SIMPLE EXPERIMENT SHOWING THE EXISTENCE OF "LIQUID WATER" FILM ON THE ICE SURFACE 1

U. Nakaya and A. Matsumoto

Snow, Ice & Permafrost Research Establishment, Corps of Engineers, Wilmette, Illinois, and Department of Physics, Hokkaido University, Sapporo, Japan

Received June 15, 1953

ABSTRACT

Two small ice spheres are suspended by thin cotton filaments. The top of one fila- ment is displaced horizontally by a screw motion. The movable ice sphere is brought in contact with the stationary sphere, and then the screw is turned back. The normal cohesion is measured by the inclination of the filament when the spheres are sepa- rated. Sometimes the ice spheres showed a rotation before separation. The rotation took place more frequently in the range of temperatures near the freezing point, but it was observed once at -7.0°C., the lowest temperature when distilled water was used. When ice spheres made of 0.1% solution of NaC1 were used, this rotation was very likely to occur and was observed quite often at -14°C. Successive rotations were sometimes observed in this ease. These phenomena are explained by considering a model of the point of contact, which is composed of a solid ice bond and the surface films of a liquid-like nature. The relation between the strength of the ice bond and the area of contact is calculated by using Hertz's equation.

EXPERIMENTS

The regelation of ice has been a problem since the days of Faraday and Tyndall. Weyl (1), treating this problem from the standpoint of modern molecular physics, has strongly suggested the presence of liquid-water film on ice surface at temperature below 0°C. This liquid-water film is not supercooled water, but is in equilibrium with its vapor phase on one side and with the ice crystal on the other.

During the course of some experiments on the adhesive force between two ice particles, carried out in the cold chamber laboratory of the Low Temperature Institute, Hokkaido University, Sapporo, Japan, we found a phenomenon which seems to show the existence of this boundary layer. Two small ice spheres were suspended by very thin filaments. One filament could be moved by a screw motion so that the top of the filament was displaced horizontally. By this method, the normal adhesive force is meas- ured by the inclination of the filament when the spheres are separated.

The ice sphere was made by freezing a drop of distilled water. A cotton

1 Published by permission of the Office, Chief of Engineers, Dept. of the Army.

41

4~ U. NAKAYA AND A. MATSUMOTO

FIG. 1. Mean diameter of the ice ball = 1.45 ram. Temperature = -5.5°C. (a) Start of the experiment; (b) before rotation; (c) after rotation.

filament was used as the suspending material. The diameter of the ice spheres was varied between 1.5 and 4 mm. The experiment was carried out in a metal box with suitable windows for taking microphotographs and was observed through a horizontal microscope. The temperature in the box was varied between -0 .5°C. and - 16°C. The movable ice sphere was brought in contact with the stationary sphere by the screw motion device, but care was taken to avoid any appreciable pressure between the spheres. The effect of the duration of contact is an element to be studied, but in this series of experiments the time was chosen as 1 min. or a little less.

The two spheres usually separated at a certain angle 0 of inclination of the filament. Sometimes, however, the ice spheres showed a rotation before separation, at an angle of ¢. Two examples are shown in Figs. ] and 2. In both cases, (a) shows the initial state, (b) the state just before the rotation, the inclination of t he filament being ¢, and (c) the state after rotation.

This rotation did not always occur, but it was not rare. For example, in one series of experiments, this rotation phenomenon was observed nine times in thirty-eight cases. The rotation took place more frequently in the range of temperature near the freezing point, but it Was observed once at -7.0°C., the lowest temperature when distilled water was used. I t some-

FIG. 2. Mean diameter of the ice ball -- 1.95 ram. Temperature = -3.0°C. (a) Start of the experiment; (b) before rotation; (c) after rotation.

"LIQUID WATER" FILM ON ICE SURFACE 43

t imes happens , t h o u g h seldom, t h a t the spheres ro ta te two or three t imes

in succession a t the angles of ~1, ~2, and ¢3, a nd t h e n separa te a t 0. This

successive ro t a t i on takes place more often when NaC1 solu t ion of 0 .1% is used, as descr ibed later. Th i s p h e n o m e n o n reminds us of Bowden ' s

s t ick-sl ip m o t i o n in his f r ic t ion exper iment . The air in the measu r ing box

TABLE I

The Angles of Rotation and Separation for Ice Spheres of Distilled Water

No.

1 2 3 4 5 6 7 8 9

10 11 12

Radius a (r~m.)

I - -1 .0 1.2 --2.0 1.2 --5.4 0.7 --3.0 1.2 --3.0 1.0 --3.0 1.0 --3.0 0.9 --3.0 0.9 --3.0 0.9 --3.0 0.9 --3.0 0.9 --3.0 0.9

Length ~b t (ram.) Rotation

12.2 30 ° 12.2 44 16.3 33 16.4 35 16.7 27 16.7 26 16.7 14 16.7 6 16.7 47 16.7 29 16.7 29 16.7 43

4' (Obs.) after

rotation

27 ° 39 31 32 26 25 13 5

44 27 27 4O

~' (Calc.) ~, , after

rotation (ram.)

27.1 - - - 7 0.5--( 39.3 0.82 31.5 0.38 30.5 0.67 25.4 0.45 24.4 0.43 13.3 0.20 5.7 0.08

44.0 0.69 27.5 0.42 27.5 0.42 40.3 0.63

x (nun.)

0.16 0.40 0.20 0.28 0.10 0.09 0.04 0.03 i 0.35 I 0.17 1 0.17 0.35

0 Separation

>56 ° 80

>66 43

>67 >66

28 >70 >65

66 66 65

dyne

7.5

5 o (h 0 t - O

T °

o Mean diameter : ' 2 . S m m

x Mean diameter : 1.7 m m

0 °C

t - 5 -10

Temperature

-15

FIG. 3. The relation between normal cohesion and temperature.

~ U. NAKAYA AND A. MATSUMOTO

must be considered as saturated at any time, because a considerable amount of frost crystals was in the box.

Some examples of ¢ and ~ are shown in Table I, in which > means that the spheres did not separate with this angle.

The normal cohesion was calculated from ~ by Eq. [5], given in the next section, irrespective of the occurrence of rotation. Cohesion was studied as a function of temperature, keeping the time of contact and the initial pressure between the spheres roughly constant. The measured values showed a wide fluctuation, which is essentially the nature of this sort of phenome- non. The mean of the values is taken for each of the temperatures. Figure 3 shows the results for two series of the experiments. A vertical bar through each of the points shows its range of mean error. In this stage of the experi- ments, we can only say that the normal cohesion tends to decrease with decreasing temperature. Although it is qualitative, this tendency is quite evident.

DIscusSION

Figure 4 shows the configuration at the moments before and after rota- tion of the sphere. The radius of the sphere is a, and the length of the fila-

!

( FIG. 4. Geometry of rotation of the sphere.

"LIQUID WATER ~ FILM ON ICE SURFACE ~5

ment is I. When rotation takes place at the angle ~, the inclination of the filament changes to ¢' after rotation. The tension of the filament T gives a horizontal component f, which causes a moment of rotation as well as the normal tensile stress at the point of contact P, the former being fa.

The moment of rotation is calculated from the geometry shown in Fig. 4.

The moment of rotation = toga tan 4~. [1]

When the resistance at the point of contact is overcome by this moment of rotation, rotation of the sphere takes place. The angle of rotation is ¢' and the initial point of contact P comes to P', as shown in the figure. ~ and ¢' are measured respectively on the microphotograph. Ct(obs.) in Table I shows this value.

¢' can be calculated from ¢. Trigonometry shows that

sin ~' = / - ~ sin ~. [2] a + l

~t calculated by this equation is given in Table I as ~'(calc.). ~' is impor- tant because it is the angle of rotation of the ice sphere. The two values of the observed and the calculated are in good agreement. This shows that the sphere rotates to the amount of angle which is required by the me- chanics.

The length of the arc PP', the sliding distance at the point of contact, is aC t, where ~' is measured in radians. For discussion of the problem of sliding at the point of contact, the geometry shown in Fig. 4 is not suffi-

• m. j

F io . 5 1 ;~ . 6

FIG. 5. T h e d i s p l a c e m e n t of t h e sphe re b y r o t a t i o n . Fie,. 6. A m o d e l of p o i n t of c o n t a c t .

Z~6 U. NAKAYA AND A. MATSUMOTO

cient, because it is only an approximation. The sphere moves down when it rotates, as shown in Fig. 5. The amount of displacement x is given by

x = lab sin ¢ -- a(1 - cos ¢), [3]i

neglecting the second term. The length of the arc PPP and the value of x calculated by Eq. [3] are also given in Table I.

In order to explain this peculiar rotation of the sphere, a model is con- sidered (Fig. 6). B indicates the supposed bridge of ice at the point of contact, and thick lines show the surface films of a liquid-like nature. I t is believed that the liquid-like boundary layer will freeze when bounded by ice on both sides. So the infinitesimal portion of the film at the point of contact will be frozen, forming the ice bridge or bond B that has been assumed by many former investigators. If the adhesion of ice is chiefly due to this bridge or bond, which is a solid material, the spheres will not rotate but will separate at a certain critical inclination of the filament. The rota- tion must be due to another property of the boundary layer, conceivably the adhesion due to the liquid-like nature of the surface film. The fact that the sphere does not rotate until a critical moment of rotation is applied is explained by the existence of the solid bond. However, after this bond is broken, with the moment of rotation reaching toga tan ¢, adhesion must be caused by surface tension of the film.

Rotation of the sphere can take place in two ways: (1) with the center of rotation fixed, or (2) with displacement of the center of rotation. In the latter case, if the displacement of the center of rotation is equal to the length of the arc traversed by a point on the surface, the locus of the point of contact is a cycloid and the motion is a pure roll. The stress given to the surface film will be normal to the film, as shown by the single arrows in Fig. 6. When the center of rotation is fixed, the moment of rotation will cause a tangential stress in the surface film, as shown by the double arrows in Fig. 6. In our experiments, the displacement of the center of rotation is

x in Fig. 5, which is not equal to the length of the arc P P ' . The difference

between PP~ and x is equal to the displacement of the point of contact

when the center of rotation is fixed. So ( P P ' - x) will give a measure of the tangential strain in the surface film caused by this mode of rotation

of the sphere. The values of ( P P ' - x), obtained from the data in Table I, are given in Table II. As for the nature of this tangential strain, present data are not sufficient for further discussion.

The moment of rotation is calculated by Eq. [1], and the results tabu- lated in Table II. If the rotation starts by breaking the ice bond at the point of contact, the moment of rotation must be related to the contact

"LIQUID WATER" FILM ON ICE SURFACE ~:7

area between two spheres. The contact area between two spherical surfaces can be calculated from Hertz 's equation:

a = 1.1,V 2-E [41

in which a is the radius of contact circle, F the force at the point of contact, r the radius of curvature, a n d E Young's modulus. For a rough approxima- tion, E is taken as 5 X 10 l° dynes/cm2., and F is assumed as 0.01 dyne. Supplementary experiments showed tha t the initial pressure between the two spheres caused a remarkable variation in cohesion; for example, an initial force of 0.1 dyne made the cohesion more than ten times larger. In this series of experiments, the initial force was made as small as possible, and we estimate it to have been about 0.01 dyne or less. So it is reasonable to assume F as 0.01 dyne. The contact area A = ~ra 2 is calculated and the result given in Table II .

The relation between the moment of rotation, which is considered to act primarily for breaking the ice bond, and the contact area is shown in Fig. 7. As the moment of rotat ion can be taken as a measure of the strength of the ice bond, Fig. 7 in effect shows the relation between the strength and size of the ice bond. The result is quali tat ively in agreement with what is ex- pected. The points are scattered over a wide range, chiefly owing to the fluctuation in F.

If we neglect the problem of rotation, the normal cohesion is roughly calculated from the angle of separation by the equation:

Normal cohesion = m g tan 0. [5]

TABLE II The Moment of Rotation and the Contact Area

( P P ' - x) rttga tan ~ Contact area d No. (ram.) dyne-era. (g~)

1 0.41 0.44 0.19 2 0.42 0.74 0.19 3 0.18 0.06 0.14 4 0.39 0.53 0.19 5 0.35 0.19 0.17 6 0.34 0.18 0.17 7 0.16 0.06 0.16 8 0.05 0.03 0.16 9 0.34 0.26 0.16

10 0.25 0.13 0.16 11 0.25 0.13 0.16 12 0.28 0.23 0.16

48 U . N A K A Y A A N D A . M 2 ~ T S U M O T O

dyne x crn

f -

0 ° ~ 4 - o 4k-

P

"6

E 0 =E

1

0 . 7 5

0 . 5

0 . 2 5

0 .12

O

O

! o ! I

0.15 O. 175 0.20 jtlZ Contact area

FIG. 7. The relation between the strength of the ice bond and the area of contact.

T h i s n o r m a l cohes ion decreases w i t h d e c r e a s i n g t e m p e r a t u r e (Fig. 3). T h e i n d i v i d u a l v a l u e shows excess ive f l u c t u a t i o n , w h i c h is cons ide red to be

m o s t l y d u e to t h e s l igh t v a r i a t i o n in i n i t i a l force b e t w e e n t h e two spheres . M o s t of t h e e x p e r i m e n t s were ca r r i ed o u t w i t h t h e i n i t i a l c o n d i t i o n s u c h

t h a t t h e force a c t i n g a t t h e p o i n t of c o n t a c t was U n m e a s u r a b l y smal l , s a y

0.01 d y n e or less. A s l igh t i n c r e a s e in th i s force causes a r e m a r k a b l e i n c r e a s e

TABLE III

The Angles of Rotation and Separation for the Ice Spheres of 0.1% Solution of NaC1 Temperature = -14°C., 1 = 16.6 mm., a - 1.2 mm.

N o .

2 3 24 4 39 6 34

10 43 14 I 26 15 ! 43 16 27 • 17 23

R o t a t i o n a n d s e p a r a t i o n

_ _ ¢ ~ ¢'1 v~ ~'~

2 3 - - I - -

36 65 62 31 66 62 39 !

3~99 i - -

25 { - - 21 36 35

65 ~ 68 °

67 a

66 a

i ~8

62 62

62

62

>65 >68 >62 >62 >65 >67 >65

51 >66

S e p a r a t i o n w i t h o u t r o t a t i o n

_ N o . _ B

1 39 5 42 7 ~ 39 8 >71 9 ~ 53

11 55 12 3>71 13 3-71

A slight shock is given to the box.

"LIQUID WATER" FILM ON ICE SURFACE ~9

in cohesion. In one example, with minimum initial force, the cohesion was about 1 dyne at - 5.5°C., the radius of the sphere being 0.7 mm. Under the same condition, when a force of 0.1 dyne was applied between the spheres by a negative inclination of the filament, the cohesion increased to more than 14 dynes, the limit of our measuring device.

Another conceivable cause of fluctuation in cohesion is the microcrystal- line structure of ice. I t is well known that the melting point of the boundary layer between component crystals is lower than that of pure ice. As a result, a large block of glacier ice is usually easily separated into its component crystals when it is kept at a temperature just below 0°C. In our experiment, the ice sphere is of microcrystaUine structure, and the area of contact might be either a portion of the surface of a component crystal or partly a bound- ary layer between crystals. The cohesion would be very different for those two cases. So we cannot expect consistent cohesion values in ordinary ice, which is made of many component crystals.

Some experiments were carried out with ice spheres made of 0.1% solution of NaC1. Several interesting phenomena were observed. Rotation of the sphere was very likely to occur, and was observed quite often at such low temperatures as - 14°C. In seventeen experiments at - 14°C., rotation took place in nine cases (Table III). Comparing angles of separation 0 in Tables I and III, we see that cohesion is far stronger between ice spheres of 0.1% solution of NaC1 than between ice spheres of pure water; cohesion of the former even at -14°C. is higher than that of the latter at --I°C. or -3°C.

Another interesting phenomenon is repeated rotation, four examples of which are seen in Table III. The superscript a shows that the second or third rotation took place when a slight shock was given to the measuring box. With ice spheres of NaC1 solution, the cohesion showed a marked tend- ency to increase after rotation. All the above phenomena suggest that some part of the impurity NaC1 is concentrated on the surface during freez- ing, so that the surface layer has a more liquid-like nature than the surface of pure ice.

All the results obtained from this series of experiments may be explained by assuming the existence of a liquid film on the ice surface, and no other explanation seems to be adequate. Therefore, the authors consider that this experiment shows the existence of liquid-water film on the ice surface.

The experiments were carried out in the cold chamber of the Low Temperature Institute, Hokkaido University, Sapporo, while one of the authors (U. Nakaya) was in Sapporo. The authors wish to thank the authorities of the Low Temperature In- stitute for the use of their facilities.

REFERENCE

1. WEY~,, W, A., Surface Structure of Water and Some of Its Physical and Chemical Manifestations. J. Colloid Sci. 6, 389-405 (1951).