The Mpemba paradox

November 1, 2013 2:24 PM

Someone appears to have an answer to why warm water appears to freeze more quickly than cool water, a phenomenon known as the Mpemba effect after Erasto Mpemba who noticed the effect in freezing ice cream. The reasons why have eluded scientists and prizes have been offered for a solution. Now a group headed by Prof. Xi Zhang out of Singapore has proposed a promising theory. The answer as they see it lies in energy stored in the covalent bonds within the water molecules which are affected by the temperature of the water. (via the Presurfer)
posted by caddis (47 comments total)

You had me at ice cream!
posted by jessssse at 2:33 PM on November 1, 2013 [3 favorites]

Hmmm. Interesting. If I understand this correctly, at some point in the cooling process, SCIENCE happens.

I really should've taken chemistry in high school.
posted by BitterOldPunk at 2:41 PM on November 1, 2013 [1 favorite]

I still think the hot water bounces around faster so it has more chances to touch cold stuff.
posted by 2bucksplus at 2:46 PM on November 1, 2013 [3 favorites]

I would have guessed hydrogen bonds. Because the last four years of chemistry have drilled into my head that answering "hydrogen bonds" will get you a correct answer on 9 out of 10 questions asking about the behavior of water.
posted by MaritaCov at 2:47 PM on November 1, 2013 [18 favorites]

The best demonstration of the paradox:

Throw boiling hot water into the air on a reaaaally cold winter day. Science!
posted by bdz at 2:48 PM on November 1, 2013 [3 favorites]

The archiv paper is actually pretty readable from a layman's perspective.
posted by Valued Customer at 2:48 PM on November 1, 2013

The graphic, on the other hand.
posted by Valued Customer at 2:49 PM on November 1, 2013

This has been making the rounds recently. It's an interesting idea, but the consenus I'm seeing is that it needs verification. Either someone needs to do a clever experiment or they need to be able to use this mechanism to predict another observable behaviour, to generalize this hypothesis into a more useful, predictive theory.

In any event, even if not found wholly correct in the end, it is very interesting work that bears a lot of thinking about. This could have implications to a number of things like solution dynamics and emulsion formation and stability.
posted by bonehead at 2:51 PM on November 1, 2013

Great article.

Water expands when it freezes.
Water expands when it warms.

Seems appropriate that warmer water put into freezing conditions takes a straight line to ice. It's already in an expanded state, so it's doesn't have much farther to go until it's frozen.
posted by JoeXIII007 at 3:01 PM on November 1, 2013 [3 favorites]

Aristotle first noticed that hot water freezes faster than cold

Then there is the strange Mpemba effect, named after a Tanzanian student who discovered that a hot ice cream mix freezes faster than a cold mix in cookery classes in the early 1960s. (In fact, the effect has been noted by many scientists throughout history including Aristotle, Francis Bacon and René Descartes.)

They really just can't give this guy his props.
posted by gucci mane at 3:14 PM on November 1, 2013 [9 favorites]

I ran across this a while ago. My mother (an educated woman with several advanced degrees, and an educator herself), always taught us as kids to put warm water in the ice cube trays before we put them in the freezer.

I later asked a physicist friend about the phenomenon, and her answer was, "water has anomalous properties".
posted by trip and a half at 3:19 PM on November 1, 2013 [6 favorites]

This is pretty timely; one of our biggest family thanksgiving dinner fights was over whether hot water or cold water freezes faster.
posted by craven_morhead at 3:21 PM on November 1, 2013

I heard this as a kid but later attributed it to misinformation. Glad to know I wasn't crazy.
posted by thorny at 3:25 PM on November 1, 2013 [2 favorites]

Once you get to second semester organic chemistry and pretty much from there on out, if you're taking a test and have no idea what goes in the blank, write in "Hydrogen Bonding" (or in this case, "The H:O non-bond") if it at all fits the question. It has about a 25% chance of being the right answer.

Another 25% of the time the answer is "resonance structures."
posted by Kid Charlemagne at 3:29 PM on November 1, 2013 [2 favorites]

Another 25% of the time the answer is "resonance structures."

Cmdr. Data! Increase phase variance in the main deflector's field array to harmonize with the alien resonance structures.

Aye, sir.
posted by m@f at 3:39 PM on November 1, 2013

They really just can't give this guy his props.

Indeed. Mind you, props also to Dr. Osborne for actually looking into the matter ("after initial consternation") once Mr Mpemba brought it to his attention and then bringing him in on the paper. Plenty of guys would have opted to be photographed alone.

Interesting that it had been observed repeatedly over the millennia but that by 1963 it was not part of the standard body of "Believe it or not" science knowledge. Makes the non-scientist in me wonder what other phenomena science appears to have overlooked or forgotten. Like marbles and bowling balls falling at the same rate of speed....
posted by IndigoJones at 4:45 PM on November 1, 2013

I ran across this a while ago. My mother (an educated woman with several advanced degrees, and an educator herself), always taught us as kids to put warm water in the ice cube trays before we put them in the freezer.

But I learned from my mom that you should never use warm water for anything food related, because the water in the heater is a good breeding ground for various murkiness! Which mom wins?
posted by ymgve at 6:01 PM on November 1, 2013 [1 favorite]

I think all theories of the Mpemba effect have the following problem:

Suppose you have a sample of water, two identical containers and a freezer with properties that don't vary in time and so big that whatever happened to half of your sample in one part of it would have negligible effects on what happened to the other half of the sample in another part.

Boil half your sample, wait ten seconds for the bubbling to subside, put it in one of your containers, and put it in the freezer.

Now wait five minutes and perform the identical procedure on the second half of your sample.

At that moment you have two samples in the freezer which are identical except that one has been in the freezer five+ minutes longer than the other, and is therefore cooler-- but that means the other sample is hotter and will, by the Mpemba effect, freeze sooner despite the fact that its been in the freezer at least five minutes less at the time it freezes than its identical counterpart, which will still be unfrozen at that time.
posted by jamjam at 6:37 PM on November 1, 2013 [2 favorites]

jamjam,

The issue is that the Mpemba effect survives pretty much all attempts at removing conflation with other sources.
posted by effugas at 6:56 PM on November 1, 2013

The answer as they see it lies in energy stored in the covalent bonds within the water molecules which are affected by the temperature of the water.

So Burhanistan wins? Cool.
posted by flabdablet at 7:24 PM on November 1, 2013 [2 favorites]

The issue is that the Mpemba effect survives pretty much all attempts at removing conflation with other sources.

effugas, a shorter, more abstract version of my point is that in order for hot water to freeze, it must first pass through every lower temperature between its high temperature and the freezing point.

To claim then that when it reaches one or more of those lower temperatures, which take time to reach, it will take more time to freeze from that lower temperature than the total time it takes to freeze from the hot starting point is highly paradoxical.
posted by jamjam at 8:34 PM on November 1, 2013 [3 favorites]

Who is this pretender Mpemba? For 2 decades this has been known as ElGuapo's Law of Phase Change Momentum.
posted by ElGuapo at 9:12 PM on November 1, 2013 [1 favorite]

I agree with jamjam. The temperature of the initially hotter water has to (at some point as it cools to freezing) reach the starrting temperature of the initially colder water. At that point, isn't the initially hotter water in state that the initially colder water started in? So, the initially hotter water has to take more time to freeze.

For this not to happen (that is, for the hotter water to freeze faster), there would have to be something about the two samples of water that differs, other than the temperature. (E.g. impurities have precipitated out of the initially hotter water, but not out of the initially colder water.. which seems unlikely if the experiment is carefully controlled.)
posted by nealeyoung at 10:31 PM on November 1, 2013

At that point, isn't the initially hotter water in state that the initially colder water started in?

The hot water gets a running start, so it has more momentum to freeze.
posted by Mayhembob at 10:39 PM on November 1, 2013

Some discussion about jamjam's argument.
posted by nealeyoung at 11:15 PM on November 1, 2013 [1 favorite]

jamjam,

The problem is the assumption of linearity, i.e. that water must pass through identical states from hot to cold to frozen.

The simplest way to break your assumption is to point out that a container of water does not possess a single temperature. There's the water in direct contact with the freezing air, there's the water at the dead center of the container, and there's the currents that form as temperatures shift. There is no rule of nature requiring these shifts to occur in such a manner that water at each point in the journey down from 99C looks like water starting at 50C.

The point of this paper, of course, is that what's actually happening is substantially more complex. But the assumption -- that nature must follow linear rules from geometry -- you're suffering from a very nice spherical cow.
posted by effugas at 12:52 AM on November 2, 2013

For this not to happen (that is, for the hotter water to freeze faster), there would have to be something about the two samples of water that differs, other than the temperature.

You're assuming that the temperature history is irrelevant, i.e. that water recently heated and then re-cooled to a given temperature is in all ways equivalent to water that has spent a substantial amount of time at the original temperature. Water is weird enough that this may not be true.
posted by flabdablet at 1:04 AM on November 2, 2013

Here's an interesting question:

Is it that water is weird?

Or is it that most things are weird, it's just water's weirdness is actually relevant due to its availability and high usage?
posted by effugas at 1:43 AM on November 2, 2013

I don't know much about science, but as a drinking man I know that if you want clear ice cubes you have to boil the water first to drive off dissolved gases. It makes sense to me that water which has been heated and therefore has fewer gaseous impurities might sometimes freeze easier than water where lots of extra non-water molecules are blocking the formation of a nice crystal structure.

This is explanation number 2 in nealeyoung's list.
posted by Segundus at 2:18 AM on November 2, 2013 [2 favorites]

The hot water eats ice cream to cool off, while the cool water is shivering trying to heat up.

SCIENCE!
posted by blue_beetle at 4:20 AM on November 2, 2013

Another problem with jamjam's scenario is that water doesn't instantly freeze when the average temperature reaches 0 degrees celsius. You can get some water well below that without it freezing (supercooling).
posted by empath at 4:39 AM on November 2, 2013

Now my village can have ice again after the tragic loss of the recipe when that old lady died.
posted by tommasz at 5:13 AM on November 2, 2013

My theory is that the hot water causes the refrigeration compressor to cycle on sooner, leading to a drop in temperature and quicker freezing. Thuh ind.
posted by Mental Wimp at 6:11 AM on November 2, 2013

So here's the thing about "temperature" - water can store energy in three translational movements (X, Y and Z). , three spin states (ω_X, ω_Y, ω_Z), and, three vibrational states (C₂, σ_v(xz) and σ_v(yz). Only X, Y and Z are included in our definition of temperature. If I follow the abstract, what Zhang is doing is looking at how energy is released from those other non-temperature states when you factor in all the interactions in bulk water.

If you think, even for a moment, that I didn't have to look up those vibrational state names, you'd be wrong.
posted by Kid Charlemagne at 8:03 AM on November 2, 2013 [1 favorite]

Is it that water is weird?

Water is highly weird. The hydrogen bonding structure supports all kind of unusual behaviour like surface tensions three times higher than other fluids, boiling and melting points much higher than similar mass compounds, non-linear temperature/density functions. It's a very long list, but one our ecology and biology is so dependent on. What we think of as normal, ice floating, capillary flows, solvation and emulsification behaviours are all atypically characteristics of water.
posted by bonehead at 8:17 AM on November 2, 2013

jamjam is hardly the first to make those sorts of arguments; historically exactly what was meant by "heated water" and "freezes faster" seems to have been pretty murky and generally a source of confusion. The late-1990s usenet FAQ by Jeng was published in 2006 in the American Journal of Physics. (The published version was substantially expanded over the public domain version, to my memory, but I haven't read either for apparently about seven years.)

If I understand the blog summary of the new paper: the structure of water ice --- the hexagonal ice crystals --- come from hydrogen bonds. In room-temperature water, you get hydrogen bonds with a different geometry. When you lower the water's temperature, some of the liquid-type bonds have to have energy added before they can break and reconfigure to form the solid-type bonds. But in hot water, there aren't any stable hydrogen bonds, and you can form the solid-type bonds directly.

There's a similar phenomenon that happens when you liquify hydrogen. The H2 molecule has some specific heat due to the motion of the molecule, and some specific heat due to the spinning of the molecule, but for some tricky reasons involving quantum mechanics there's para-H2 with spin 0,2,4,etc. and ortho-H2 with spin 1,3,5,etc. Room-temperature H2 is three-quarters ortho-H2, and cold hydrogen wants to be all para-H2, the ground state, but a single ortho-H2 molecule can't spontaneously convert to para-H2 --- you have to let two ortho-H2 molecules find each other, and they can convert into two para-H2 molecules. So what happens when you liquify room-temperature hydrogen is that you first produce a liquid which is mostly orthohydrogen; the huge density change means all the ortho-H2 molecules can find each other and convert to para-H2, a conversion process which releases enough heat to re-boil all of your liquid; then your new para-hydrogen liquifies and stays liquid this time. If there were some higher-temperature state where para-hydrogen were preferred, then you could liquify hydrogen much faster by heating it first. Even as things are, it's the case that hydrogen which has been liquified and boiled will, for a few hours or days, require less cooling to liquify than hydrogen that's been at room temperature for a longer time. Not quite as bizarre as the Mpemba effect, since the hydrogen is somehow "remembering" being cold, but certainly the same sort of thing.

The difference, though, is time scales. I don't have any idea why forming and breaking hydrogen bonds in water would be slow enough to change the heat capacity over many tens of minutes. And the language in the arxiv paper is mostly about bond lengths, and it's too far past my bedtime for me to make sense of it, and maybe I've talked myself into a corner. Hmmm.
posted by fantabulous timewaster at 8:55 AM on November 2, 2013 [1 favorite]

to Kid Charlemagne: you can only say that the spin and vibrational states are excluded from the temperature when the coupling between the spin/vibration states and the translational motions becomes weak. This is why the heat capacity of simple molecules generally increases with temperature: as there's more heat sloshing around the system, you start to be able to store heat in the more exotic modes. But there certainly are materials which have modes which are always weakly coupled to translational temperature. For example, if you can get all the nuclei in a gas to spin the same way, you could say that the gas has a very low "spin temperature," even if the "kinetic temperature" that you measure with a thermometer is pretty high. (And this has predictive power, since the strength of the coupling between the spin temperature and the kinetic temperature helps to determine how long the gas will stay polarized.)

Temperature is a statistical phenomenon, and we poor humans are mostly bad at statistics.
posted by fantabulous timewaster at 9:08 AM on November 2, 2013

you can only say that the spin and vibrational states are excluded from the temperature when the coupling between the spin/vibration states and the translational motions becomes weak.

You've put your finger on why I think this is interesting, but needs more elaboration. I'll need to see how the symmetry breaking of the sort-of covalent h-bonds affects coupling, which is more or less the heart of their argument. The authors have put forward a semi-classical model in their paper, but one that doesn't explain it in terms which could be extended to a quantum-mechanical stat mech simulation.
posted by bonehead at 9:34 AM on November 2, 2013

The hot water gets a running start, so it has more momentum to freeze.

Don't be silly. Standing water freezes faster than running water.
posted by weapons-grade pandemonium at 10:14 AM on November 2, 2013

I skimmed a few articles about this in the American Journal of Physics a few years back. (The AJP is the physics teaching journal. You won't find any Mpemba effect stuff in, say, Physics Review Letters.) I remember being impressed by the people who had been doing calorimetry studies over periods of years. I'm not really qualified to comment on the new paper, but I will just say that calorimetry is harder than it looks.

And by the way, does hot water actually give you clear ice cubes? Like, clear all the way through? It hasn't worked for me. This guy did a whole bunch of experiments and concluded that the best way to get clear ice is to 1) freeze from only one direction 2) cut/melt off the resulting cloudy bit by hand.
posted by Standard Orange at 11:03 AM on November 2, 2013

Handwavey explanations are fun. Here's mine.

As has already been noted, a sample of water suddenly exposed to extreme cold won't have a single temperature. On any line drawn between the surface of the sample and the interior there will be a temperature gradient, with higher temperatures furthest from the cold surface. And that gradient will in general not be smooth - there will be a fairly sharp step in it right where a layer of water molecules is rearranging itself into a layer of ice. If my hands are waving correctly, the steepness and suddenness of that step is key to understanding what's going on with Mpemba.

When water freezes, two things happen: (a) it gives up its latent heat of fusion, thereby adding heat to whatever is touching it and (b) its thermal conductivity increases by a factor of about four.

If the bond structures prevalent in hot water are in fact less resistant to rearranging themselves into an ice crystal lattice than those in cool water, then sudden application of extreme cold to the outside of a hot water sample might plausibly result in the instant formation of an extremely thin layer of surface ice. The latent heat of fusion would dissipate in two directions - outward into the cold, and inward into the already hot interior, and the temperature gradient between inside and outside would show an extremely sharp step between the ice on the outside and the water on the inside.

The same process would continue as the ice layer grew inwards, with heat removal remaining relatively quick due to the existence of a relatively large temperature difference across a layer of ice with relatively high thermal conductivity.

So yes, the hot water would have to cool through the temperature of the cool water on its way down to 0°C, but this process would be happening in a very thin layer just inside the solidifying ice coat, thereby maintaining conditions that speed the process of heat removal from the bulk of the sample.

By contrast, in an initially cool sample the layer of near-0°C water inside the ice coat might quite plausibly remain substantially thicker for the whole process. The resultant reduction in overall thermal conductivity, coupled with the reduced temperature difference between the sample's interior and exterior, might plausibly lower the speed of overall heat removal enough to account for the Mpemba effect.

If this is right, then we don't need bond energy mechanisms with a "memory" of tens of minutes. Microseconds would probably do.
posted by flabdablet at 7:11 PM on November 2, 2013

It would be interesting to run experiments with hot vs cold water freezing using different freezer temperatures. If I'm right about the importance of rapid ice skin formation, I would expect the Mpemba effect to become more pronounced as the freezer temperature drops, since this would tend to help keep the developing ice coat well under 0°C, which I would expect would make sudden freeze and steep temperature gradient step effects persist deeper into the water sample.
posted by flabdablet at 7:41 PM on November 2, 2013

Oh, the Mpemba effect must be a fabulous thing to know about if you have some interest in physics research but limited funding and time. It's a demo you might be able to run over the interval of a lecture; it's counterintuitive enough to hook a student; you can poke around in the parameter space using standard kitchen equipment; you can make an interesting measurement by sticking your head in the kitchen a few brief times during a busy day.

Flabdablet, your ice-layer model is interesting, but it breaks a "rule" that I learned as an undergraduate and haven't quite been able to replace with a more correct rule: that you don't get a phase change until you have "all" of a material at the phase change temperature. The context for this rule was that you don't know the temperature of an ice cube until it goes slippery in your hand, at which point you can safely treat both the entire ice volume and the water in contact with it as having temperature 0ºC. Certainly the correct statement isn't "all" the material, since the oceans contain both icebergs and boiling undersea vents; but the best I've been able to come up with is that a phase boundary will be surrounded by a region of uniform temperature whose size is determined by the cooling (or heating) power, the latent heat of the transition, and the temperature conductivity on either side.

In any case, flabdablet, I think you can only have heat flowing from ice to liquid water if the liquid is supercooled, and the temperature of the liquid won't raise any higher than the freezing point. I suspect that entropy considerations even mean that the temperature gradient in the liquid has to get softer over time, rather than sharpening as you suggest, but I could be convinced otherwise there.

I wonder if you could say something quantitative about the hydrogen bond lifetime by ascribing the heat of fusion to the hydrogen bond formation energy and observing that most videos of supercooled water freezing show the ice front moving at sort of 1 cm/s ?
posted by fantabulous timewaster at 9:16 PM on November 2, 2013

the best I've been able to come up with is that a phase boundary will be surrounded by a region of uniform temperature whose size is determined by the cooling (or heating) power, the latent heat of the transition, and the temperature conductivity on either side.

Yeah. What I suspect from such Mpemba effect demos as I've seen is that effect shows up most strongly when the cooling power is fairly extreme, which would tend to keep the 0°C liquid layer nearest the phase boundary fairly thin.

I think you can only have heat flowing from ice to liquid water if the liquid is supercooled

Seems to me that the latent heat of fusion has to go somewhere. Maybe it does all escape via conduction through the ice side of the phase boundary. Maybe there's a layer a few molecules thick on the liquid side of the boundary that could reasonably be described as supercooled due to bizarro surface-tension-like skin effects. Dunno.

I suspect that entropy considerations even mean that the temperature gradient in the liquid has to get softer over time, rather than sharpening as you suggest, but I could be convinced otherwise there.

I didn't really have it in my mind that the gradient would get sharper over time, just that if there were indeed some bond-geometry-derived tendency for sudden freezing to be easier given a higher starting temperature, that the gradient step within an initially hot sample would start out sharper and stay sharper than that within an initially cool sample. I would indeed expect the gradient step in both samples to soften as the ice layer deepened inwards simply because the ice is not a particularly good heat conductor (about four times better than water but still nowhere near as good as, say, copper) and would therefore reduce the available cooling power as it got thicker, but it may well be that the hot sample maintains both a higher core temperature and a sharper temperature step until freezing is complete.

It would also be interesting to find out what the ice temperatures were in both samples at the instant both completed freezing. I would expect the initially-hot sample's ice to be warmer overall than the initially-cold sample's ice, simply because it must have had more heat flowing through it from the water inside.

If the thinner-boundary-layer hypothesis is right then the cold sample's thicker boundary layer would slow heat transfer more than the hot sample's thinner one; the freezer would therefore do more work causing phase change in the hot sample than in the cold sample, and more work pulling down the temperature of existing ice in the cold sample than in the hot sample.
posted by flabdablet at 11:00 PM on November 2, 2013

Seems to me that the latent heat of fusion has to go somewhere.

Into the refrigerator, right? The heat can't go uphill into the warmer liquid.

It would also be interesting to find out what the ice temperatures were in both samples at the instant both completed freezing.

Wouldn't it be 0ºC ?
posted by fantabulous timewaster at 9:41 AM on November 5, 2013

The heat can't go uphill into the warmer liquid.

As I understand these things, and please correct me if I'm wrong: heat is nothing more than uncorrelated molecular and atomic kinetic energy. The process of freezing involves molecules arranging themselves into a solid lattice, and any such lattice inherently has a much higher degree of internal correlation than the same molecules do when in a liquid or gas phase. The latent heat of fusion is a measure of the energy required to break that lattice correlation, or equivalently the amount that is released as it forms; I see it as pretty much a bookkeeping trick that allows us to speak meaningfully of temperature when comparing measurements of substances in different phases.

Energy won't go uphill from a place with less to a place with more. In the usual case where no phase boundary is involved, that means that temperature can't spontaneously go uphill either. But given that temperature is a statistical aggregate measure, and given that the matter in the region we're thinking about here does have a phase boundary right through the middle of it, I see no reason to reject on fundamental principles the idea of a temperature gradient map with a very sharp step, perhaps even including a tiny thin spike, on the liquid side of the moving phase transition.

Because it seems to me that a temperature drop to 0°C doesn't actually cause water's phase transition to the frozen state; rather, in the usual case it merely fails to prevent it. The existence of supercooled water demonstrates this: it's quite feasible to cool water well below 0°C and keep it liquid if you deprive it of crystallisation seeds.

So if there exists some handwavey bond energy consideration that permits water we would normally consider anomalously warm to switch from liquid freedom to solid lattice, given the presence of an existing lattice with sufficient heat removal capacity on the solid side: I see no first-principles physics reason to assume either that the liquid side of that phase transition must be at 0°C, or that some of the heat energy necessarily dumped by the physical rearrangement that constitutes freezing could not help maintain a sharp temperature step between liquid and solid phases as the freezing proceeds inward.

Or perhaps we could riff a bit more on the reality of supercooled water, and claim that any such warm-water-freezing process might necessarily involve the transient existence of superheated ice. It may well be that water molecules can briefly hold energy in some form that allows a solid lattice to form above 0°C.

And then there's endless speculative handwaving available about the effects of a possible low pressure shockwave, something akin to reverse detonation, at the freezing front. Who knows WTF water can do? Not me, that's for sure.
posted by flabdablet at 5:22 PM on November 5, 2013

I'm thinking of entropy considerations. The definition of temperature that has served me best is 1/T ≡ ∂S/∂U: a thing is cold when a little extra energy dU produces a lot of extra entropy dS. "Heat goes from hot things to cold things" is just the second law of thermodynamics. The refrigerator is removing both energy and entropy from the ice; the still-liquid water is supplying energy and entropy to the ice, until the internal energy and entropy of the liquid water run out, at which point it freezes.

Not to say a supercooled fluid can't solidify and raise the temperature of the surrounding medium. My favorite example of that are the reusable sodium acetate hand-warmers. Sodium acetate solidifies at about 60ºC, but is pretty easy to purify enough to supercool; you buy some as liquid in a sealed plastic bag and shock it, and crystals zip through the bag and all of that heat of fusion is released over a few minutes. But the warmest part of that system is the fresh crystal; it's your hand, stubbornly stuck at 35ºC, that sucks all the heat from the solution.

Now there will certainly be local fluctuations in the temperature at the liquid/solid boundary, since the molecular motions and vibrations and rotations are drawn from probability distributions; these temperature fluctuations are larger when you consider smaller volumes. There'll be regions that are supercooled (which will tend to solidify) and regions that are above the temperature boundary (which will tend to liquify, if they're solid yet). I don't know how to estimate how small a region you have to look at to get temperature variations of a certain size, nor how long the variations last, but I think that "constant temperature" is not a terrible approximation.

But the Mpemba effect --- at least in the data quoted in the arxiv paper discussed here --- seems to involve a faster change in the temperature of the water on the way down to the freezing point. The data all seem to stop around 0ºC. I'm pretty sure the freezing skin is a small correction at the end of the freezing process. But, hmmm.
posted by fantabulous timewaster at 7:30 PM on November 5, 2013