21 . . . 1.108 .26 1.039 1.063

.22 . . . 1.097 .27 1.031 1.056.23 . . . 1.087 ,281 1.025 1.050

.24 1.056 1.078 .29 1.018 1.043Klopsteg, Science, 60, 319 (1924).* MacDougall, i b i d . , [N. S . ]62, 290 (1925).


14/22

1764 W I L L I A M D. H A R K I N S A N D H U B E R T F . JORDAN Vol. 52


15/22

May, 1930 S U R F A C E TENSION FROM PULL ON A RING 1765


16/22


17/22

Ra; V1.501.551.601 6 51 . 701 7 51.801 . 851.901 . 9 52.002.402.202.302.402.502.602 . 7 02.802.903.003.103.203.303.403.50R3/ V1.501.551.601.651.701.751 . 801.851 901.952.002.102.202 . 3 02.402.502.602.702.802.903 .00

', 1930 S U R F A C E T E N S I O N F R O M PULL O N A R I N G

R r = 3 00.8356,8327

,8297,8272,8245,8217.8194,8168,8143,8119.8098,8056,8015,7976,7936,7898,7861,7824,7788,7752.,7716,7677,7644,7610,7572,754250

0.8995,8970,8947,8927,8906,8886,8867,8849,8831,8815,8798,8768,8738,8710,8680.865l,8624,8598,8570,8545,8521

T AB L E IIIECORRECTIONACTORSF ) FOR THE R32 34 36 38 40

0.844 0.853 0.861 0.868 0.8744, 8 4 1 ,850 ,858 ,866 ,8722,839 ,848 ,856 ,863 ,8700,836 ,845 ,853 ,861 ,8678.834 , 8 4 3 ,851 ,859 ,8658,831 ,840 ,849 ,857 ,8638,829 ,838 ,847 ,855 ,8618,827 ,836 ,845 ,853 ,8596,824 ,834 ,943 ,851 ,8578,822 ,832 ,841 ,849 ,8559,820 ,830 ,839 ,847 ,8539,816 ,826 ,835 , 843 ,8502,812 ,822 ,831 ,839 ,8464,808 ,818 ,828 ,835 ,8428,804 ,814 ,824 ,832 ,8393,800 ,811 ,820 ,828 ,8360,797 ,807 ,817 ,825 ,8325,793 ,803 ,813 ,822 ,8291,790 ,800 ,810 ,818 ,8260,786 ,796 ,806 ,815 ,8230,783 , 7 9 3 ,803 ,812 ,8200,779 ,790 ,800 ,809 ,8170,776 ,787 ,797 ,806 ,8140,772 ,753 ,793 ,803 ,8113,769 ,780 ,790 ,800 ,8083,766 ,777 , 788 ,798 ,805752 54 56 58 60

0.904 0.908 0.912 0.916 0.9190,901 ,906 ,910 ,914 ,9171,899 ,904 ,908 ,912 ,9152,897 ,902 ,906 ,910 ,9133,895 ,900 ,904 ,909 ,9116,893 ,898 ,902 ,907 ,9097,891 ,896 ,900 ,905 ,9080,889 ,895 ,899 ,903 ,9066,888 ,893 ,897 ,902 ,9047,886 ,891 ,895 .900 ,9034,884 ,890 ,893 ,899 ,9016,881 ,886 ,890 ,895 ,8991,879 ,883 ,887 ,892 ,8962,876 ,880 ,884 ,890 ,8938,873 ,878 ,882 ,887 ,8910,870 .875 ,879 ,884 ,8884,868 ,872 ,877 ,882 ,8859,865 ,870 ,874 ,880 ,8837,862 ,867 ,872 ,877 ,8813,860 ,865 ,870 ,875 ,8790,858 ,863 ,868 .873 .8770

IN G METHOD42 440.881 0.886

,878 ,883,876 ,881,874 ,879,872 ,877,870 ,875,868 ,873,866 ,871,864 ,809,862 ,867860 ,865

,856 ,862,853 ,858,849 , 855,846 ,852,843 ,849,840 ,846,836 ,843,834 ,840,831 ,837,828 ,834,825 ,832,822 ,829,820 ,827,817 ,824,814 , 8 2 265 70. . . . . .. . . . . .

0.922 0.928,921 ,927,919 ,925,918 ,924,910 ,922,915 ,921,913 ,919,912 ,918,910 ,917,908 ,914,905 ,911,903 ,909,900 ,907,898 ,904,895 ,902,893 ,900,891 ,898,889 ,896,887 .894

4 60,891

,888,886,884,882,880,878,876,874,872,870,867,864,861,857,854,851,848,846,843, 8 4 1,838,835,833,831,82975

0.933,931.930,929,927,926,925,923,922,920,917,915.913,910,908,906,904,902,900

1767

4 80.895

,893,891,889,886,884,882,881,879,877,875,872,869,866,863,860,857,854,852,849,846,844,842,840,837,83580. . .

0.9382,9365,9354.9341,9328,9317,9305,92919281

,9270,9247,9226,9206,9185,9166,9145,9126,9107,9089,9068


18/22

1768 WILLIAM D. HARKINS AND HUBERT F. JORDAN Vol. 52TABLE IIIE (Concluded)

Ra/V 50 52 54 56 5 s 60 65 70 75 so3.10 0.8494 0.855 0.860 0.866 0.871 0.8750 0.8 85 0.89 2 0.899 0.90493.2 0 .&I72 ,853 ,858 ,864 .869 ,8730 ,883 .890 .897 .90303. 30 .8449 ,851 ,856 .862 .866 ,8710 .881 .888 .895 .go123.40 ,8424 ,849 ,854 .860 .864 .8688 ,879 ,886 .893 .89933.50 .8404 .847 ,852 ,858 ,862 ,8668 .877 ,884 ,892 .8974pseudo-ring method are too high, the values seem to be improved, but thisis done only by introducing a second error. The theory indicates thatthe zero point should be taken a t the weight of the dry ring in air. Theweight of liquid which adheres to one of our rings is constant if the air issaturated with vapor, and values of the weights of liquid which adhere tosome of the rings are given in Table IX.TABLEX

WEIGHT O F RESIDUAL ROPSRing Ringno. Water Benzene no. Water B en zen e

2 0.0013 . . . . . . 8 . . . . 0.00333 .0015 . . . . . . 9 0.0018 .00095 .0033 ...... 10 ,0167 .00196 .0044 . . . . . . 11 . . . . .00447 .0081 . . . . . . 14 ,0155 0029

11. The Variation of the Pull on the Ring with the Height of the Ringabove the Free Liquid SurfaceDorseyg has recently suggested that many workers, particularly those

using the DuNoiiy tensiometer, might be measuring the pull of af i lm ofliquid upon the ring rather than the maximum pull of the liquid. It wastherefore considered important to study the variation of the pull on thering with the distance i t is raised above the free surface of the liquid. Thevalues, which are shown graphically in Fig. 9, are given in Table X. Ring10 was used.

TABLERESULTS

Pull i n Height in Pull in Height ingrams cm. grams cm.0.3064 0.062 0.5894 0.290

.4064 .120 .5909 .300

.4564 .151 Maximum = 0.5912 . . .,5064 .186 0.5898 to 0.5899 .305,5264 ,203 .5836 to .5895 .319.5464 .223 .5823 to ,5875 .324.5664 ,248 ,5730 to .5839 .338.5764 ,262 .5616 to .5712 .352.5864 .279 .5425 to ,5606 .365,5884 .287 ,5066 to . . . .380, height a t detachment

Dorsey, Science, 69, 187 (1929).


19/22

May, 1930 S U R F A C E TENSI ON F ROM PULL ON A R I N G 1769It is evident that as the ring is pulled out of the liquid the pull on it

increases to a maximum and then decreases.It is at once evident that there is no danger of measuring any otherthan the maximum pull with the balance with the technique used, sincegreat difficulty was experienced in measuring points beyond the maximum.After the maximum pull had been reached, the balance pointer swungto the left and could be made to return only by decreasing the weightby fifteen or twenty milligrams, when it would swing quickly to theright and remain there. During this time its motion was restricted bythe beam rest to one division in either direction from the scale zero. In

P n grams.Fig. 9.-Variation of pressure with height of ring.

order to make any measurements of even low precision beyond the maxi-mum it was necessary to attach a stop which would allow the pointerto swing from zero to a point one-half scale division away in one direc-tion a t a time. The weight tha t would just suffice to make the pointerleave zero in one direction and then the weight to make it leave in theother direction were determined. In this way the limits of the pull onthe ring were determined for the heights above the height of maximum

It was noticed, particularly in the case of the smaller rings, that theliquid column had a tendency to adhere to the ring and be pulled o u t intoa film after the pointer had swung to the left, signifying that the maxi-mum pull had been reached. If, however, the beam rest is further re-leased from under the balance beam the liquid breaks. Until the maximumpull is reached the edge of the liquid meniscus appears to be attached tothe ring.

pull.


20/22

1770 W I L L I A M D . H A R K I N S A N D HUBERT F. JORDAN Vol. 5212. Preliminary Application of the Ring Method to Interfacial Tension

Measurements of the interfacial tension between water and benzenewere also made in order t o see whether the ring method is a practical onefor such measurements.

The general method of measurement was the same as for surface tensionwith only slight modifications. The measurements were carried out in a2-liter Erlenmeyer flask provided with a special long neck. The ringwas connected with the aluminum rod running up to the balance beam bymeans of a length of platinum wire 0.1 mm. in diameter. This was quitefine, in order to reduce the effect of surface forces and the effect of buoy-ancy. The layer of benzene was several centimeters deep, so that thering and its stirrups were completely immersed throughout the measure-ments. The initial weight was the weight of the ring completely im-mersed in benzene. The results obtained with Rings 7 and 5 are givenin Table XI. The interfacial tension is calculated by use of the correctionfactors ( F ) .

TABLE IRESULTS

7 0.5345 34.33 4.335 0,4132 0.995 34.165 ,4190 32 ,2 3 3.398 ,3070 1.051 33.91t , 25"; (D - d ) = 0.1233; y by the drop weight-volume method, 34.71.

On account of the steepness of the correction curves in this region,better results could probably be obtained with larger rings (of as small orsmaller wire).I n the ring method the angle of contact between the interface and thering must be zero, a condition which is more difficult to meet, in general,with interfacial than with surface tension.

There are probably a number of additional factors to be considered inthe measurement of interfacial tension by the ring method, but the devia-tions from the standard value are not greater than is to be expected fromthe first preliminary determinations.

Measurements were also made with smaller rings and the values of r/p

Ring A4 P v R3/V ./P t

TABLE I1DATA

Ring M P v R8,/I7 ?/P1 0,1272 23.95 1.032 0.0689 1.4492 ,2103 27 .O B 1.706 ,1308 1.2833 ,1680 25.68 1.363 ,0997 1.3524 ,3120 30.13 2.530 ,2083 1.1349 ,1513 25.23 1.227 ,0835 1.376

10 2281 27.95 1.850 ,1395 1.242y, 34.71; (D- ) = 0.1233.


21/22

May, 1930 S U R F A C E T E N S I O N FROM P U L L O N A R I N G 1771were calculated by assuming that the interfacial tension measured had thestandard value. The purpose of this was to show the magnitude of theerror that may be introduced by neglect of the correction factors. Thedata are given in Table XI I .It is seen that as high as 45% error may be incurred by this neglect inthe measurement by the use of a moderately small ring, since R 3 / V isvery small, and the curvature in this region of the curve is very great.The neglect of the correction with the ring furnished with the Cenco Ten-siometer gives results which are 20% too low, which accounts for theextremely inaccurate results which have been obtained in the measurementof interfacial tension by the ring method.

SummaryUntil three years ago there was no ring method for the measurementof surface tension, since, in general, all that was determined was the pallon a ring, and this pull was incorrectly assumed to be equal to the surfacetension multiplied by twice the mean circumference of the ring. Even incases in which attempts were made to use the incomplete theory of the ringmethod, i t was found that rings of the dimensions required by the theorywere incapable of use. Three years ago Harkins, Young and Chengapplied the principle of similitude to this problem, and determined thevalues of the function F in the correct equation

1.

M M? =& X f ( R 3 /V , / r ) = -3R FIn this paper a larger number of values of F , determined to a higherdegree of accuracy, are given. These were obtained by determining thevalues of the maximum pull (P =M g ) for sixteen rings with radii from 0.4to 0.8 cm. made from wire with radii between 0.009 and 0.05 cm. and withvalues of R / r between 13.9 and 78.3.

The values of the maximum pull were determined for three liquids:water, benzene and bromobenzene. Accurate determinations of the sur-face tension by the capillary height method gave for the liquids used 28.23dynes per cm. for benzene and 35.73 for bromobenzene a t 25.

3. Various sources of error in the experimental methods were investi-gated. (a) The error introduced when the plane of the ring is not hori-zontal is proportional to the square of the angle of tip when the angle issmall. An angle of 0.4 degree causes an error of 0.1% and 1.0 degree of0.45%. The diameter of the vessel which confines the surface of theliquid should be not less than 8 cm. (c) An error is introduced if thering does not lie in a plane.

An apparatus for the accurate determination of surface tension bythe ring method is described. This consists of a chainomatic balance,supported by a machine which raises or lowers it with a minimum amount

2.

(b)

4.


22/22

1772 B. B. FREUD AND H. 2.FWUD Vol. 52of vibration, and a special flask, designed to give a clean liquid surface,buried under the water of a thermostat.It was found that the accuracy of measurement of the dimensions ofthe rings depends greatly upon the method of illumination employed,and apparatus for these measurements was developed.It was shown tha t a t a certain height above the surface of theliquid the pull on the ring reaches a maximum. This maximum pull iswhat was determined in the measurements reported.A necessary condition of the ring method is th at the angle of contact

5.

6.

7.between the ring and the liquid be zero.used for the determination of interfacial tension.

8. Preliminary measurements indicate that the ring method mayCHICAGO,LLINOIS

[CONTRIBUTION FROM THE KENT CHEMICAL LABORATORY OF THE UNIVERSITYCHICAGO AND FROM ARMOURNSTIT UTE OF TECHNOLOGY]

be

OF

A THEORY OF TH E RING METHOD FOR T HE DETERMINATIONOF SURFACE TENSION

BY B. B. FREUDN D H. 2. FREUDRECEIVEDECEMBER, 1929 PUBLISHEDAY , 1930

The most convenient method for the determination of surface tensionis perhaps what is known as the ring method. It has been used exten-sively, for example, by DuNoiiy' in the case of numerous biological liquids.It is convenient because the experimental procedure necessary to obtaina fair degree of accuracy can be made very simple, although of course itbecomes much more complicated when a higher degree of accuracy issought. The essentials of the procedure are a ring, capable of beingwetted by the liquid whose surface tension is to be measured, suspendedhorizontally in the flat surface of that liquid, and some device to measurethe force necessary to separate ring and liquid. Th at the applied forcemay be changed gradually, a torsion balance is often used but a beambalance of the chainomatic type is also satisfactory. From this measuredforce, expressed as a weight, a quantity which many assume to be thevalue of the surface tension is often obtained from the relationshipwhere R is the radius of the ring, the surface tension and W the maxi-mum weight of liquid held up or the pull on the ring at the instant ofrupture. Modifications have been introduced into this equation, such asthe substitution of (R, +R2)/2 for r , where R1 and R, are the inner andouter radii of the ring. But the validity of this relationship is not a t allobvious. An experimental study of i t by Harkins, Young and Cheng2 and

W = 4 ~ R y (1)

DuNoiiy, J.Gen. Physiol., 1, 521 (191&1919), etc .2 Harkins, Young and Cheng, Science, 64, 93 (1926).

hrakins jordan

Documents