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When I was a kid, my family used to put our gallon jugs of milk and orange juice into the freezer when we'd go away on vacation so that they would keep longer. As I remember it, if we were gone for a week or more the jugs would be frozen solid, but if we were only gone for a couple of days, instead they would be filled with thin, crisp flakes of ice suspended in their respective liquid. Additionally, when we would begin to thaw a completely frozen jug, it would thaw into a mixture of ice flakes and liquid (usually with a big chunk of flaky ice floating right in the middle). And just today I noticed that the carton of milk at the back of my refrigerator had partially frozen and formed these flakes.

Why do milk and orange juice freeze in this way? What effect does this have on how quickly milk and orange juice freeze and thaw compared to water?

(The orange juice was always pulp-free, by the way.)

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I suspect this relates to the phase diagram of sugary water. When a liquid contains a solute (sugar for example) that lowers the melting point of water, then as you cool it down you get a segregation: a small ice crystal forms, and at the tip of that crystal pure water will crystallize. The sugar is pushed into the solution where it further lowers the melting point. Now just as snow flakes tend to grow as flakes, so these flakes will grow preferentially in 2D because the tips of the flakes are energetically more favorable for ice to grow (and given that you have to push sugar away to make the ice, this makes sense).

The following generic phase diagram (source: http://www1.lsbu.ac.uk/water/images/glass_transition.gif) gives you an idea of what is going on:

enter image description here

Starting somewhere in the top left, slow cooling will get you to the point where ice starts forming, and the remaining liquid becomes more saturated - so after initially moving vertically, you then follow the red curve until you reach the eutectic point (labeled $T_{eu}$ where everything becomes a solid. If the cooling happens faster, you may take a different path (which does not get you all the way to the eutectic mixture).

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  • $\begingroup$ Oh, that'd be great! Actaully, that is another thing I was wondering about: You are not saying that the flakes are pure ice, are you? Surely there are some impurities in the flakes. Do you know what the relative increase in concentration for the unfrozen solution would be? $\endgroup$ – Geoffrey Jan 2 '15 at 2:54
  • $\begingroup$ I am saying that the flakes are "pretty pure" water - not exactly, but entropy does drive the sugar into the solution while the ice prefers to be "pure". Actually a variant of this is known as "zone purification" - it is used to create very pure crystals by moving a melting zone through material (especially silicon). The impurities stay in the melt, and the crystal becomes more and more pure. This can be repeated multiple times to increase purity - so no, in a single pass you don't get pure ice. $\endgroup$ – Floris Jan 2 '15 at 2:57
  • $\begingroup$ My ignorance is showing, but what is meant by "glass" in the diagram? I'm a little confused because I would assume that $T_g$ is the point where everything becomes solid. $T_{eu}$ appears at first blush to be the point where the solution that remains begins to be super-saturated. $\endgroup$ – Geoffrey Jan 2 '15 at 3:07
  • $\begingroup$ Strictly speaking the eutectic point is the lowest point where liquid with solute can exist - the supersaturated regime exists because things won't always freeze right away, and if you reach the glass temperature the liquid becomes immobile without having crystallized properly ("solid but microscopically disordered" as www1.lsbu.ac.uk/water/rheology.html calls it). It's a bit complicated to explain in a 600 character comment... see that link for more info. $\endgroup$ – Floris Jan 2 '15 at 3:50

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