Thursday, August 23, 2018

Numbers in the News: Can I Really Have a Set of Artificial Gills?

According to a story in CNN, you may soon be able to slip into a set of artificial gills, and take to the water without having to haul along a pressurized tank of the atmosphere.

Sure. Why not? After all, fish do it all the time. Oddly enough, it never occurred to the evolutionary algorithms that brought us whales and dolphins to re-evolve time-tested gills, even though mammals managed to reacquire flippers in lieu of fins, and modify their bodies in gobs of other ways, in order to live in the water.

Designer Jun Kamei's vision for the gills we'll all need as the oceans rise.
So, if you wanted a set of gills that pulled oxygen from the water, how much oxygen would you need them to provide? The easiest way I can think of to estimate that is to begin by figuring out how much oxygen I'm using as I type this.

How Much Oxygen do We Need?

The typical breath of a resting human (like me) is about a half liter.

The air we breath is roughly 20% oxygen.

So, to plug in the numbers, we inhale

(0.5 liters of air)*(0.2 oxygen/air) = 0.1 liters of oxygen per breath

The amount of oxygen dissolved in water is usually estimated in grams, so I want to convert the volume above to mass.

For typical gases, one mole (that is, one Avogadro's number) of molecules takes up 22.4 liters of volume at room temperature and atmospheric pressure. And one mole of oxygen has a mass of 32 grams. So

(0.1 liters of oxygen per breath)*(1 mole/ 22.4 liters)*(32 grams/mole of oxygen)  = .14 grams of oxygen per breath

How Much Oxygen is in the Water?

Highly saturated water can have up to 10 milligrams (0.010 grams) or more of oxygen per liter. So there's very nearly enough oxygen in highly saturated water to supply a person relaxing at a keyboard with one breath of air, if you extract every molecule of oxygen from a little over 10 liters of water.

Can We get Enough Oxygen from Water To Swim with the Fishes?

Divers relying on conventional equipment use oxygen two to five times faster than I do sitting here. An artificial gill would need to process as much as twenty liters of water for every breath they take.

Divers swim at roughly a 10-20 meters a minute, so a gill system that had a 20x20 centimeter inlet could extract just enough oxygen from water to supply a diver provided:

1) the water is completely saturated with oxygen
2) the extraction system is perfectly efficient
3) you never exert yourself too much
4) you never stop moving for long (or you had a pump to push water through the system even when sitting still)

That sort of a device would be about the same size as a typical pressurized scuba tank, with the added benefit that you never have to surface. But it's worth noting that an elaborate gill system like this would probably add significant drag in the water, making it more difficult to get that 20 meter per minute speed without exerting yourself too much. If you include the pump so you can get that extra push, or so you can stop and smell the coral (so to speak), you need to factor in the size of the battery and motor. Once you've got a battery onboard, though, he whole "never having to surface" thing goes out the window.

And if you want to explore the ocean, you'll spend a lot of time in places where the oxygen content of water is a fraction of 10 milligrams per liter. There's kind of a catch-22 here: oxygen and other gases are more soluble in cold water, but cold water saps your body heat quicker, increasing your oxygen requirements—see the breathing techniques of famed "iceman" Wim Hof, for example. In the tropics, on the other hand, you'd have to be prepared for 5 milligrams per liter or so. That doubles the amount of water your gills need to process. If you have gills that are about as efficient as our lungs (5%), you need to scale things up by another factor of twenty.

To put it in perspective, my typical breath is about a half liter, and the water I would need to process to supply that breath could be between 10 liters (the very optimistic estimate) and 200 liters (the pessimistic estimate).

This makes artificial gills seems challenging, but just barely doable.

The fact that oceanic mammals have kept their lungs instead of evolving gills suggests it's not a great option if you burn a lot of energy keeping your body temperature stable. Fish, who take on the temperature of the water around them, can get by well with gills because they need far less oxygen than we warmblooded animals do.

TL:DR

Yes you can have artificial gills, in theory, if we build nearly perfect technology. They will be huge, may need  external power source to flow enough water through them, and they will likely be a lot less convenient than taking along your own air supply, as scuba divers and every marine mammal currently does.

But keep the dream alive, Jun Kamei! At least your artificial gills look ridiculously cool.

Buzz Skyline (AKA James Riordon)

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