STUDIES 11; DROP FORMATIOX AS RETEALED BY T H E HIGH-SPEED MOTION CAMERA' H. E. EDGERTON, E. A . HATSER,
AND
W. B. TUCKER
Massachusetts Institute of Technology, Cambridge, Massachusetts Received J u n e 26, 19dY
Measurements of the weight of drops, or of drops formed from a given volume of liquid, have long been used for the calculation of surface tension a t liquid-vapor interfaces, and for the determination of interfacial tensions between liquids. Many investigators (notably Tate, Worthington, and Rayleigh) have attempted the formulation of theoretical equations to make possible the calculation of surface tension from the volume or weight of a drop detaching itself from a tip of given size. Unfortunately, most of these equations were based on plausible but false assumptions. The drop-number method proposed by Traube (2, 4) gives only rough approximations, and its results are unreliable. K. D. Harkins and F. E. Brown (3) have developed an excellent technique for obtaining self-consistent data on the surface tension of liquids by the drop-weight method, and in 1918 they presented empirical curves which make the accurate determination of surface tension possible. Preliminary inveqtigations conducted a year ago in these laboratories with the aid of the high-speed motion picture camera (4)seemed to shouthe value of direct observation of the mechanism of drop formation in surface tension research. The empirical surface tension correction curves offered by Harkins and Brown are very interesting, in that they show a distinct minimum followed by a maxiniuni (figure 1). It %as hoped that actual observation of the formation of drops from tips of various diameters might throw some light on the cause of the peculiar shape of the surface tension correction curve. For this purpose, a set of twenty-three brass and copper tips was constructed by methods similar to those described by Harkins and Brown. These tips are shown in section and their dimensions are tabulatrd in figure 2. In order to time the falling of the drops closely cnough to photograph Presented a t the Fourteenth Colloid Symposium, held at Minneapolis, Minnesota, June 10-12, 1937.
1017
1018
H. E . EDGERTOK, E . .4. HAUSER, A S D W. B . TUCKER
0.8 0.9 1.0 1 . 1 1.2 1.3 14 1.5 r.6 r Radiua of tip ECube root of volume of drop V% Drop-weight d o n s . (Note: Point I does not belong oa the curve since the benzene a w l e d up the side of the tip.)
0.3
0.4
0.5
0.6
0.7
FIG.1. Empirical surface tension correction curves of Harkins and Brown
Copper
Drill 'a '
Copper
30
i
T 05Ou
-I
L'q
9
TIPS 1-5, 7-23
IO II
I2 13 14 0125
16
Brass Brass Brass Biass
19 20 21
22 23
T
Brass
Brass
18
0200'
Brass
15 17
0300"
Brass Brass Brass Bless
Brass
Brass Brass Brass
40 40 40 30 30 30
30 30 30
30 30 30 30 30 30
8 0 80 79 78
77 76 73
72 70 70
0200 0268 0295 0315 0 355
0 395 0473 0512 0551
0508 0681 0749 0800 0 902 1 003 I201
I300 I400
0570
1.448
69
0596
1514
68
0607
67 64 60
0635
I542 I613
TIP 6
FIG.2. Details of stalagmometer tips
0711
1.806
0791
2009
1019
STUDIES IS DROP FORMATIOX
them during the single second that it is practical to run the high-speed camera, the stalagmometer shown in figure 3 was constructed. Fullsized drops were formed on the tips and then suddenly detached by a slight turn of the thumb screw. This method, while not suitable for precise quantative determinations, introduced relatively small errors in the actual weight of the drops formed. Three series of pictures were taken. The first series was taken for the
FIG.3. Stalagmometer
0
Hq Tube
--
__I P'
1000 volts
D.C.
m
v
800 n
-
aI
Condenskg
Lens
Camera
Impulses from Thyrotron
FIG.4. Apparatus for silhouette photography
purpose of attempting to determine the reasons for the peculiar shape of the surface tension correction curve. Conductivity water was used for these tests. The second series was made to discover whether the minimum in the curve of surface tension versus concentration of certain organic chemicals in aqueous solutions (as described by McBain, Ford, and Wilson ( 5 ) ) may be observed on freshly formed surfaces, or is only developed as the surfaces age. Solutions of sodium oleate in water were used. The
1020
H. E. EDGERTON, E . A. HXUSER, Ah-D W. B. TUCKER
third series was undertaken for the purpose of determining whether solutions having identical surface tensions as determined by the du Xouy ring method (using moderately aged surfaces) would all form drops in an identical manner. For this purpose, nitrobenzene and solutions of sodium oleate in water, alcohol in glycerol, and alcohol in water were used. Motion pictures (see figure 4) were taken at the rate of 800 pictures per second of drops of water falling from each tip. Significant frames were
TIP D I M
0191
0501
I001
WATER
I613 cm
, I I
FIG.5
FIG. 6
FIG.7
FIGS.5, 6, and 7 . Drops of water falling from tips of various diameters
selected from each roll (figures 5 , 6 , and 7). Measurements of the diameters of all of the primary and secondary drops were made on enlarged photographic prints and are tabulated in table 1. From these measurements the weights of the individual drops were calculated and totaled, and the results were compared with the average drop weights obtained by weighing several sets of ten drops each (see table 2). As may be seen, the calculated values agree rather well with the directly measured values.
1021
STI-DIES I N DROP FOR>XATION
The stem lcngth at thc instant of detacliiiieiit of the primary drop n as also determined troni tlic mlargemmts. One of thc firct pointh of interest is t h lariatior1 in shape niid size of the pmciant drop 1u.t prior t o tlic iiictant t h a t inctnbility sets in. I t nil1 bc noticed in figure 5 tiitit for tip. n-lio~rc1innieit.r ic crnaller than 0.5 mi., thc pendant drop ha-. :i diametrr grcatcr than the diameter of tlie tip. T I w pendant drop on larger tip- Iia~:a sninllrr diameter than the tip on n-hich it i q forniccl. TABLE 1 Dinicnsions cf d r o p s in centimeters
L;y2;H
DIAMETER
TIP
DROP DI%\fETERS ~
Primarv ~
~
6 7 Q '
9 10
becondari
3
4
5
0191 0 254 0 343 0 508 0 681
020 0 3E 0 43 0 64 0 E4
040 0 42 0 46 0 52 0 56
0 749 0 800 0 902 1 003 1 201
0 94 0 99 I 07 1 25 1 63
0 0 0 0 0
57 59 60 62 65
0 17 0 17 0 18 0 19 0.26
0 16 0 16
0 14
0 11 '
1 75 1 83
0 67 0 70
0 26 0 28
0 16 0 20
0 14 0 14
0 14 0 14
2 00 2 03
0 72 0 72
0 32 0 32
0 22 0 22
0 20 0 20
0 18 018
2 08 2 16 2 24
0 72 0 72 0 72
0 32 0 32 0 32
023 0 25 025
020 0 20 020
018IO16 014 0 18 0 16 0 13 0 1 8 ~ 0 1 6 1 0 1 3
I
, 0 14 0 16 I
11
12 13 14
15
7
6
_ _ -__
~
I
I
16 17
300 400 448 514 542
19 20
1 1 1 1 1
21 22 23
1 613 1 806 2 009
18
I
I
0 14 014
~
0 16 016
I
1
Consider a static clrop of liquid hanging from a tip. The entire weight of the drop must be supported by adhesion of the liquid to the surface of the tip. I n figure 8 the silhouette of a drop is presented. Now suppose an imaginary horizontal plane is passed through n drop a t any point. Line a--a represents such a plane dramm through the neck. The sum of t h e vertical components of all the forces acting at this section must be zero. These forces are ( a ) surface tension around the perimeter, and ( b ) compressive stress in the liquid. Graphical analysis of the drop in figure 8 (surface tension i 2 dynes per centimeter) shows a vertical upward component of surface tension at section b--b of 0.103 g., 0.038 g. of water
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H. E. EDGERTOX, E. A . HAUSER, A S D W. B . TUCKER
hanging from this plane, and a resultant net conipressivc force of 0.427 g. per cm2.over the area of the section. Similar analysis at &--a shows the vertical component of the surface tension of 0.095 g., 0.0632 g. of water hanging from the plane, and a resultant net compressive force of 0.236 g. per cm?. A t the surface of the tip the component due to surface tension is 0.104 g., 0.094 g. of water is supported, and the net compressive force is 0.0574 g. per cm2. This is therefore a stable drop. The difference in hydrostatic head between the tip and a--a is 0.179 cm. of water, and the TABLE 2 Drop weights calculated f r o m measurements in table 1 as compared w i t h actual drop weights
I
TIP
CALCULATED DROP WEIGET
ACTUAL DROP WEIGHT
~
grams
grams
6 7 8 9 10
0.034 0.039 0.051 0.074 0.094
0 0325 0 0396 0 0522 0 0717 0 0956
11 12 13 14 15
0.100 0.110 0.116 0.131 0.156
0 0 0 0 0
16 17 18 19 20
0 171 0 198 0 221 0 221
0.1868 0.2071 0.2131 0,2201 0.2224
0 229 0 231 0 231
0 2295 0 2257 0 2314
21 22 23
I I ~
I I
-
1033 1086 1202 1388 1737
__
.-
difference in net compressive force is 0.178 g. per ern?.,a good check. The hydrostatic head between a--a and b--b is 0.192 cm. of water, and the difference in net compressive force is 0.191 g. per cm2. This agrees with &\. M. Worthington’s conclusions (6). The conditions given above are normal for a stable pendant drop. hdditional liquid can be added to the drop until the net compressive force at the neck approaches zero, at which time instability sets in. .It this instant the problem changes from one of static forces to one of dynamic motions. Unbalanced forces are opposed by accelerations and viscous
1023
STTDIES IS DROP FORMATIOX
drag. It becoinea practically impossible to predict the mechanism of detachment on a theoretical basis because of the complexity of the motions of the drop, its qtem, and secondary drops. This is illustratcd by figure 9, which shows the actual mechanisni of drop formation for water falling from a large tip. It is interesting to note how complicated the drop formation becomes with largc tips. Irvtability first shows itself by a lengthening and reduction in the diameter of the neck. The neck breaks off close to the priniary drop, which oscillateq as it falls. Thenecknow begins to break up into segnwnts and detaches itself from the residual fluid remaining on the tip. The segments of the neck now become independent secondary
DROP OF WATER PENDANT FROM A 0.508 ern. TIP
FIG.S
FIG.9
FIG.8. Drop of water pendant from a tip having a diameter of 0.508 cm. FIG.9. Actual mechanism of drop formation for water falling from a large tip, the diameter of which is 1.542 r m .
drops, faIliiig after the primary drop a t unequal velocities; some of them may coalesce. Tate assumed t h a t the weight of a drop equaled the product of the surface tension of the liquid by the circumference of the tip on which it formed. This wouId be true if the wall of the drop were vertical where the liquid joins the tip, if there were no conipresk-e forces across the plane, and if all of the pendant drop actually detached. Unfortunately, this ideal condition is never niet in actual practice. The pictures show clearly that it is very rare for the wall of the drop t o be vertical a t its juntion n i t h the tip, the conipressive force is not zero, and there i q always a very considerable reqidual drop left on the tip.
1024
H. E . E D G E R T O S , E. .%.
H I C S E R , A S D TV, B . T C C K E R
Harkins and Bronn have used Tat?’& lan- ab a point of departure. and contributed an empirical correction curve which makes it possible to determine from a knowledge of the volunic of Tate’s “ideal” drop t h e volume of the drop which actually falls. Figure 10 shon s thi- curve, together with pictures of drops formed from various tips. A i tthe left-hand side of the diagram the actual falling drop is a large portion of the ideal drop. The decrease from here to the minimum is due to dccreabe in diameter of the drop relative to the diameter of the tip. The increase between the minimum point and the maximum is probably due to the increase in the thickness of the stem and the detachment of a greater portion of the pendant drop. -It the maximum, the maximum size of primary drop is attained, and although the stern length continues to increase, the increase in the size of secondary drops formed from it is small compared to the increase in circumference of the tip, and the curve falls off rapidly as the tip diameter is increased. This is paralleled by the difficulty of completely wetting‘ large tips effectively. The curve of profile of the pendant drop becomes nearly tangent to the tip at the point of junction. As a result, the main component of the surface tension forces is toward the center of the tip, tending to sweep the liquid toward the center into a drop of smaller diameter and surface. This leaves a thin film of moisture on the tip, which tends to evaporate very rapidly, owing to its practically colloidal dimensions. McBain, Ford, and Wilson (5) have pointed out t h a t while the addition of small amounts of certain organic chemicals to water causes a reduction in surface tension, a definite minimum surface tension is reached, after which further additions of the organic chemical increase the surface tension. Sodium oleate is such a substance. The experiments on which their results were based were conducted on aged surfaces. As may be noted from the preceding figureq, a large amount of new surface is always formed when a drop falls from a surface, and if the drop is formed just prior to the time of detachment, it is possible to study a surface which has aged for only a few hundredths of a second. Drop formation, therefore, presents an excellent method for determining if the minimum surface tension mentioned above is dependent on the rather slon- formation of surface structure implied by the usual concept of concentration of a surfaceactive substance a t an interface. I n the paper mentioned above, the mininlunl surface tenqion was observed for sodium oleate in water solutions Tyhen the concentration reached about 0.1 per cent by weight. Solutions of sodium oleate in water of 0.001, 0.01, 0.1, and 1.0 per cent by weight were used for the experiments. A check on the variation of du Nouy ring surface tensions showed that the 0.1 per cent solution gave the minimum surface tension in accordance with the above reference The four largest tips in the set were used, since they
1025
S T U D I E S I S DROP FORJfATIO?-
offered opportunity for the greatest possible variation in the method of drop formation. Figures 11, 12, and 13 show typical results from thiq series of tests. The predicted mininiuni is quite pronounced. Figure 11 shows t h a t the 0.1 per cent solution produced the smallest primary drop and the shortest
.
.
I
0001 1 1 %
FIG. 11
v I
0
0
I 0
1
0
r
i
01
001
. 10
01
0 01 W I x
10
* @ OOO1rlr
SODIUM OLEATE IN WATER
SODIUM OLEATE IN WATER
FIG.12
FIG.13
FIG.10. Empirical correction curve of Harkins and Brown, together with pictures of drops formed from various tips. FIGS.11, 12, and 13. Results obtained with sodium oleate solutions
stem. Figure 12 emphasizes the shortening of the stein. Figure 13 shows the effect of concentration of the sodium oleate on the number of secondary drops formed by segmentation of the stem. This result indicates that, a t least with the system under investigation, the appearance of a minimum surface tension does not depend on aging of the surface. The experiments conducted last year Tyith moderate-sized tips showed
1026
H. E. EDGERTOS, E. -4. HAUSER, A S D W . B. TCCKER
that the mechanism of formation of drops of glycerol is markedly different from that of the formation of drops of water, for example, particularly in regard to the length of stem formed and the method of segmentation of that stem. This raises the question of the validity of the measurement of the surface tensions of viscous liquids and of solutions of surface-active materials by the drop-weight method. In order to study the problem, solutions were made which had identical surface tensions as shown by the du Nouy ring method, but which differed widely in their other physical properties. The approximate compositions of the solutions used are given in table 3, but no unusual precautions were taken in prcparing the chemicals used. Tips No. 1 , 4 , 18, and 23 were used with each solution. Typical results are shown in figures 14 to 16. Tips 18 and 23 were, of course, too large to obtain reliable values of surface tension by the drop-weight method with solutions of such low surface tension. TABLE 3 Solutions having the samc surjace tension as determined by the d u Nouy ring method SOLUTIOS
COldFOSlTIOS
Nitrobenzene .4lcohol-water
48
,
47 8
I
Sodium oleate-Rater Glycerol-wat er _____-
1 I
1
48 1 47 7
-
’ 1
1
SPECIFIC GRAVITY
100 per cent commercial nitrobenzene 85 6 per cent water 0 973 13 7 per cent ethyl alcohol 0 7 pel cent methyl alcohol 0 00068 per cent sodium oleate 99 99932 per cent a ater 90 8 per cent glycerol j 1 219 9 0 per cent ethyl alcohol 0 2 per cent methyl alcohol I -
If the drop-weight, or the dropnumber, method were to be reliable, the minimum requirement would be that the shape and size of the pendant drop at the instant instability sets in, and the portion of this drop finally detached from the tip should be the same for each of the liquids (1). Admitting that the drop-n eight method as conducted in these experiments, and to some extent regardlws of the details of technique, gives the surface tension of fresh surfaces. whereas the du Soiiy ring method uses aged surfaces, the sodium oleate in water solution may be excused from conforming with the “normal” liquid, nitrobenzene. The alcohol in water solution is qualitatively similar to the nitrobenzene, but the glycerol is very different. Our conclusion is that the drop-weight and drop-number methods may be reliable for pure liquids, but that their use for determining the surface tension of solutions and of viscous liquids is questionable.
102i
STUDIES I N DROP FORMATIOX
The tenacity of the extremely small filaments of glycerol which are f'ormcd 9s the detached stem segments is remarkable. Many pairs of
NlTROeENZEK
. ' S K W 4 OCEATE
WATER
F I G . 14. Drop formation in the case of solutions having the same surface tension
I*
s.rr/.
, 4 1 1 :_
0
GLYCERINE AND ALCOHOL
/ s O."/
i.
1,1
-
GLYCERINE AND ALCOHOL
FIG. 15 FIG.16 FIG.15. Drop formation in the case of a solution of glycerol and alcohol (see table 3), using a tip having a diameter of 1.448 cm. FIG.16. Drop formation in the case of a solution of glycerol and alcohol (see table 3), using a tip having a diameter of 2.009 cm.
drops remained joined by practically invisible threads, but these threads contracted and pulled the drops together so that they coalesced. Some
1028
H. E. EDGERTOS, E. -4. HAYSER, A S D W. B. TUCKER
of these threads showed in the original enlargementi. but are lost in subsequent reproduction. Other pairs of drop. roalecced u-hich werc not joined by visible threads. There is a good chance that these were joined by invisible filameiits. The ability of visrous liquids to ioriii thread< may throw nen- light on the actual nature of viscosity. I t is quite concc4vahlc t h a t microscopic or colloidal liquid filanientq are formed n-hen an atttmpt is made to shear or stir a viscous liquid. SUMJIARI
1. Accurate graphical analysis of thc itresiei in a pendant drop can be made providing a sharp qilhouette is arailable. 2. There are net comprrsbive forres at all plaiic. in a itable drop. 3. The mechanism of drop formation from large tips is very complex, and the use of large tips for surface teiiiion nieaiurrnients is not advisable. 4. Primary drops from small tips may be of larger diameter than the tip itself, but the primary drops from large tips are .mall compared to tip size. 5 . The number of secondary drops formed by the segmentation of the stem varies both with the tip size and with t h e nature of the liquid used. Drops formed on the smallest tips detached n-ithout the formation of any secondary drops, while fifteen secondarieq were formed during the detachment of a drop of an alcohol in glycerol solution from a large tip. 6. The occurrence of a minimum surface tensioii of soap solutions, as predicted by IllcBain, Ford, and Kilson, was readily verified by examination of motion picture. of drops of qonp solution falling from large tips. 7. It was found that the physical properties of a liquid have a large effect on the mechanism of drop formation. Viscosity and surface activity are both important. 8. Dynamic methods for determining surface tension should be used with extreme caution unless the methods of calculation are known t o be applicable t o the particular liquid bcing ztitdied. Static methods are preferable. REFEREIL’CES (1) ADAMS,N . K.: The Physics and Chemistry of Surfaces, p 317. The Claieiidon Press, Oxford (1930). (2) FERGERSON, A : Fifth Report on Colloid Chemistry, p 7 (1923). (3) HARKING AND BROWX: J. Am Chem S o r 41,499 (1919). (4) HAUSER,EDGERTOX, HOLT,AND Cox: J Phps. Chem. 40, 973 (1936). This article gives a more complete bibliography. (6) MCBAIX,FORD,AND WILSON:Kolloid-Z. 78, 1 (1937). A 31 : Proc. Roy. Soc (London) 32,362 (1881). (6) WORTHINGTOX,
