Making Cooled Clothing

Summer gets really hot, and it's not going to get better anytime soon. At my place, it isn't actively dangerous yet, but it's still unpleasant.

A normal air conditioner uses a low boiling-point liquid: something like liquid propane can boil down to -42 C. Just like water, it's evaporation absorbs a lot of heat and the remaining liquid will become very cold.

Of course, releasing the gas would be wasteful and dangerous, so the vapor is collected and compressed: This increases the boiling point, allowing it to condense back into a liquid.

To complete the cycle, the condensed refrigerant is cooled to ambient in a radiator before being passed through a flow restriction to reduce it's pressure:

A fridge or AC (depending on the size of the box)

While excellent for cooling a building, there's no way to fit this inside a shirt: the compressor and hot-side radiator are bulky and require a source of electricity.

Thermometric cooling sounds great: replace the plumbing with a semiconductor junction.

Except they don't work particularly well. Most coolers produce several times more heat than they remove: this causes them to overheat unless they have a huge radiator.

... on top of their massive power draw and high cost...

They do find some use in ultra-small scale applications, but suck for everything else.

Evaporative cooling is the single most common hot day "hack": just a bit of water and some airflow for instant "AC".

... but it only works at low humidity. In most climates (including mine) it's entirely useless when you'd need it the most.

Ok, but what if I could leave the fridge at home and take the cold with me?

Melting one gram of ice will bottle up a whole 333 joules of heat while it stays at a constant temperature.

... but 0 C is just too cold: direct skin contact is painful, so the ice needs to be insulated from the body. On a hot day, it's >30 °C below ambient, so it must also be insulated from the environment.

What's needed is a (cheap, safe) material with a freezing point around ~20 C — which is low enough to stay cool, without being difficult to transport or use.

Pure glycerin looks promising:

It's melting point is 17.8 °C and heat-of-fusion is around 200 J/g.

However, commercial grades contain a few percent water, which pushes the freezing point below regular ice... and I don't know of any easy way to purify it. (which is why the factory doesn't bother)

Sodium sulfate is a very boring chemical:

It's non-corrosive, non-reactive, and less salty than regular salt.

... but it can form "decahydrate" crystals which are ~ 55% water by mass. Above 32 °C, the decahydrate decomposes into water and regular sodium sulfate. When cooled, this mixture reforms hydrated crystals.

Thermodynamically, releasing trapped water is the same as melting ice: melting one gram of decahydrate absorbs 252 J of heat.

32 °C is just slightly too warm for personal cooling but, just like ice, its "freezing point" can be reduced by adding regular salt: the eutectic mixture gets down to around 18 C.

Perfect.

As a bonus, this stuff can be frozen by leaving it in a basement, or any other deep hole in the ground: no electricity required.

18 C "ice" mixture:

The preparation is mostly just "mix and heat", but I do recommend adding the thickener last because it makes the salt dissolve slower:

1. Heat the water, sodium sulfate and salt until the solution is saturated (small crystals should form on its surface) Use a covered container to minimize evaporation.
2. Mix the borax and thickener as powders and slowly add them to the hot solution. (if you have an immersion blender, this is a great chance to use it)
3. Lightly boil for ~15 minutes.
4. Let cool to room temperature. It should solidify into a solid gel, which can easily be handled without spilling.

These measurements are slightly above the solubility limit in hot water, so there will be some residual salt: this doesn't cause problems.

The thickener can either be Carboxymethyl cellulose (CMC) or Xanthan gum: use whichever is easiest/cheapest to buy. Guar gum and alginates should work, but I have no idea what a good ratio is.

It's job is to prevent the crystals of decahydrate from settling or forming a hard mass. Otherwise, the different components could separate out with repeated thermal cycling.

Xanthan gum is rather clumpy: I find it helps to mix it with another dry powder before adding... but don't use sodium sulfate because that also likes to clump.

The borax helps with crystal nucleation and prevents mold growth. It's allowed as a food additive in the EU (E285) at 0.4 %, so accidental exposure shouldn't be a problem. Very large exposures can cause damage, but it doesn't accumulate.

Even so, I've occasionally had the mixture refuse to crystallize at 18 °C during its first cycle: if that happens, aggressive mixing or further cooling should fix it. If supercooling is a recurring problem, try increasing the borax concentration to around 5%.

I recommend adding a water soluble dye: this makes it easier to find leaks and tell apart different batches in case one has a problem.

Packaging:

I initially tried using plastic sandwich bags, but they always leaked. Double and triple bagging slows the inevitable, but still resulted in a mess.

A better option is heat-sealable polyethylene bags: these are able to hold liquids and can withstand quite a bit pressure. By being a little creative with the sealer, it's also possible to create partitioned bags like this:

These are great because they can be as big as you want without the goo falling to the bottom.

Sealing wet plastic is somewhat questionable, and I've had a few leaks. These can be fixed with hot-melt glue (one of the few things that will bond to polyethylene)

On their own, these bags work excellently as seat cushions, but aren't much good while standing.

To make them wearable, the heat sealed edges can be directly sewn to a strip fabric:

Ugly, but it works

I attached this strip to simple shoulder straps to hold the packs against my chest. For stronger cooling, additional straps can be hold them tightly.

I recommend wearing a t-shirt under the ice packs to stop them from getting nasty, and putting on some a light colored, loose-fitting clothes over everything to protect them from sunlight.

Test results & design notes:

To get an idea of how well the salt works, I built a simple "calorimeter" that melts a sample while I measured the amount of power needed:

For the first test, I prepared a sodium sulfate brine at 90 C and chilled it down to 25 C. Re-heating the salt to 32 C, it absorbed around 171 J/g

... 67% of the theoretical for sodium sulfate decahydrate.

The problem is that even a saturated solution doesn't have enough sodium sulfate: it's maximum solubility is 0.50 g/mL @ 32.2 C. Near boiling, it drops down to 0.41 g/mL.

41g Na2SO4 + 100g water = brine (hot)

On paper, this is enough sodium sulfate to form a 52% decahydrate slurry... but that's assuming the left over water is pure — in reality, the product is a mixture of decahydrate and saturated brine:

78g Na2SO4 + 100g water = decahydrate
28g Na2SO4 + 100g water = brine (25 C)

let:
  x       = decahydrate fraction
  (x - 1) = brine fraction

41 = 78 x + 28 (x - 1)
41 = 78 x + 28x - 28
41 - 28 = 78 x + 28x 
41 - 28 = (78 + 28)x
(41 - 28)/(78 - 28) = x
x = 0.48 [67% is within experimental error]

This is a inherent problem with any Na2SO4 based thermal storage: Even if you do make pure decahydrate, instead of melting, it would decompose into brine and anhydrous sodium sulfate. The dry salt has a tendency to settle out, which prevents it from reforming decahydrate.

A water-rich mixture prevents separation... at the cost of ~50% of the heat capacity. The leftover brine isn't necessary a bad thing: since there's always liquid water, the pack stays flexible and the gelling agent can stay dissolved.

As a bonus, such a mixture is easy to make: no filtering, continuous mixing or grinding needed.

Adding the 7.5% sodium chloride reduces the heat capacity to around 90 J/g:

Sample weight: 11 g
Sample temp: 12 C -> 22 C
Calorimeter temp: 24 C
Heater: 5 A @ 1.8 V for 2m 47s

Energy delivered: 1.5 kJ
Heat used to warm sample: 500 J (assuming specific heat is similar to water)
Excess cooling: 1 kJ = 90 J/g

This means the cold mixture is ~36% decahydrate and roughly 30% as effective as pure ice, The full formula with additives performs similarly.

Solubility with multiple salts is complicated, so I don't have any theoretical values. However, my result is similar to the published heat-of-fusion for low temperature decahydrate mixtures: most papers claim somewhere between 60-140 [J/g].

Replacing the sodium chloride with a salt that can also form hydrates (i.e. sodium carbonate) could improve this, but all the options I could find are at (least slightly) caustic or/and expensive.

Also, adding another salt reintroduces the separation problem:

Decahydrate can sink to the bottom, forming a layer with low chloride concentration that won't melt. Fortunately, since the mixture never fully freezes, preventing this is easy enough with a thickener.

In a less scientific "hot day" test, two 600g, 1cm thick packs stayed cold for around an hour when worn as described. Using data from the lab tests, they have a combined 108 kJ of cooling capacity and remove 30 W of heat.

Long excursions will require spares, but considering that the material costs pennies, this isn't a big problem.

Related:

• DOI: 10.1109/ITHERM55368.2023.10177562: A reference with a very similar mixture (paywalled, but easily pirate-able)
• https://www.youtube.com/watch?v=qv0IJM3BV9Y: The vapor compression route
• https://www.youtube.com/watch?v=Nqxjfp4Gi0k: More eutectic NaSO4/NaCl