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When water phase-transitions into ice it expands. The water usually contains dissolved air. Freezing forces the air out of the solution into bubbles.

Are these bubbles at a lower or higher pressure than atmospheric pressure?

I can see arguments both ways: when a washer expands, both the outer and inner radius increase. This would imply bubbles are at a lower pressure, but perhaps the ice expands differently and squeezes the bubble and it is at a higher pressure. However, if they were squeezed I would expect them to try to expand, and propagate along weak fraction lines in the ice, and I do not see this - bubbles are usually round, suggesting low pressure environments.

Edit: Two papers on the subject, but neither sheds direct light on the answer:

  • "Bubbles and bubble pressures in Antarctic glacier ice" (A. J. Gow, J. Glaciol. 7 no. 50 (1968), pp. 167-182) shows that the bubbles shrink with increasing pressure. These are therefore presumably high-pressure bubbles. However, the internal bubble pressure is due to ice compressing as more ice forms on top, not just the freezing process.

  • "Air Bubbles in Ice" (A. E. Carte, Proc. Phys. Soc. 77 no. 3 (1961), p. 757) talks about bubble formation, but not internal bubble pressure.

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    $\begingroup$ I think the question of size of the bubbles may be isomorphic to the common demonstration looks at the size of the hole in an annular metal ring before and after heating. That would suggest lower pressure than they started with, but we can't begin to guess if freezing would or would not force more dissolved gas out of solution and into existing bubbles. Now would I wager more than about one US dollar on the claim of isomorphism to the heated annulus. $\endgroup$ – dmckee --- ex-moderator kitten Jul 13 '13 at 17:46
  • $\begingroup$ So you have some reasons to believe that it's low pressure; what arguments do you have that would support the other option? $\endgroup$ – mehfoos Jul 23 '13 at 12:27
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Fluid inclusion analysis techniques are used by geologists to gather information on the pressure, volume, and temperature conditions during the crystallization of the mineral (here ice) containing the inclusion.

There are three assumptions that usually made in dealing with fluid inclusions:

• The composition of the trapped fluid has not changed since inclusion formation

• The density of the trapped fluid has not changed since inclusion formation

• The volume of the inclusion has not changed since inclusion formation

Natural fluid inclusions will contain multiple chemical components (impurities) and may contain multiple phases (gas, liquids, precipitated crystals).

The analysis of fluid inclusions (say to determine the pressure of formation) therefore involves measuring the composition and density and then applying the appropriate equation of state calculations to calculate unknowns.

Fluid inclusion measurements and analysis are not simple to perform. I would not think you can say whether the pressure is higher or lower than the formation pressure without doing a complete analysis.

The analysis of air bubbles in ice are important for the study of the past composition of the atmosphere and climate change.

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Since the air in the bubbles was below the surface of the water before the freezing, I would expect it to be above atmospheric pressure, albeit maybe just a little, depending on the hydraulic head.

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    $\begingroup$ Yes, good observation. But that baseline pressure would change based on the freezing process, and that change is what I am trying to understand. $\endgroup$ – mankoff Jul 13 '13 at 21:57
  • $\begingroup$ I think this answer is correct withing desired precision. Pressure should be atmospheric plus depth on which it was formed. Last term can be big if we are talking bout iceberg for example. $\endgroup$ – Asphir Dom Jul 16 '13 at 19:50
  • $\begingroup$ Icebergs generally melt so bubbles are not forming at depth. The bubbles likely formed high up on a glacier at less than 1 atm. Anyway, since I asked the question I get to define "desired precision" :). What about a bubble forming in an ice-cube tray 0.1 mm below the surface. Pressure term here is negligible, and may be less than pressure change from the freezing process. $\endgroup$ – mankoff Jul 17 '13 at 1:18
  • $\begingroup$ @mankoff Note that glacier ice is not formed by freezing, but by the compactification through high pressures of ice crystals in snow. Since snow is formed directly from atmospheric water, I would expect the air content of glacier ice to come from the spaces in between snowflakes. $\endgroup$ – Emilio Pisanty Jul 19 '13 at 12:54
  • $\begingroup$ @EmilioPisanty Yes, and those bubbles are under pressure when they are extracted (or calve into an iceberg), as seen in the first reference. $\endgroup$ – mankoff Jul 19 '13 at 13:11
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This is how I imagine it would happen, As Ice begins to freeze, outer surface first followed by the inner surface, the concentration of the air in the water would increase.

As more and more of the ice begins to freeze, the water would eventually be saturated with air, and hence be forced to from a bubble. The final size of the bubble is same as the cavity that is created when water freezes.

If you have a sphere full of water(with dissolved air), and it is frozen, outer to inner, We know the size of the cavity inside the ice. We also know the the total amount of air water can hold at 0 degrees Celsius.

http://www.engineeringtoolbox.com/air-solubility-water-d_639.html,

The numbers can be calculated more correctly, but just to get an idea, the website indicates that the solubility of Oxygen in air is 14mg/l at zero degrees.

14 mg at STP = (14/1000g)/(16 g)*22.4 = .0196 litre

the empty space created when water freezes is ~8.3 pc(http://en.wikipedia.org/wiki/Ice), ~.08 litres of space per liter of water frozen.

Therefore one can conclude that the pressure in the air bubble is lower. The numbers will change if you add the total air dissolved in water(the conclusion will still probably hold. This calculation is for an atmosphere of oxygen at 1 atm)

Ref http://academic.keystone.edu/jskinner/Limnology/Water_Chemistry_LectureNotes.htm

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I love this question so I want to add my opinion here.

I would think that the column of atmosphere above the ice would contribute more pressure than the expansion pressure on an air bubble in an ice cube. But I have no data on this.

As we know, the decrease in temperature results in some moles of air coming out of solution as gas. This would decrease the volume of the solution--except that the gas is trapped and is still part of the total volume. Since the air occupies more volume when in this gas state, the pressure would be some magnitude.

At the same time, the crystal structure of water is forming an organized system, which increases the volume of the solution as it expands in all directions--noticeably outward. The ice typically freezes from the outside to the inside, which would provide some containment pressure on the gas bubbles. It would be interesting to compare the air bubble pressure at the core versus in a superficial layer.

As a test at sea level, I would set up high-definition/magnification cameras on air bubbles in ice, surrounding with a low viscosity, non-polar dye solution. I would then observe one bubble as its sphere is first broken upon melt. If there is a spurt of air from the bubble then we conclude the air bubble pressure is higher than atmospheric and if some of the color is observed to rush into the air bubble--which I would suspect--then we can conclude the bubble pressure is less than atmospheric.

Interestingly, the bubble pressure could turn out to be close enough to atmospheric pressure to not notice anything.

As an aside for further reading on a variant of this topic, look into the crystallization of the molecules in glass in a Prince Rupert Drop.

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An answer for glacier ice is different than frozen water - the glacier ice has formed under different processes. Still, it is interesting to see the argument laid out by Pettit et al. (2015) that bubbles in glaciers are at higher pressure than atmospheric pressure.

As ice flows toward the terminus, overburden pressure decreases, the ice viscously relaxes, and pore pressure is reduced. However, once the difference in pressure between the pore space and the ice crystal lattice is less than about 10 bar, deviatoric stresses are insufficient to permit further pressure equalization due to the nonlinear rheology of ice [Gow, 1968]. Air-filled pores in melting glacier ice, therefore, will always be at a higher pressure than atmospheric pressure. Scholander and Nutt [1960] measured the pressure in the pores of west Greenland icebergs and found them typically not only between 5 and 10 bar but also up to 20 bar.

From http://dx.doi.org/10.1002/2014GL062950

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