Title

Air Bubble Formation in Ice Crystals

Author(s)MAENO, Norikazu

Citation

Physics of Snow and Ice : proceedings, 1(1), 207-218

Issue Date

1967

Doc URL

http://hdl.handle.net/2115/20297

Typebulletin (article)

Note

International Conference on Low Temperature Science. I. Conference on Physics of Snow and Ice, II. Conference on
Cryobiology. (August, 14-19, 1966, Sapporo, Japan)

File Information1̲p207-218.pdf

Instructions for use

Hokkaido University Collection of Scholarly and Academic Papers : HUSCAPAir Bubble Formation in Ice Crystals*

Norikazu MAENO
1ltr

!Ilf

~

-

The Institute of Low TemperatU1'e Science
Hokkaido Univel'sity, Sapporo, Japan

Abstract
Formation of air bubbles in ice crystals was investigated to reveal the mechanisms of regular,
sometimes periodic distributions of air bubbles in natural and artificial ice crystals. When an ice
crystal grows in water, air bubbles develop between solid particles and the ice-water interface,which suggests that surfaces of solid particles provide the seats of air bubble nucleation. Most of
the solid particles migrate with the advancing ice-water interface leaving rows of spherical or cylindrical air bubbles in the ice crystaL
The metamorphism of air bubbles trapped in ice crystals was observed under various conditions
and discussed in reference to defects in ice crystals.

I. Introduction
Ice crystals grown from melt usually contain spherical or cylindrical air bubbles
which are distributed in the freezing directions. These air bubbles may be considered
as gas enclosures filled with air which was dissolved in water- The concentration of
air in water may be increased at an ice-water interface as the freezing proceeds, because
ice does not incorporate with the air in the crystal lattices. When the concentrationof air reaches some supersaturation small air bubble may be formed at the ice-waterinterface and develop to visible size, then it is captured by the interface and becomesa gas enclosure.
The formation of gas enclosures or air bubbles during solidification from melt has
been noted by many metallurgists and crystallographers, but so far few studies havebeen made for the air bubble formation in ice crystaL Carte (1961) carried out an experiment of unidirectional freezing of a film of water contained between two glass plates,
and found that the number and the sizes of air bubbles trapped in ice were dependent
upon the rate of freezing and the amount of air dissolved in water. Corte (1963) observed the migration of solid particles which had been placed on a growing ice-waterinterface, in order to investigate the mechanism of sorting of soil particles during freezingthawing cycles in permafrost layers. He observed that unless the rate of freezing was
high, almost all solid particles migrated with the interface, while the air bubbles weretrapped as oriented in row in the ice crystaL His main attention was not directed tothe interaction between particles and the ice-water interface or the formation and inclusion of air bubbles in ice. The phenomena, however, are very interesting and closely* Contribution No. 782 from the Institute .·of Low Temperature Science.

208

N. MAENO

correlated with the mechanism of frost heaving.
When an ice crystal is subjected to various thermal or mechanical disturbances, thecontained air bubbles may change their characters. The metamorphism of the air bubbles
involves not only the change in shape or arrangement but also in size. If an ice crystal
is kept for a long time near the melting point, air bubbles shrink in size, suggestingsome kind of diffusion process of defects in ice crystal.
The main purpose of the study is to clarify the formation process of air bubbles at
a growing ice-water interface with regard to their nucleation and growth, and interaction
between solid particles and the interface, and to observe the metamorphism of air bubbles
under various conditions.

II. Air Bubble Formation at an Ice-water Interface
Experimental apparatus.
Figure 1 shows a simple apparatus to observe the formation of air bubbles when solid particles are placed at an ice-water interface. The
water container, 8 em X 2 cm X 8 em, consists of glass
walls (1 mm thick) and a brass bottom (2 cm thick),and its side walls are insulated thermally so that thezwater in the container begins to freeze from the boto~
tom when the container is placed in a cold room. An-'

5lz
electric heater suspended in the upper part of the container prevents freezing from the water surface andcontrols the rate of freezing. The rate of freezing waschanged within a range of 0.4 to 15.0 IJ./sec to maintain
Fig. 1. Experimental apparatus
a smooth planar ice-water interface. Cellular or dendritic growth was observed for the rates of freezing higher than about 151J./sec. Temperature distribution in the water was recorded automatically by six copper-constantan
thermocouples suspended in the container with intervals of about 5 mm. The record
showed a gradual decrease of temperature from the bottom without changing the temperature gradient.
Concentration of oxygen dissolved in water was measured to estimate the total
concentration of air in water. Winkler's method* was employed for the chemical analysis.
The concentration of free oxygen was 65% for ordinary distilled water, 20% for distilledwater boiled for 30 minutes, and 95% for distilled water mixed with air by shaking andstirring, where the normal solubility of oxygen in water is 10.29 cm3/(1 liter of water)
at ooe and 1 atmospheric pressure. In this study most experiments were conducted withthe distilled water saturated with air.

Formation and stability of air bubbles.
When a solidification occurs slowly frommelt or solution, the impurities are generally rejected in front of the advancing solidliquid interface. The main impurity in the distilled water is considered to be air. The
molecules of air must be rejected and accumulated ahead of the ice-water interface, sincean ice crystal does not incorporate with them and their diffusion coefficient is very small* This is an iodometry frequently· adopted in the oceanographical observations. The procedureis given in a text book by Taylor (1949).

AIR BUBBLE FORMATION IN ICE CRYSTALSa

209

200u. b,,Fig. 2.

An air bubble formed at an ice-water interface

A: ~Water, B: Ice. Time: a, 0 sec (5 sec after the formation); b, 90 sec; c, 180 sec; d, 270 sec

m water and is 1.1 X 10- 5 cm 2/sec at O°C and under 1 atmospheric pressure (Carte, 1961).
In our experiment, the maximum density water existed at a higher level than the interface
and caused a faint convection reducing the concentration of air at the interface. However, some degree of supersaturation of air may be always created at the developing
interface because air-saturated water was used.
When a critical supersaturation is reached, an air bubble is nucleated and grown toa visible size at the ice-water interface. A formation of an air bubble and the process
by which it is trapped in ice is shown in a series of photographs in Fig. 2, where A andB denote water and ice, respectively. Its nucleation and growth was almost instantaneous.
The average rate of freezing was 3.3 tJ./sec. The nucleus of the air bubble cannot beseen in the photographs, but the existence of some kind of foreign nucleus may not be
doubtful.
According to our observation some of the nucleated air bubbles escaped away fromthe interface because of their bouyancy, but most of them were trapped at the interface
soon after the formation. Careful observation of Fig. 2 shows that when an air bubble
is captured by the interface, ice climbs up along the surface of an air bubble. If thebouyancy of the air bubble is large enough to overcome the adhesive force to the interface, it must riseup to the water surface. Figure 3 illustrates a schematic diagram of an air bubble trapped at an ice-waterinterface. In this case, the adhesive force between the
air bubble and the interface may be caused by thesurface tension, and it can be roughly estimated as
2rr XO w sin {}, where 2x is a diameter of the contact
area between the bubble and the interface; Ow and {}are the surface tension of water and the observed contact angle between the air 'bubble and the ice surface,respectively. If we denote the volume of the air bubble,

AIR

Fig. 3. Schematic diagram ofan air bubble fixed at an
ice-water interface

210

N. MAENO

densities of water and air, and the acceleration of gravity by V, Pw , Pa , and g, respectively,
the criterion, at which the bouyancy of the air bubble overcomes the adhesive force
may be written as follows;(1)

If we take (]w=80 dyne/cm and (}=75° (the angle dispersed among 60°-100°) and we
consider a spherical air bubble having a radius of 100 p, the diameter of the contact
area, 2x, is only 0.17 p. This suggests that the nucleated air bubbles can be easily
trapped by the ice-water interface. This estimation, however, is available only when
no water film exists between the air bubble and the ice surface as shown in Figs.
2 and 3. The other case will be discussed in section V.
The shape of an air bubble in water may be determined by the following equation,
2(]w
( 1
1 )
----p:;=Pw(h-ho)g+(]w Rl + R2 '(2)

where Ro is the radius of curvature at the top of the air bubble 0, and Rl and R2
are those at an arbitrary point on the surface in contact with water A; h-ho is thedifference of head in water.
Growth of air bubbles.
Air bubbles nucleated at an ice-water interface grows as far
as the surrounding water is supersaturated with air. The supersaturation of air is maintained by a continuous development of the ice-water interface. When an air supply toan air bubble is reduced or stopped, it may be enclosed in ice in the shape of an egg
as shown in Fig. 2. When the air supply is continuous and constant the air bubble
grows in the shape of a cylinder. Assuming that a cross section of air bubble is a
circle, the volume of air bubble was estimatedafrom the microphotographs and plotted against
10
time in Fig. 4. The growth curves a, band9
c are for the air bubbles of egg-type, and d
and e for the long cylindrical air bubbles.
8
When the rate of growth of ice or adm:L 7
vancement of ice-water interface changes pe:L~oriodically, a wavy change in diameter may be -; 6observed on cylindrical air bubbles. If thegrowth rate is intermittent, spherical or eggshaped air bubbles may be distributed in linewith definite intervals. A row of spherical
air bubbles found in natural ice crystals canbe also formed as a result of thermal metamorphism of a cylindrical air bubble. The
phenomenon will be discussed later.
Nucleus of air bubbles.
As expectedfrom the nucleation theory, some kind of nucleus must be necessary to form an air bubble.
In our experiment the ice-water interface was
kept so smooth that there were no irregularities

~5

w
:L

d

::J

-1

0

>

150

200

250

300

( SECONDS)
Fig. 4. Growth curve~ of air bubbles.
Average rate of freezing (fl/sec):a, 3.3; b, 6.2; c, 2.7; d, 5.5; e, 3.3

211

AIR BUBBLE FORMATION IN ICE CRYSTALS

a

100.u
~

b

Fig. 5.

Air bubble formation along a scratched line on ice surface.
a:

5 sec after nucleation,b:

20 sec after ato act as the nucleation site for the air bubble formation, and grain boundaries did not
act as the nucleus. It was often observed that no air bubbles were formed after thesmooth interface grew substantially. However, when the ice surface was scratched witha fine glass rod, a number of tiny air bubbles were nucleated only along the scratchedline (Fig. 5 a). This simple experiment proves that a supersaturation of air has beencreated at the growing ice-water interface, but no air bubbles were formed because there
existed no nuclei. The growth of the air bubbles was not homogeneous as shown in
Fig. 5 b. The air bubbles located apart from others grew continuously, while the air
bubbles situated closely could not develop enough because of the poor supply of air.
In order to investigate what kind of materials act as the nucleus to form air bubbles
and how they behave at an advancing ice-water interface, various kinds of particles,
metallic, nonmetallic or liquid, have been placed at the interface. Carborundom particles
were carefully washed and soaked in distilled water near oec and then transferred to a
growing ice-water interface in such a way that their surfaces were not exposed to theair. Air bubbles were formed between the particles and the ice surface, suggesting thatthe surfaces of carborundom particles acted as the nucleation sites for bubble formation.
After the particles were soaked in methanol or dilute hydrochloric acid, and rinsed in
distilled water, they were placed again on the ice-water interface. In this case, no air
bubbles were formed. Similarly, the particles boiled previously in distilled water for
thirty minutes did not produce any air bubbles. The same tests were repeated withsmall lead and glass particles. The results indicated that untreated surfaces of theseparticles nucleated many air bubbles, but their nucleation abilities were lost after thetreatments.

212

N. MAENO
To study the nucleation ability of liquid surface, insoluble organic liquids such as

chloroform, aniline and ethylene dichloride, were examined. None of them produced air
bubbles when small droplets of them were placed on a growing ice-water interface. The
small droplet of liquid metal, mercury, showed the same result as the organic liquid.
From these results it may be concluded that the surfaces of solid particles can act
as the nucleation sites for air bubble formation unless they are treated chemically or
physically. When the carborundom particles which had been boiled to destroy their nucleation abilities, were dried completely and tested again, they recovered the nucleation
abilities. This experiment implies that the adsorbed air on solid surfaces play an important role for the nucleation of air bubbles.

HI. Particle Migration and Air Bubble Formation
Corte (1963) observed that various particles which had been placed on an ice-waterinterface developing upward, migrated without being captured in ice. He found, however,many rows of air bubbles left in ice. Uhlmann et al. (1964) studied the critical velocities
of solidification above which particles were trapped at a solid-liquid interface. The factthat particles are not trapped by a growing ice surface suggests that there was no directcontact between them, or that there existed a layer of water and that solidification must
be continued at a speed sufficient for their migration with the ice surface (Taber, 1930;
Corte, 1963). The continuous replenishment of water between them can be suggestedby the fact that particles migrate with the ice-water interface leaving rows of air bubbles
at definite intervals.
Figure 6 shows carborundom particles being pushed by an ice-water interface, andtwo air bubbles which were formed by them. The air bubble a was already enclosed in
ice and b has just been formed between the particle and the ice surface.
were situated at a lower level with the ice surface when
the air bubble a was formed. Such a process is shown

The particles

aschematically in Fig. 7.

The shape and size of the airbFig. 6.

Air bubbles formed between carborundom
particles and ice surface, b, and enclosed inice, aFig. 7. Schematic process of the
air bubble formation between asolid particle and an ice surface

AIR BUBBLE FORMATION IN ICE CRYSTALS

Fig. 8.

A vertical thin section of a Shimobashira.
solid particles on a ground surface

213

A-B indicatesbubble seems to depend on the character of nucleation site on particles and the modeof diffusion of air in the layer of water.
Figure 8 shows a vertical section of a "Shimobashira"* which grew to about 3 cmfrom a ground surface into the air. A Shimobashira is usually composed of bunchesof long needle ice crystals, and it stands erect from the soil surface. A-B indicatesthe boundary between the Shimobashira and the ground surface. Many small air
bubbles are distributed along the growth direction as seen in the ice crystals grownfrom melt. This air bubble formation in a Shimobashira seems to be very important III
understanding the growth mechanism of Shimobashira.
The formation of a Shimobashira has been considered to be a crystallization ofwater at a ground surface where the water is transported through the soil from underground. When a Shimobashira grows on a ground surface, the temperature of thesurface is maintained at O°C, but the air is colder than O°C and the ground is warmer
than O°C. Therefore, the water-saturated soil particles on the ground surface makecontact with the bottom of the Shimobashira, forming an ice-water interface. Thissituation is quite similar to that of our experiment except that the interface advances
downward in this case. It may be concluded from our experimental results that thenumerous air bubbles contained in the Shimobashira were formed in a layer of water
between soil particles and the Shimobashira and captured in the ice. The average diameter of air bubbles in the Shimobashira suggests that a fairly thick layer of water* Shimobashira is a Japanese name and it is most descriptively translated in English as "soilneedle ice" (Takagi, 196fi).

214

N. MAENO(at least 30 or 40 I~ in thickness) should have existed between the soil particles and theice to form the air bubbles.

IV.

Metamorphism of Air Bubbles

lvletamorphism under an isothermal condition.

The air bubbles enclosed in ice

tend to change their shapes. The metamorphism of air bubbles proceeds by reductionof the surface areas under the action of surface tension. Sometimes cylindrical air
bubbles were observed to split into smaller spherical ones when a block of ice was
kept slightly below the melting point of ice for a long time. In Fig. 9, a series ofphotographs shows the splitting of cylindrical air bubbles into rows of spheres. The
block of ice was soaked in kerosene to keep it from sublimation. The splitting ofa cylindrical air bubble occurred at several points where the diameters were alreadysmaller than other parts. The metamorphism was often observed in cylindrical air
bubbles whose diameters were less than 500 /1, but it was noted that larger air bubbles
did not split easily.

Fig. 9.

Metamorphism of air bubbles under an isothermal condition (-100C).
Time; a, 0 hr; b, 20 hr; c, 120 hr

As seen in Fig. 9, shrinkage and disappearance of alr bubbles were also observed
when the ice was annealed in kerosene for a long time. This phenomenon may suggest
a dissolution of molecules of air into ice, or a mass transportation through diffusion ofsome kind of defects in the ice crystal.
lvletamorphism under a thermal gradient.
Migration of vapor figures III a single
ice crystal under a thermal gradient was extensively studied by Nakaya (1956). According

AIR BUBBLE FORMATION IN ICE CRYSTALS

Fig. 10.

215

Metamorphism of an air bubble under a faint thermal gradientindicated by an arrow. The photographs were taken three (a)and eight (b) days after applying the thermal gradientto his observation the vapor figures migrated toward the warmer direction revealing the
crystal faces only on their warmer sides, but when a slight amount of air was introduced
in a vapor figure its migration was almost stopped and finally it was filled with numerous
hoar crystals.
However, under a very faint thermal gradient air bubbles can undergo a metamorphism, forming solid ice crystals in them. Figure 10 shows the metamorphism of a cylindrical air bubble in ice across which a faint thermal gradient (smaller than a hundredthof one degree per centimeter) was applied in the direction of the arrow at -15°C. After
three days ice crystals of solid-very-thick-plate-type grew with somewhat regular intervalsof 100 /J. on the colder side (Fig. 10 a). After eight days they reached the warmer sideand resulted in a splitting of the air bubble (Fig. 10 b).

lv[etamorphism under a mechanical stress.
An ice bar was cut from a block ofsingle crystal ice and was bent. The direction of load was perpendicular to the bar andparallel to the c-axis. The bar was deformed by slip along the basal plane, and it wasobserved that the air bubbles contained shrank in the direction of the slip. Hitherto
the deformation of air bubbles under stress or flow has been assumed to occur only
following an increase of pressure inside them. However, the air would be able to diffuse
into the surrounding ice crystal, since the spatious lattice of ice may be much distortedby the mechanical disturbances.

v. Discussion
When water freezes slowly a high supersaturation of dissolved air IS created at anadvancing ice-water interface, and air bubbles are formed as a result of heterogeneous
nucleation. Air bubbles are formed on the surfaces of solid particles. The nucleation

216

N. MAENO

sites may be provided by the alr adsorbed or trapped on the surfaces of solid particles,
which is a similar result obtained in the experiment of bubble formation in boiling water(Dean, 1944).
Solid particles migrated upward with a developing ice-water interface, leaving rowsof air bubbles in ice.

In a crystal of a Shimobashira which was formed by suction ofwater through soils, a number of tiny air bubbles were observed. Our experimental
result led to a conclusion that there might exist a thin layer of water between soil particles and the ice surface of a Shimobashira, and its thickness was estimated approximately
as 30 or 40 /J. because the thickness of water might be needed to form the air bubbles
in it. For the particles to migrate and for a Shimobashira to grow, water must be transported between particles and ice surface.
Most of the air bubbles were trapped III Ice immediately after the formation. This
fact may imply that there no layer of water existed between the air bubble and the ice
surface. When an air bubble was nucleated at an ice-water interface, it developed toabout 50 p, in diameter almost instantaneously; so that the layer of water between the
air bubble and the ice surface would be soon evaporated into the air bubble, allowing
the appearance of a dried ice surface within the air bubble. The dried area makes theactual contact between the air bubble and the ice surface. In this case, the air bubble
may be fixed on the ice surface by surface tension, and cannot rise unless the bouyancyof the air bubble overcomes the adhesive force as shown in the formula (1).
It is not always the truth that no layer of water between an air bubble and an ice
surface exists.

Fig. 11.

This can be shown by a simple experiment: an air bubble of 1.17 mm

A simple experiment to show an existence of a thin layer of water between
a fixed air bubble ane! a growing ice surface. The air bubble escapee! (F) justafter the stage e, when the plate was inclined. Time: a, 0 min; b, 3 min;c, 5.5 min; d, () min; e, 7 minAIR BUBBLE FORMATION. IN ICE CRYSTALS

217

diameter was fixed about 2 cm ahead of a developing ice-water interface, under a small
plate suspended in water. As the surface of the plate was coated with a thin film ofparaffin, the air bubble could escape if the plate was inclined slightly. Figure 11 a shows
the air bubble and the advancing ice-water interface. As the interface approached to the
air bubble, the ice surface just under it rose up as shown in Fig. 11 band c. This phenomenon may be attributable to the thermal insulating effect of the air bubble; as the direction of heat flow is from above in the photographs, the water under the air bubble may becolder than other portion of water of the same level. When the interface reached the air
bubble, ice growth just under the bubble almost terminated, but the overall advancementof the interface continued enclosing the air bubble (Fig. 11 d and e). After the stage ofe, the plate was inclined gently to allow the rise of the air bubble. The air bubble roseup from the ice surface as shown in Fig. 11 f. It may be suggested that the air bubble
was not in close contact with the ice surface, that is, there existed a thin layer of water
between the air bubble and ice. If we assume no layer of water between them and take
tJ=87° in the formula (1), the diameter of contact area, 2x, required for the air bubble tobe fixed against its bouyancy, is calculated as 0.03 mm. The diameter of the apparent
contact area in the photograph was 0.72 mm, but the air bubble floated up easily.
From this result, it may be concluded that when a developing ice-water interface
touches an air bubble, a thin layer of water can exist between them just as in the caseof solid and liquid particles (Corte, 1963; Uhlmann et al., 1964). However, the continuous transportation of water through the layer does not seem probable, because theair bubble was trapped by the ice :,urface when it was brought into contact with theinterface for! a long time. If the layer of unfrozen water exists between the air bubble
and ice surface for a long time, the air bubble may be compressed and deformed by the, advancing ice-water interface. But no such phenomenon was observed in our experiment.
The existence of the supercooled water on an ice surface must be a very interesting
problem, but there is no evidence indicating whether the layer of water is the same as
proposed by Weyl (1951), Nakaya and Matsumoto (1954) and Fletcher (1962).
When an ice block was annealed under an isothermal condition, the contained air
bubbles were observed to split or shrink into smaller ones. The mechanism of the phenomenon does not seem to be simple. The evaporation-condensation process is a possible
one, but may be too slow to explain the phenomenon; according to Yosida's calculation
it would take 6 years at O°C for a 5 p. thinning in radius of an ice cylinder (100 p. III
diameter) to grow to 10 p. through evaporation-condensation due to the difference incurvature (Yosida, 1954).
The shrinkage of air bubbles may be explained in two ways: through the dissolutionof molecules of air or through the diffusion of some kind of defects in the ice crystal.
Many chemical analyses revealed the existence of air or other gas in ice crystals, andthe author observed the appearance of tiny air bubbles from a block of commercial or
glacier ice melting in kerosene under a microscope; so that the former process would
no doubt occur. The latter is a process which can be accomplished by a diffusion ofsome kind of defects such as vacancies. The two processes are quite probable in suchan open lattice configuration of ice crystal, and have been recently discussed for theshrinkage of air bubbles in snow crystals by Maeno and Kuroiwa (1967).

218

N. MAENO

Acknowledgments
The author would like to express his gratitude to Prof. D. Kuroiwa of the Instituteof Low Temperature Science, Hokkaido University, for supporting and giving valuablecriticisms on this res each.

References
1) CARTE, A. E. 1961 Air bubbles in ice. Proc. Phys. Soc., 77, 757-768.
2) CORTE, A. E. 1963 Vertical migration of particles in front of a moving freezing plane.
CRREL Res. Rept., 105, 1-8.
3) DEAN, R. B. 1944 The formation of air bubbles. J. Appl. Phys., 15, 446-45l.
4) FLETCHER, N. H. 1962 Surface structure of water and ice. Phil. Mag., 7, 255-269.
5) MAENO, N. and KUROIW A, D. 1967 Metamorphism of air bubbles in a snow crystal. J.
Glaciol., 6, 561-564.
6) NAKAYA, U. and MATSUMOTO, A. 1954 Simple experiment showing the existence of "liquidwater" film on the ice surface. J. Colloid Sci., 9, 41-49.
'7) NAKAYA, U. 1956 Properties of single crystal of ice, revealed by internal melting. SIPRE
Res. Rept., 13, 1-80.
8) TABER, S. 1930 The mechanics of frost heaving. J. Geol., 38, 303-317.
9) TAKAGI, S. 1965 Principles of frost heaving. CRREL Res. Rept., 140, 1-24.
10) TAYLOR, E. W. 1949 The Examination of Waters and Water Supplies (Thresh, Beale andSuckling), 6th ed., J. & A. Churghill Ltd., London, 278 pp.
11) UHLMANN, D. R., CHALMERS, B. and JACKSON, K. A. 1964 Interaction between particles
and a solid-liquid interface. J. Appl. Phys., 35, 2986-2993.
12) WEYL, W. A. 1951 Surface structure of water and some of its physical and chemical
manifestations. J. Colloid Sci., 6, 389-405.
13) YOSIDA, Z. 1954 A quantitative study on metamorphosis of snow crystal. Low Temp. Sci.,~ 13, 11-28. (In Japanese with English summary).