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Surface Tension of Liquids in Micro-Capillaries
Fedyakin, N. N.
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Preface
The change of s u r f a c e t e n s i o n of water i n c a p i l l a r - i e s of l e s s than one micron i n r a d i u s has been t h e sub-
j e c t of a number of i n v e s t i g a t i o n s . The m a t t e r i s one of importance i n r e l a t i o n t o fundamental s t u d i e s being c a r r i e d o u t i n t h e B u i l d i n g . M a t e r i a l s S e c t i o n of t h e Division of Building Research.
Work h e r e i n r e p o r t e d concerns t h e e f f e c t of c a p i l l a r - i e s from 10 t o 0.08 micron r a d i u s on t h e s u r f a c e t e n s i o n of w a t e r . P r e s s u r e s developed i n c a p i l l a r i e s which a r e
,
closed a t one end, when t h e o t h e r open end was brought i n c o n t a c t with water, were measured and compared w i t h t h e p r e s s u r e s c a l c u l a t e d by t h e Laplace e q u a t i o n f o r t h e same s i z e of c a p i l l a r i e s u s i n g t h e value f o r s u r f a c e t e n - s i o n of bulk water. The experimental and c a l c u l a t e d value agreed and it i s concluded t h a t f o r t h e above range of
c a p i l l a r i e s t h e p r o p e r t i e s of bulk water i n them do not change.
The D i v i s i o n of Building Research r e c o r d s i t s thanks t o M r . V . Topchy f o r t r a n s l a t i n g t h i s paper.
Ottawa
December 1961
R.F. Legget, D i r e c t o r
Title:
NATIONAL RESEARCH COUNCIL OF CANADA
Technical Translation
998
Surface tension of liquids in micro-capillaries
(Poverkhnostnoe natyazhenie zhidkosti
v
mikro-kapillyarakh)
Author : N .N
.
FedyakinReference: Trudy Tekhnol. Inst. Pishchevoi Prom.
(8):
37-4191957
SURFACE TENSION OF LIQUIDS IN MICRO-CAPILLARIES
In the absorption of liquids by porous materials through ca- pillaries, vapour condensation in the pores of sorbents and the drying of capillary-porous substances, the intensity of the process depends on the surface tension of liquids. However, so far it re- mains an open question whether the surface tension of liquids in micro-capillaries is the same as in an ordinary container. Many investigators, as for example Kubelka (ly2), assume that the sur- face tension of liquids in capillqries is different from normal.
M .M. Dubinin")
,
studying adsorption on metallic oxide gels, concluded that the surface tension remains unchanged in pores down to 0.01 microns but increases in pores of smaller dimensions.B.V. Deryagin and his assistants (4-7) showed in their numerous works that on a solid substrate a film of water of 0.075 microns acquires properties different from those of an ordinary liquid and resembles a solid substance.
Eversole and Lahr
(8)
consider that a film of liquid on thesurface of a solid body has properties similar to those of the solid body if the film is less than 0.01 microns thick. It would appear from this that if the dimensions of capillaries are close to the thickness of the film possessing these special qualities, the sur- face tension of liquids in such capillaries will be considerably different from normal
.
Besides being influenced by the walls of the capillaries, the surface tension of liquids in capillaries must also depend on the curvature of the meniscus. In order to study this question It is necessary to neutralize the influence of the capillary walls, which is easiest to do by considering small drops.
S.V. ~orbachev(~), assuming that the increase of surface ten- sion in a drop is proportional to the increase of the sum of arcas of exposed molecular surfaces (treating the molecules as balls), obtained the following dependence
where
-
t h e s u r f a c e t e n s i o n of l i q u i d on t h e s u r f a c e of t h e drop, " 0-
t h e s u r f a c e t e n s i o n of l i q u i d w i t h a f l a t s u r f a c e ,rm
-
r a d i u s of a molecule of t h e l i q u i d , r,-
r a d i u s of t h e drop, andk
-
t h e c o e f f i c i e n t of t h e change of molecular compaction a t t h e s u r f a c e of t h e drop with a change of c u r v a t u r e .L .M
.
Shcherbakov ( l o ) c o n s i d e r s t h a t t h e s u r f a c e t e n s i o n de- pends on t h e t h i c k n e s s of t h e l a y e r o f l i q u i d and d i f f e r s from nor- mal i n f i l m slo-"
-
lo-'
cm t h i c k and l e s s , while i n drops i t de- pends on t h e r a d i u s of t h e drop. H e a r r i v e s a t t h e i d e a t h a t t h e r e a r e c a p i l l a r y e f f e c t s of Type 11, caused by t h e changes of s u r f a c e t e n s i o n with t h e change of t h i c k n e s s of t h e l i q u i d l a y e r . The f o l - lowing dependence i s deduced f o r t h e drops:where
rx
-
t h e r a d i u s of t h e drop, andk
-
t h e c o e f f i c i e n t of t h e dependence o f t h e s u r f a c e t e n s i o n of l i q u i d on p r e s s u r e ( i t i s of t h e o r d e r of 0.2-
0.5
lo-').
From t h e works mentioned above and from o t h e r l i t e r a t u r e (11)
it f o l l o w s t h a t a p e r c e p t i b l e change of s u r f a c e t e n s i o n can be ex-
0
pected only i n drops s e v e r a l dozen Angstrbm i n r a d i u s o r i n c a p i l - l a r i e s l e s s t h a n 0.01 microns, i f t h e w a l l s of t h e c a p i l l a r i e s have no s i g n i f i c a n t i n f l u e n c e on t h e l i q u i d a t a d i s t a n c e g r e a t e r t h a n
s e v e r a l times t h e diameter of molecules. Consequently, t h e only r e a s o n f o r any change of t h e s u r f a c e t e n s i o n i n c a p i l l a r i e s of t h e
0
s i z e of t h e o r d e r of a hundred ~ n g s t r b m can be a change i n t h e pro- p e r t i e s of t h e l i q u i d under t h e i n f l u e n c e of s o l i d w a l l s .
So f a r t h e s u r f a c e t e n s i o n was measured i n c a p i l l a r i e s down t o 2 microns i n r a d i u s ( 1 2 ) , although according t o B.V. Deryagin and h i s a s s i s t a n t s t h e p r o p e r t i e s of l i q u i d s must d i f f e r from nor- m a l i n c a p i l l a r i e s 0 . 1 microns i n r a d i u s . It i s necessary, there-
f o r e , t o measure t h e s u r f a c e t e n s i o n i n t h i s i n t e r v a l , s i n c e i t I s
paper is concerned with the measurement of surface tension in such capillaries.
Methods of Measuring
One way to measure the surface tension of liquids in capillar- ies is to balance the capillary pressure by gas pressure, i.e. to exert a pressure on the meniscus equal to the capillary pressure, so that the liquid in the capillary will not rise. The gas pressure, which is equal to the capillary pressure, is measured and the sur- face tension is calculated from it. If the capillary is 0.1 microns in radius, a pressure of 15 atmospheres is required, which results in great difficulties in making the apparatus and taking the meas- urements during the experiments. We have changed somewhat this method and simplified the experiments as far as possible. We used
a cylindric capillary with thick walls
5
-
10 cm long, one end ofwhich was closed by fusion. The open end was put in contact with a water surface, and the water entered the capillary under the in-
fluence of the capillary pull, compressing the air in the capillary. The liquid continues to rise in the capillary till the pressure of the compressed air is equal to the capillary pull.
Let us adopt the following signs:
Vo
-
the volume of capillary channel,Po
-
the initial air pressure in the capillary, i.e. atmos-pheric pressure,
V,
-
the volume of the capillary occupied by compressed air,p,
-
the pressure of compressed air.According to the Boyle-Mariott law, the pressure of compressed air in the capillary is
where l o
-
the length of the capillary channel,C ,
-
the length of channel occupied by compressed air.The compressed air in the capillary balances both the capil- lary and atmospheric pressure. The pressure counterbalancing the capillary pressure therefore is
This formula can be used as long as conditions of the Boyle-
Mariott law are operative. Since at a pressure of 15
-
20 atmos-pheres the departures from this law are small and can be accounted for, this formula is fully applicable to capillaries 0.l.microns in radius. Compressed air in the capillary is not absorbed by the liquid since it is balancing the capillary pressure, and therefore the liquid in the capillary is under a pressure equal to the pres-
,
sure inthe vessel containing the rest of the liquid. If we assume that compressed air is absorbed by the liquid, its concentration in the liquid in the capillary would be greater than that in the remaining liquid, and therefore the air would pass into the latter. The liquid would therefore be able to fill the capillary completely,
which did not occur although these capillaries
were
left in contactwith the liquid in the vessels for several days.
The table gives the results of the experiment. The first two columns give the dimensions of the radii of the capillaries, the next column gives the initial length of the capillary channel,
column 4 gives the length of the part of the capillary occupied by
compressed air, column
5
the capillary pressure calculated from ourexperimental data according to formula (3), and the last column gives the capillary pressure calculated according to the Laplace equation on the assumption that the surface tension in capillaries remains unchanged, i.e. the same as in the liquid under normal conditions.
The table shows that there are no substantial differences be-
tween the experimental data on capillary pressure and its values calculated according to the Laplace equation even for capillaries
-7
-
Table
Making of Capillaries and Measurement of their Radii
Capillaries for the experiment were drawn from thick-walled capillaries
6
-
10 rnm thick with a channel diameter of 0.1 mrn. Such a capillary was uniformly heated over a special burner and then uniformly stretched by two men into a new capillary3
-
4 m long; the resulting capillary had an outer diameter0.5
-
1 mrn anda
channel of less than a micron. A.15
-
20 cm length of uniform outward thickness was then selected on this capillary. This piece was then divided into three equal sections of 4-
5
cm. The time required by the liquid to pass through the two end capillaries in this group of three capillaries was measured. If the time was the same in both cases, the openings of both capillaries were of the same diameter and consequently the capillary in the middle was Radius of capillary m t cm 0' 21. 9
22.2 16.4 18.7 17.1 15 .I18
.9
7 -25
.5
3.2155
97
3.24.9
4.28
8
Calculated9-5
-
0.577
o
.67
0.43
o
.68
-
0.32 0.356
0.286
0.17 0.160.167
0.143
o
.0785
Measured 9.8 1.68 0.5
0.65
0.4
o
.65
0-3
093
-
-
-
-
-
-
-
t i , cm 19-75
10.74.4
6.153 -8
4-75
3
1.25 1.05 0.515 09595
0.310.53
0378
0.42 p in atm 0 .l450.93
2-73
2.243
-5
2.45
03
4
-77
4.25 5.246.85
9-6
8
.3
10.3
19 .OB Po in atm 0.153 0-9
2.6 2.153
-75
2.25
4
-7
4.25
-25 8.82 9-4
8
.5
10.38 19.02c y l i n d r i c a l . I S t h e time taken by t h e l i q u i d t o pass through t h e end c a p i l l a r i e s showed a d i f f e r e n c e , a new pLece of t h e c a p i l l a r y was s e l e c t e d and t e s t e d t i l l a c y l i n d r i c a l s e c t i o n was found. The
c a p i l l a r y t a k e n from t h e mlddle was t h e n c l o s e d by welding a t one end and t h e open end was put i n t o l i q u i d . The movement of t h e l i q - uid i n t h e c a p i l l a r y was observed w i t h t h e a i d of a s p e c i a l l y
adapted microscope. The t h i c k n e s s of t h e g r a d u a t i o n s of t h e micro- meter on t h e microscope used i n our experiments was 0.03 mm. The
same microscope was used t o measure t h e l e n g t h of t h e channel oc- cupied by compressed a i r . A f t e r t h e experiment t h e r a d i u s of t h e c a p i l l a r y was measured under a microscope magnifying 1,350 times; f o r t h i s s e v e r a l s e c t i o n s 1 cm i n l e n g t h were c u t and s e t up v e r - t i c a l l y on t h e p l a t e of t h e microscope, so t h a t t h e r a d i u s of a c a p i l l a r y was measured i n 4 - 5 p o i n t s . With a r a d i u s l e s s than 0.5 microns t h e accuracy of measuring under t h e microscope i s low.
I n such c a s e s t h e r a d i i of t h e c a p i l l a r i e s were c a l c u l a t e d w i t h t h e a i d of t h e known equation: acc cos 8 where r
-
t h e r a d i u s of t h e c a p i l l a r y , 1-
t h e c o e f f i c i e n t of cohesion of t h e l i q u i d , 1-
t h e l e n g t h of t h e c a p i l l a r y , a-
t h e s u r f a c e t e n s i o n of l i q u i d ,T
-
t h e time t a k e n by t h e meniscus t o t r a v e r s e t h e capillar.y,0
-
t h e edge a n g l e .Since we c a l c u l a t e d t h e r a d i i of c a p i l l a r i e s l e s s t h a n
0.3
m i - c r o n s with t h e a i d of t h i s equation only, t h e n i n c a s e of a change i n t h e cohesion o r s u r f a c e t e n s i o n we would g e t a n i n c o r r e c t r e s u l t . Let u s c o n s i d e r t h i s f u r t h e r . Assuming t h a t i n c a p i l l a r i e s of t h e r a d i u s of t h e o r d e r of 0 . 1 microns t h e cohesion and t h e s u r f a c e t e n -s i o n i n c r e a s e t o t h e same degree, t h e value of t h e r a d i u s obtained by u s would be c o r r e c t , s i n c e i n formula
( 4 )
t h e c o e f f i c i e n t of t h ec o h e s i o n i s i n t h e numerator and t h e s u r f a c e t e n s l o n i n t h e denomi- n a t o r . I n t h a t c a s e i n d c t e r l n i n j n g t h e c a p l l l a s y p r e s s u r e from compressed a i r we would have a g r e a t e r v a l u e t h a n that c a l c u l a t e d a c c o r d i n g t o tile L a p l a c e e q u a t i o n , s3 ncc t h e s e rneasurcmcrlts do not; depend on c o h e s i o n . If i t I s assumed t h a t i n t h e capillaries t h e c o h e s i o n changes more t h a n t h e s u r f a c e t e n s i o n , t h e n t h e r a d i u s of t h e c a p i l l a r y c a L c u l a t e d a c c o r d i n g t o formula ( 4 ) would b e smaller* t h a n t h e a c t u a l r a d i u s and t h u s t h e c a p i l l a r y p r e s s u r e would y i e l d
a s m a l l e r v a l u e ( s i n c e it does riot depend on t h e c o h e s i o n ) t h a n t h a t c a l c u l a t e d a c c o r d i n g t o t h e L a p l a c e e q u a t i o n , b e c a u s e i t would be c a l c u l a t e d f o r a s m a l l e r r a d i u s t h a n t h e a c t u a l r a d i u s . The
correspondence o f t h e r e s u l t s of measurements o f t h e c a p i l l a r y p r e s - s u r e i n o u r e x p e r i m e n t s w i t h v a l u e s c a l c u l a t e d a c c o r d i n g t o t h e L a - p l a c e e q u a t i o n t h u s p r o v e s n o t o n l y t h a t t h e s u r f a c e t e n s i o n remains t h e same i n c a p i l l a r i e s o f a r a d i u s down t o 0.038 microns b u t a l s o t h a t t h e c o h e s i o n of t h e l i - q u i d remains t h e same, i . e . i n such c a - p i l l a r i e s t h e p r o p e r t i e s o f water remain unchanged.
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637,
1 9 3 1 -Kubelka, P . K o l l o i d 2 . 55: 129, 1931;
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Deryagin, B.V. Z h u r . F i z . K h i m .
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( 2 - 3 ) , 1934.Rbrosimova, N.I. and Deryagin, B.V. Doklady Akad.Nauk SSSK, s e r . k h i m . ( 6 ) ,
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Alcaci. Nauk SSSH, s e r . khim.(5),
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(5),
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Cohan, L.M. and M e y c r , G.E. Am. Chem. Soc. 62: 2715, l31!0.
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