So, separate from my opinion on this series as a whole, the discussion last chapter about freezing water by putting it under vacuum sent me down such a deep physics rabbit hole. I know that this is possible (you can look up youtube videos of this demonstration). However, what got me so deep into this (even breaking out some of my old textbooks from grad school), was trying to figure out if this is something they could have done with the level of technology shown in the story.

tl;dr - It is plausible they could do this at a really small scale as shown in the manga, but they definitely would not be able to scale up very much at all.

The main problem with scaling up ice production in this way is that they don’t have good vacuum pumps. The scientist has no idea what electricity is, so it’s clear that there isn’t an electric vacuum pump that they can use. Well, no problem you might say, piston-driven vacuum pumps have been around since the 1650’s, and that’s way before electricity. Well, the issue is pumping speed.

The way that you freeze water under a vacuum is that you have to rapidly reduce the pressure of the air above the water. This reduced pressure lowers the boiling temperature (this is why some recipes have high-altitude instructions). If you reduce the pressure quickly enough, the water boils quite violently, with the water molecules wanting to become water vapor. It takes some energy to change from a liquid to a vapor, so water molecules that boil off will steal that energy from other, nearby water molecules. This reduces the energy that is left in the water left behind, and therefore the temperature. If you can cause enough rapid boiling, the water that doesn’t turn into vapor will lose so much energy that it can freeze solid.

However, this all changes if you have a slow vacuum pump. Basically, you might be able to reduce the pressure to cause boiling, but the water vapor that boils off is now occupying the space in the chamber, raising the pressure and the boiling point. So, the water will boil for a bit, wait for the pressure to drop again, boil for a bit, ad infinitum. It will result in the water just riding the liquid/gas phase change line down to the triple point until there isn’t any water left to freeze because it all boiled away.

Without the benefit of electric pumps (or rubber seals instead of leather), it would have been extremely difficult to scale up this process. The more water you try to freeze, the more water vapor is generated when it boils. So, your vacuum pumps need to be even better and even faster. I work with freeze-dryers professionally, and this is something we can run into and needs to be assessed even with extremely good vacuum pumps. We call the case of the vacuum being compromised due to excessive water vapor as “Choke Flow” (some light reading on the topic).