Home made cold slab ice cream

Executive summary: With an 11 pound slab of aluminum chilled in my freezer overnight, I can make one small 30g serving of ice cream.  Other promising avenues include brine instead of aluminum, and dry ice + alcohol (which gets waaaay colder than your freezer).

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I was daydreaming about 3D ice printers, and it occurred to me that I might be able to make Cold Stone style ice cream if I put a big chunk of metal in the freezer.

My first thought was to use steel, but aluminum turns out to have almost twice the specific heat of steel and about 4 times the thermal conductivity.  So for a given weight it can absorb more heat, and do it faster.

I had an 11 pound hunk of 4"x4"x12" aluminum left over from the rotary mill, so I cleaned it up and put it in the freezer for a few hours.

The tape was to help me more accurately measure the temperature with an infrared temperature gun, but I think a contact thermometer would be better.

I used a 1:1:1 mixture of cream, sweetened condensed milk and fresh strawberries.  I'm not sure how much the cream adds to the experience, so I think it'd be worth trying just sweetened condensed milk + strawberries.

But even after lots of waiting and pushing it around on the plate, it never quite froze (but read on!).

Doing the math: should we expect it to work?

Later it occurred to me to work out the heat of fusion of the ice cream and see how that compares to the heat required to take the plate from my freezer's ~0F to 32F.  Wolfram Alpha tells me that "specific heat of aluminum * 11 pounds * 15 K difference" takes 67,700J, whereas 100g of water (~5.5 moles) needs to lose about 30kJ to freeze.  So that says my big chunk of aluminum should be able to absorb 2x as much energy as I need to freeze a small serving of ice cream, but that's assuming it starts at 0F and doesn't count any other losses (like ingredients that need to be cooled down to 32F, and absorbing ambient heat from my kitchen).

So I'll give it another go with the plate freezing overnight, but I suspect I'd need to start out colder than 0F to really make it work.  

And that makes me think this guy's clever solution of dry ice (-109F) cooling a griddle through an interface of liquid alcohol is probably a better solution.

Take 2:

On second thought, I think my IR thermometer may have been telling me something useful.  On my first attempt, it claimed the plate was only down to about 20F.  Leaving it in the freezer overnight and turning down the thermostat a bit, the plate got down to under 10F, and I made my first successful batch:

One spoonful of cream, one spoonful of sweetened condensed milk, and one spoonful of strawberries came out to about 30g.

Still marginal:

I tried a second serving right after the first, but it wouldn't freeze.  So 30g seems to be about the limit for this plate at this temperature.  I'm not sure how much of that is due to the ingredients warming up, the plate warming up as a whole, or the first batch putting too much heat into the surface of the plate (and it not being able to dissipate quickly enough into the core).

I pulled out the Flir One to see if I could sense one face of the plate being warmer than the others.  Aluminum tends to reflect thermal IR, and in the video below you can see it acting like a mirror:

Mostly it's reflecting heat from the rest of the room and the cold towel it's sitting on.  You can see some fingerprints after I touched it, and I'm not sure if that's something to do with condensation or with giving it more heat to emit, such that it's noticeable over the reflection.

To combat emissivity issues, I put a strip of tape around the four sides, since the tape won't reflect LWIR like the aluminum does.  Unfortunately, I only did this test after rinsing off the plate in the sink, which seems to have warmed it up (or at least the outer region of the plate) quite a lot and overwhelmed any evidence left from the ice cream session.

But based on earlier photos like this one, I'd guess that the heat gain is more uniform than localized.  (And I think this photo shows less reflection than the video because there was icy condensation on the plate at that time).  Maybe somebody with a better background in thermals could comment with a back-of-envelope calculation on how fast we'd expect the heat to dissipate into the core of the plate.

Saltwater instead of aluminum?

Also note Damien's suggestion below about using brine as a cold source.  Looks like a salt water solution above 33% freezes to -6F, so it gets cold enough for us.  And looks like its heat capacity is about 3300 J/(kg * K) compared to Aluminum's 910 J/(kg * K).  So it holds over 3x as much cold by weight (and since it's lighter, it has a smaller advantage by volume as Damien cites).

Weirdly though, for thermal conductivity, aluminum is reported as 205 W/(m*K) and brine says it's around 0.4 -- that's a 500x difference!  I expected completely the opposite, since liquids have natural convection and good thermal interfaces to neighboring materials.  So maybe the way they test thermal conductivity somehow controls for those factors, because I'd certainly expect putting my hand in freezing brine to be at least as chilling as putting it on a slab of aluminum.

Of course salt water is also way cheaper than aluminum.  So a thin hollow vessel, say, a box made out of thin stainless steel plate, ought to be cheaper and more effective by weight, assuming my intuition is right about brine's conductivity.  The most annoying part might be keeping the box sealed and avoiding bubbles, since we want to freeze our cream on the top surface of the box, and air bubbles won't conduct heat very well at all.

While we're on the topic, normal water ice also has better heat capacity than aluminum by weight, and like brine is listed as having less than 1% of aluminum's conductivity.  But it's easier for me to believe that solid ice could be a much worse heat conductor than solid aluminum.  So I wouldn't expect a block of ice at 0F to work as well as an aluminum slab or liquid brine.

One more thought on brine: rather than chilling it in a freezer overnight, you could also apply salt to ice traditional ice cream makers do.

Anyone got an answer to the mystery of low brine conductivity?