Friday, February 23, 2018

The Joy of Physics: Kitchen Mysteries

As regular readers of the site know, we try to take time each week to answer an interesting or informative question that lands in our "Ask a Physicist" inbox. Part of the reason why we do this is to make sure that we're addressing your urgent questions and wild what-ifs, but it's also to demonstrate the amazing things you can do with physics. It's almost a superpower, a kind of "second sight" that lets us understand things that would otherwise be frustrating puzzles.

One of my favorite examples of this is a question that we received a little over a year ago. A reader was making couscous and, after measuring out the grain into a bowl atop a digital food scale, added some hot water as per the recipe. As the water soaked into the grain and the couscous expanded, he noticed the weight readout of the scale creeping slowly upward!

If you're a physics fan, you should know there's something wrong here—a bowl of cereal can't just magically gain mass, can it?

It wasn't, of course, and after thinking about the problem for a bit (and asking the inquirer to run a quick experiment or two), we had the mystery solved: It turned out that the asker was using a very modern-looking scale, with a sleek, razor-thin housing made of brushed metal—and while it was a beautiful design, it wasn't very well insulated. Heat was being conducted away from the water through the bowl, into the scale's weighing plate, and then down to the spring that supports the plate. Because spring scales determine an object's mass by measuring how far the spring is compressed, and because heat makes metal more flexible, adding the hot water caused the scale to slowly deviate from its initially accurate reading.

The culprit. It's gorgeous, but might mean making a trade-off between cabinet space and the ability to accurately weigh hot things.
Image Credit: Soehnle
As trivial as it might be, solving that one was a thrill to me; I felt like Professor X! Closing my eyes, not only could I see into this guy's kitchen 4500 miles away, but I could look into the heart of the malfunctioning gadget, and help him solve his problem.
So maybe that's why, when we got another "kitchen physics" question this week, I was inordinately excited and got to work immediately. Apologies to everyone with unanswered questions about the pyramids and dark matter...Scott from Chicago wants to know what's wrong with his ice trays, and physics is here to help.
"I have two ice cube trays, stacked one on top of another. When I make ice in my ice cube trays, the ice cubes always slide easily out of the top ice cube tray, and always stick and crack up when coming out of the bottom ice cube tray. Switching the trays with each other makes no difference. If the two trays are identical matches or not makes no difference. I have even replaced my refrigerator since I first noticed this phenomenon, and the results in the new fridge are exactly the same: the cubes in the top tray come out easily, and the cubes in the bottom tray come out with great difficulty and crack into pieces on their way out of the tray. Why??"
While "I can only make ice properly about half the time" sounds like a self-deprecating joke about his cooking abilities, I've also encountered the same phenomenon of stubborn, shattery ice before, but never thought too much about it until now. 
My first guess—let's call it a hypothesis—was that it had something to do with the way heat is transferred away from the water. If the tray on the bottom is in contact with the freezer floor, it's losing heat through conduction, while the one resting on top of that is relatively insulated—it's losing heat primarily by giving off infrared radiation from its surface and sides, as well as through contact between the water's surface and the cold air in the freezer.
Now, water is peculiar in that there are very few materials where the solid form will float on top of the liquid.  But like most other fluids, liquid water gets denser the colder it gets. Warm water, like warm air, rises—it's only once it makes the phase transition to solid that it gets floaty.
So, in your top tray, the warmest water rises to the top, gives off some of its heat as IR radiation, and then—having cooled—sinks back down again. This is pretty standard convection, and it means the water's going to freeze like a lake in the winter—from the top down. When water freezes in this fashion, you can think of it as a large, single crystal forming, as water molecules drifting by give up some thermal kinetic energy and click nicely into their place in the lattice, at an angle of ~106° relative to their neighbors.
As demonstrated in this stressfully fast-paced simulation
In your bottom tray, however, the main point of thermal loss is on the bottom of the tray, rather than at the top. From the water's perspective, this is all wrong; the ice crystals likely start forming on the bottom of the tray, molecules clicking into formation around tiny cracks and imperfections in the plastic. The ice is buoyant, and may float up to the top once a crystal is large enough that its buoyancy overcomes its adhesion to the tray. Perhaps, when this happens, another crystal starts forming at the bottom, and again drifts up.
The point is that, in the top tray, you've got something close to a nice big single crystal of ice. But in the bottom tray, I think you're seeing a bunch of crystals that started forming independently of one another, meaning their lattices don't fit together nicely; they're all at funny angles relative to one another, and too bulky to shift around and find that 106° sweet spot that would let them click together properly. The lines along the edges of these domains—called grain boundaries, in crystallography—serve as natural weak points in the structure of the larger solid. When you flex the top tray to pop your cubes out, the strength of the crystal—and its relatively weak adhesion to the tray, since it froze from the top down—make it a cinch to get it free. The bottom tray, on the other hand, has lots of little grain boundaries and might have frozen from the bottom-up (which would give it stronger adhesion to the tray), which could make it  easier to break the cube than to break it free of its slot.
Now all this theoretical thermodynamics is fun to think about, but it's not great physics in that I don't have math to back it up. What's worse, in cases like this the math is likely to be so bewilderingly complex—involving thermal transfer coefficients, viscosity and density calculations, convection rates, and very precise measurements of the properties of your trays and freezer—that it's not worth bothering at all, because it's far simpler to figure things out by experimentation. 
As we say in this line of work, experiment is king, so I asked Scott to try a few tests that might help us figure out what's going on. 
The first was to leave the ice cube trays stacked as normal, but insulate the bottom one from the freezer's floor with an empty egg carton, to tell us if heat conduction to the freezer floor is playing a major role. The second experiment was to leave one tray on top of the egg carton, and one tray on the floor of the freezer with nothing on top of it—to tell us about the relative importance of interactions between the two trays.
The results were a little surprising! Leaving the trays stacked but insulating them from the floor had no effect—the top cubes came out nicely, while the bottom ones were still a mess—but unstacking them, even when they were left on the freezer floor, caused both trays to form perfect, easy-to-remove cubes. That means heat conduction through the bottom of the tray isn't the answer, so my first hypothesis—bottom-up freezing—is out.
It's important not to get down on yourself when a hypothesis turns out to be incorrect; as Randall Munroe said, you don't use science to prove yourself right—you use science to become right, and that just means changing your hypothesis so that it fits with all the available data, or developing a new one! 
The crackliness of the ice makes me think there's still something to the idea of disjointed freezing, and the results of the experiments make it clear that the interaction between the trays is key—so a solid second-round guess might be that the top tray is keeping the bottom one warm, and this affects the freezing process in the bottom tray. The egg carton experiment tells us that thermal conduction to the freezer floor isn't the main issue—which means that the bottom tray is losing its heat through conduction with the cold air of the freezer, and by giving off infrared radiation.
The top tray suppresses both of these mechanisms in the bottom tray—the plastic of it will absorb and re-radiate some of the IR radiation from the surface of the water beneath it, effectively reflecting it back, and also prevent air from reaching the surface as easily to carry heat away. Effectively, the stacked trays act like one object, freezing from the outside in. In the top tray, that means the top down, but on the bottom, that means from the sides and bottom inward.
There's one more factor to consider—a concept called heat of crystallization. Paradoxical as it may seem, water actually gives off a substantial amount of heat in the transition to ice. Since the top tray is exposed to more cold air than the bottom one, it'll freeze faster and give off this heat—which could theoretically slow the top-down freezing of the bottom tray even more.
Freezing from the sides would create a tight bond between the ice crystals and the tray, along with the multitude of grain boundaries among crystals that started freezing at different points. As the crystals grow, meet, and solidify together, the water's need to expand might create further stress at those boundaries—which could all add up to an ice cube that shatters more easily than it comes out of its tray.
How else could we explain the results of these experiments? What other tests could we do, to further refine our hypotheses? Leave your ideas, your experiments, and your results in the comments! As it stands, we've solved this mystery well enough to ensure that you won't have to substitute crushed ice for cubes at your next cocktail party, but there's still lots to unravel. 
And yes, any cocktail snob worth their salt rim will insist that it matters enormously.
Image Credit: Behind the Bar
After all, as a famous physicist once said, "...sure, it may give some practical results, but that's not why we do it!"

—Stephen Skolnick


  1. If the top tray giving off heat of crystallization is the cause of this effect, then one way to test it would be to pre-freeze the top tray and then see if the bottom tray still cracks.

    Alternatively, one could put no water in the top tray at all, to see if it is simply the configuration of trays that causes the effect to occur.

  2. I think you are right that the lousy ice results from crystals forming indepently in different orientations. I think it is primarily due to water vapor in the region between the trays. In the top tray, the most energetic molecules leave the water and leave it colder at the surface. But in the lower tray, some of them leave, and some of them recondense in the region between the trays. That keeps the water from reaching the characteristically lower temperature at the surface. And freezing in a downward fashion. Rather, because the temperature is more uniform, seeds start in different regions, with different orientations. Also, I believe there is a property that slower freezing results in less uniform crystals, but I don’t know the reason. I know that is why commercial freezers can freeze you food way better than a regular kitchen freezer- because the slow freezing results in large crystals of ice that deform the tissue of the food and make it limp and soggy.