[Physics] Flakes of Ice in Frozen Milk and Orange Juice

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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.)

Best Answer

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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