THE FUNCTION O F THE WALLS IN CAPILLARY PHENOMENA S. L. BIGELOW AND F. W. HUNTER
The purpose of this investigation was t o determine whether the material of which a capillary tube is made has any effect upon the height to which a liquid will ascend in it. The literature upon capillarity, which is extensive, does not furnish the desired information. G. Quincke’ believed that water rose to different heights in tubes of different kinds of glass. P. Volkmann’ subjected this conclusion to an exceedingly careful investigation and decided that the nature of the glass made no difference. Inferences may be drawn from the measurement of flat drops on different surfaces, but direct measurements of capillary ascension in tubes other than glass do not appear to have been attempted, probably on account of the fairly obvious difficulty arising from the fact that such tubes are not transparent. It occurred to one of us that such measurements could, however, be made with great facility by applying a simple, well-known principle. The height of a column of liquid in a capillary tube is determined by the radius of the tube ut the meniscus, and the size or shape of the tube below the meniscus makes no difference. Accordingly, if a tube of any convenient radius, say 3 mm be closed at the top by a thin plate of any material, through which a small hole is bored; if the whole be immersed in a liquid, and then gradually raised; a meniscus should form in this small hole, and the whole tube should remain full of liquid, until the height of the column is equal t o that which would have been obtained with a long enough tube of the material of the plate, and of uniform bore the same size as the hole. When this point is reached, the meniscus should break away from the lower surface of the ~
-
___
Wied. Ann., 52, I (1894). Ibid., 53, 633 (1894).
368
S.L. Bigelow and F . W . Hunter
plate and the tube should empty. We found the facts agreed with this simple deduction in the most gratifying manner. Apparatus A cross section of the essential part of the apparatus we constructed for measuring capillary ascensions is shown on an enlarged scale in Fig. I . The complete arrangement is shown on a diminished scale in Fig. 2 with the plate removed and as it appears while a height is being determined. A is the plate with the small capillary hole in it, resting on the glass tube B. This is carried by an arm C, which is raised or lowered by a ratchet and pinion mechanism such as is used for the coarse focussing adjustment on microscopes. Thus the tube and plate may be lowered until entirely submerged in the liquid in the beaker, and then 'it may be raised until the meniscus a t the small hole breaks and the tube empties. At first we cemented the plates to the tubes, but cements dissolve and the solutions having different surface tensions are apt to produce irregular results. We discarded cements, put a rubber stopper on the tube and laid our plates on that. Only then did we realize that a further application of the principle on which we are basing our whole method made rubber as superfluous as cements. Suppose there is a crack between the plate and the top of the tube. It will fill with the liquid by virtue of the capillary forces, and will stay full and will not '' leak" unless its width is equal to, or greater than, the radius of the hole in the plate. It is a very easy matter to grind off the top of the tube and to use flat plates so that the break, when it comes, comes always a t the hole. We, therefore, merely laid the plates on the tubes and proceeded to make our observations. This simplification may appear trifling, but it is not, in fact, for three reasons. First, it much diminishes the time required to prepare for an experiment; second, it makes it much easier to clean the plates between experiments; third, it enables us to avoid substances which might contaminate our liquids or their surfaces. After the liquid had fallen, we removed the plate, brought the point D to the surface of the liquidin the beaker, utilizing
Function of the Walls in Capillary Phenomena
Fig.
I
369
37 0
S . L. Bigelow and F . W . Hunter
the reflection of the point on the surface in the usual manner, and then brought the point E onto the edge of the glass tube. These points are carried by extensions independently movable, on one of which extensions is a scale in millimeters, on the other a vernier. We thus read the height to one-tenth of a millimeter, the limit of accuracy of our present instrument. We have in mind the construction of another with a micrometer screw to measure to 0.01mm. Two corrections must be applied to the height thus measured. First, the liquid falling out of the tube raises the level of the liquid in the beaker. From the diameters of the beaker and the tube and the height of the column, this correction is easily calculated. We found it more expeditious in most cases, however, to make a preliminary experiment to determine about the height to expect. We then repeated more carefully, and, after having raised the plate to within two millimeters of the breaking point, set the point D, then raised gradually till the break came, removed the plate and set the second point E. The second correction is as follows: the meniscus in the plate remains near the top at first, but when a height is reached within the thickness of the plate of the maximum height, the meniscus descends until it hangs by the lower edge, as indicated in Fig. I . We assumed, for obvious reasons, that just before breaking it was hemispherical, with a radius equal to that of the hole. We, therefore, subtracted this radius from the measured height. It would have been more accurate had we subtracted 2 / 3 of the radius, but this refinement falls at the limits of our experimental errors. . It should be mentioned that we lay no particular stress on this ratchet and vernier instrument, and recognize that a cathetometer telescope would have certain advantages. It would take longer to make the readings with the telescope, but they would be somewhat more accurate. For drilling the holes in the plates, we used a jeweller’s lathe and drills, holding the drill stationary and revolving the work. We examined the holes and measured them I
Function of the Walls in Capillary Phenomena
371
with a good microscope, a stage micrometer and micrometer ocular. We had the customary difficulties in our efforts t o secure strictly round holes. None of them were round within the limits of our measuring instruments, but they were as nearly round as the bores of the tubes used by previous investigators of capillary phenomena. Our measurements of the diameters of the holes were within z microns of right. On each hole we measured I O t o 1 2 diameters and took the average. The difference between the maximum and minimum diameters on one hole was never less than 5 microns. If this difference exceeded 20 microns, we did not use the plate. With the very thinnest metal plates and with salt plates, we were obliged to content ourselves with somewhat less regular holes. With some salts the deviation equalled 8 percent of the smallest diameter. Not infrequently, when we thought we had prepared a useful plate, we observed differences between maximum and minimum diameters as large as 60 microns. The holes in the plates were inspected and measured under the microscope before and after each group of observations, and if measurable differences were observed that group of observations was discarded. This was an absolutely necessary precaution in, our work with soluble salt plates, and a reasonable precaution in our work with such metals as zinc and copper, owing to our method of cleaning. Metal plates were washed by immersion in dilute sulphuric acid ( I : 3) for from 30 to 60 seconds, then transferred t o distilled water, dried with filter paper and then dried at a distance of 2 0 cm above a bunsen flame. They were then washed in benzene, dried with filter paper and then again at the same distance above a bunsen flame. The salt plates were merely dried as rapidly as possible with filter paper after removal from the solution. We secured the desired temperature and held it constant within 0.5' by standing the beaker in a large shallow jar of water t o which we added hot or cold water as needed. After having developed the method as described above,
372
S. L. Bigelow and F . W . Hunter
we discovered that Oersted' had devised a similar apparatus based on the same principle, in 1841. In Oersted's apparatus, one arm of a U tube carried a plate with a hole in it. A side arm enabled him to alter the level of the liquid in the other arm of the U tube. He raised the level here till liquid was forced out through the capillary and measured with a cathetometer the liquid pressure required. He also lowered the level in the other arm until the meniscus broke away, as in our work. This is a less convenient application of the principle than ours and less free from possible errors. He determined that an amalgamated copper tube and a glass capillary tube raise water to the same height. He also determined the capillary ascension of mercury in an amalgamated copper tube and that is all. The article is but three pages long. He expresses his intention of continuing this line of investigation, but we have not found anything further by him. He died in 1844. It is indeed strange that no one else appears t o have utilized his apparatus.
Results Although we felt reasonably certain that the thickness of our plates could make no difference, we carried out a set of experiments to prove the fact. Our results are contained in Table I. This, and the succeeding tables containing our results, are self explanatory, and require but few remarks. All measurements are expressed in millimeters. The first column contains the thickness of the plates, the second the radius of the capillary hole in the plate, the third, the highest ascension obtained, the fourth, the lowest, the fifth, the number of separate observations, the sixth, the average, and the seventh, the product of this average into the radius. The values in the seventh column should then be constant. Each horizontal line represents an entirely separate group of experiments, in many, if not most instances, carried out on different days. A microscopical inspection of the hole preceded and followed each of these groups. J. C. Oersted: Pogg. Ann., 53, 614-16 (1841).
Function of the Walls in Capillary Phenomena
373
Our glass plates were sections cut off a capillary tube and ground down to the given thickness with fine carborundum and a solution of camphor in turpentine. TABLEI Copper Plates-Water.
Temp. 20.5-21
_ -~ _ _
O
Thickness of plate I
0.07 0.14 0.15
0.316 0.250 0.243 0.243 0.296 0.289 0.293 0.285 0.240
0. I O 0.20
0.68 0.81 0.83 I . 13
I
47.9 60.3 62.3 62.8 51. I
I
59.3 62.3 61.5
4
51.2
5
62.6
3
52.I
51.9 53.8 62.7
47.61 60.11 62.31 62.31 so.95 52. IO 51.72 53.78 62.70 Av.
TABLE2 Platinum Plates-Water.
~-
_ _ ~ __ _ _ ___ _~_ __ _ _
0.08 0.08 0.08
Temp. 20.5-21 O -_______ - 5 52.15 I 14.76 54.58 1 14.69 46.83 I 14.70
l-
Av.
~~ ~
0.24 0.24 0.24 0.24 0.24 0.24 0.24
~~~
___________
0.304 0.306 0.293 0.271 0.308
0.309 0.306
50.5 49.3 51.2 56.0 49.5 49.5 50.1
50.0 49.1 51.1 55.6 49.2 48.9 49.7
_ __ __ _ _ __
5 3 4 5 5 5 4
~
14.72
~
50.24 49 * I5 51.14 55.81 49.25 49.19 49.93
_
_
15.27 I5 -04 14.98 15.12 15.17 15.20 15.28
_
S. L. Bigelow and F.W. Hunter
3 74
TABLE4 Nickel Plates-Water.
Temp. 20.5-2
'
____. I
Radius of hole
Thickness of plate
0.304 0.299 0.306 0.274 0.269
Highest I Lowest 1
No. of readings
IO
4 verage
hr.
49.37 49 * 81 48.90 54.74 55.70 49.34 54.99
15.01 14.89 14.96 15 .oo 14.98 15.05
AV.
15.00
!$,9'
Average
hr.
4 5 5
55.98 157.26 157.18
14.61 14.89 14.75
Av.
14.75
.
49.2 48.5 55.2 1 54.6
15. I 2
TABLE5 Silver Plates-Water. Thickness of plate
0.28 0.28 0.28
I
Temp. 20.5-21
O
I
Radius of , hole
Highest
Lowest
0.261 0.260 0.258
56.2 57.3 57.3
55.6 57.0 57.1
!
TABLE6 Aluminium Plates-Water. 0.87 0.87 0.87 0.87 0.87 0.85 0.86
0.298 0.299 0.312 0.302 0.306 0.295 0.299
49.3 49.6
49.3
~
1
20.5-21
O
____
49.00 14.75 49.10 14.63 49.30 14.74 47-50 14.82 49.43 14.93 49.16 15.04 49.69 14.66 49.07 14.68
48.7 49.0
48.7
Av.
14.78
TABLE7 Glass Plates-Water. .87 1.90 I
Temp. 20.5-21
O
4 1
Av.
14.69
Function of the Walls in Capillary Phenomena
375
TABLE8 Celluloid Plates-Water. I '
Thickness of plate
1
Radius of hole
Temp. 20.5-21
Lowest
No. of exps.
57.7 60.9 59.1 58.0
4 5 7
5
I5 I .50 I .65
IO
6 5
TABLEI O Paraffin Plates-Water.. Temp. 20.5-2 2.5 2.0
1.8 1.8
I ~
0.258 1 37.5 0.305 1 31.5 0.268 I 37.2 0.272 1 36.4
I 1 ~
36.5 30.1 36.4 36.4
1
Average
hr.
7
I.
-
1
'.
I
5 6
~
I
Av.
14.12
138.48 41.45 41.08 141.92
13 .OS 13.05 12.98 12.99
Av.
13.02
i
IO
137.10 30.91 136.87 36.4
1
1 1
9.57 9.43 9.88 9.90 I _
Av.
9.69
In Table I I , we have condensed the results given in detail in Tables 1-10, and have entered the substances in the order of the average values for rh obtained with them. This order is strikingly similar to that of the electromotive series of the metals. Aluminium falls out of place, doubtless owing to a protective coating of oxide upon it. We have included the highest and the lowest value for each substance to make it perfectly clear that our results overlap. Though the values for the different metals are not far apart, yet the lowest value for zinc is larger than the highest value for silver, and the highest value for glass is less than the lowest for nickel, etc.
S. L. Bigelow and F . W . Hunter
376
_
~
_
__ _ _ ~__ _____~ - _._ __ __
~~
High
1
i
Low
Average
14.98 15.03
1.5. I5 15.11
14.89 14.63
15 .oo 14.78
I
1
Zinc Copper Nickel Aluminium
I
'
I
15.28 15.32 15.12
15.04
I
I
It both surprised and interested us t o find that with substances commonly spoken of as " not wetted," namely, with celluloid, beeswax and paraffin, we could not only get ascensions, but high and regular ascensions. Our results with these substances agree with each other as well as the results with plates of other materials, as may be seen by reference to Tables 8, g and IO. We believe that our results are numerous enough, and have been obtained with sufficient care, to justify the statement that water rises to different heights i.n capillary tubes of different materials. This is a somewhat more pregnant statement than it might at first appear to be. The surface tensions, (y) , of liquids are frequently calculated from measurements of capillary ascensions, employing the well-known formulae y
=
rhs
-,2
(s
=
specific gravity), when the angle
of contact between liquid and wall is
0,and y =
a when VhS
that contact angle (0) is greater than 0. A polemic arose between Volkmann,l who maintained that the contact angle 1 P. Volkmann: Wied. Ann., 17, 353-90 (1882); 53, 633-66 (1894);56, 457-91 (1895); 62, 507-17 (1897).
Function of the Walls i n Capillary Phenomena
377
between clean water and clean glass was 0 , and Quincke,’ who maintained that under certain circumstances this angle had a measurable value. Volkmann, employing many precautions in his experiments, obtained the value, 7 = 7.40 for the surface tension We claim no such high degree of accuracy of water at 20’. as Volkmann’s, for our separate results, yet our average for water and glass (see Table 7) was 14.69, and half this, or 7.35 would then be the value of j-; a satisfactory agreement. Now if that is the value for the surface tension of water at 2 0 ° , what are we measuring when we obtain our higher values with practically all the metals we have tried, and when we obtain our lower values with celluloid, beeswax and paraffin? The surface tension of one liquid at one temperature must be a constant, and since we obtain different values, it cannot be surface tension which we are measuring. It is possible that the contact angle between water and glass is not 0,and that this angle is more nearly o between water and those substances with which we obtained higher ascensions. This view is the more probable as other methods for measuring the surface tension of water, the drop method, the bubble method, the ripple method, all give somewhat higher values than those obtained from the ascensions of water in glass capillary tubes. But one has not much more than stated the problem when he has demonstrated that the angle is o in some cases and greater than o in others. What interests us is, why is the angle different in different cases, or as we prefer to state it, why is the ascension of a given liquid different in tubes of different materials? This is a field in which but little, if any, direct experimental evidence has thus far been obtained, owing to the lack of a convenient experimental method. A liquid rises and is held at a definite height in a capillary tube through the action of two forces, first, the cohesion between the like particles of the liquid which, in the surface layer is denoted by the phrase “surface tension” and second, G. Quincke: Wied. Ann., 2, 145-94 ( 1 8 7 7 ) ; 27, 219-28 (1886); 52, (1894); 61, 267-80 (1897).
1-22
S. L. Bigelow and F . W . Hunter
3 78
the adhesion between the liquid and the walls. The arrangement may be likened to a chain with two links, and when such a chain is strained t o the breaking point it is the weaker link which gives way. So, here, whichever is the weaker, adhesion, or cohesion must break first. The cohesion of a given liquid a t one temperature must be considered as constant, not varying. We find the phenomenon of " breaking " at different strains, therefore we must be measuring the force of adhesion. The force of cohesion must be greater in all our experiments, except those giving the highest results, and in those cases we have no sure means of knowing which of the two forces it is which gives way. Because of these considerations, we have intentionally avoided the use of the conventional values for 7 and have expressed our results in terms of the product of the radius into the height into the specific gravity, which is a measure of weight held up, and leaves open the question as to what relation these values bear to surface tension. For the above reasons, we call these values of ours adhesion values. We wished to determine whether the capillary ascensions of other liquids than water were different with tubes (plates) of different materials. Tables 12-17 give the detailed results with benzene of specific gravity (s) 0.879 a t 20.5'. Table 18 summarizes the results. It will be observed that the capillary ascensions show differences greater than can be attributed to experimental errors, and furthermore, that the order inwhich thesubstances fall is practically the same as with water, with the exception that silver and copper have changed places. TABLE12 Benzene Sp. gr. 0.879. Temp. h in mm Glass plates ___
__
..
__
3
I
1
1.87 1 0.312 1.90 I 0.312 2 . 7 7 1 0.312
& oO.2
___
Iighes
I 2
20.5'
lverage
..-
21.6
21.4
21.2
21.1
21.6
21.5
1 ~
5 4 4
!
I
hr.
21.48 1 6 . 7 0 21.16 6 . 6 0 21.54 , 6.72
Av.
6.675
hrs.
1
i
5.866
Function of the Walls in Capillary Phenomena
379
TABLE13 Benzene Sp. gr. 0.879. Temp. 2 0 . 5 ~f oO.2 Platinum plates h in mm
0.283 0.269 0.314
0.08 0.08 0.08
3 4 5
24.2 25.6 21.8
23.9 25.2 21.6
5 5 5
24.15 21.72
Av.
6.839
6.012
Av.
6.909
6.073
TABLEI 4 Aluminium plates 0.87 0.87 0.87
2
3 4
0.298 0.299 0.312
TABLE15 Copper plates 3 5 6
____~
I
0.15
1
0.20
1
0.68
I ;?:; I 1 __
.~-
0.248 0.302 0.290
27.6
- --
----____
5
27.4
27.54 6.83 122.82 1 6 . 8 9 23.57 6.84
-
Av.
6.852
6.023
TABLE16 Nickel plates
-
~ __ __ _ _
--
0.53 10.333 20.9 2 0 . 7 0.53 0.333 20.9 20.8. 0.53 0.336 2 0 . 9 1 2 0 . 5 ~
1
4
2
~
20.81 6 . 9 3 1 20.88 6.95 I 120.76 1 6 . 9 8
I
Av.
TABLE17 Silver plates -
___ I
1
,
-
0.28
0.28 3 0.28 K . I . ] 0.29 2
K.2
~
0.30
__
~
-
0.261 0.260 0.258
. -
__ ~
~ ~~
-~
~~
27.6 27.7 27. I
27.5 27.6 26.6
4 5 5
0.352
19.9
0.315
21.9
19.5 21.5
5 5
' '
__
-
27.53 27 62 26.82
6.953 6.112
-___7.18 7.18 6.92
19.64 16.91 81 6.87
21
Av.
7.014
1 6.165
380
S . L. Bigelow and F . W . Hunter
~~
-
Silver Nickel Aluminium Copper Platinum Glass
--________ 6.16 6.11 6.07 6.02 6.01 5.87
