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I’m referring to an entomological plastron which is a structure that traps a bubble of air next to the insect's body but permits contact between the air and the water. As the insect consumes oxygen and releases carbon dioxide the carbon dioxide diffuses out of the bubble into the water and oxygen diffuses in. The rigid structure of the plastron makes the air bubble incompressible and therefore permanent. In this way, the plastron acts as a sort of artificial gill. As long as the surface area of the bubble is of sufficient size to allow diffusion to keep up with the needs of the animal it will never have to surface.

Now, my question is how large (in surface area) does a plastron or artificial gill need to be to accommodate the oxygen needs of a human indefinitely? Since I imagine it will be large let’s assume it isn’t mobile but rather acts as a stationary structure that the human can swim in and out of (with an airlock of course). Essentially, imagine an undersea base where the walls are rigid and gas permeable.

One other minor issue with this system is that all of the nitrogen in the plastron will gradually be replaced with oxygen and this, combined with the increased pressure of being underwater, will lead to a highly toxic oxygenated atmosphere. For my purposes I don't care because I’m actually designing an alien species of spider-like creatures who weave rigid gas-permeable cocoons deep underwater inspired by the Diving Bell Spider. My species will have evolved to tolerate these high oxygen environments but will have similar metabolic needs to humans and I feel it makes the question much easier to answer and potentially useful to others if we leave it as humans.

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  • $\begingroup$ Just an FYI, you don't need an airlock. You don't even need a door. Just put the entrance to the plastron on the bottom, and the pressure inside will keep the water out, just like a bowl or a glass will if you put it in the sink upside-down. $\endgroup$
    – Morris The Cat
    Aug 28, 2018 at 15:47
  • $\begingroup$ @MorrisTheCat I'm not sure on this but you might be right. My issue with the "diving bell" design was that the airspace would no longer be incompressible and so as nitrogen was lost the bell would fill from the bottom, but once all the nitrogen is gone I think perhaps you could open up the bottom and it would be stable. $\endgroup$
    – Mike Nichols
    Aug 28, 2018 at 15:54
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    $\begingroup$ Hang on, I don’t understand why the nitrogen is being replaced with oxygen. Surely nitrogen will also be diffusing in from the dissolved nitrogen in the water to replace any that’s being lost in some way? Or do oxygen and nitrogen diffuse differently through your membrane? $\endgroup$
    – Dubukay
    Aug 28, 2018 at 16:00
  • $\begingroup$ @Mike Nichols Air is never incompressible. The Diving Bell works because the air inside the bell is ALWAYS compressed to the same pressure as the water outside because physics. The only reason the Diving Bell wouldn't work would be if the water pressure could force the air mix inside to diffuse through the plastron until it's all gone. $\endgroup$
    – Morris The Cat
    Aug 28, 2018 at 16:04
  • $\begingroup$ @Dubukay As I understand it nitrogen has a relatively low partial pressure in water and so as nitrogen diffuses out it tends to be replaced by oxygen to maintain the same volume. Source aquatic respiration $\endgroup$
    – Mike Nichols
    Aug 28, 2018 at 16:17

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Lets try a quick back of the envelope calculation. A human lung is about 75 square meter,but water contains a lot less oxygen than air (~1/20th) so that's about 1500 sq meters you need to get the same amount of oxygen, Area of a sphere A=4πr^2. That gives us a sphere of roughly 22 meters across big but not insane. keep in mind this assumes oxygen rich water in brackish, deep, or poorly oxygenated water it will need to be larger, much larger in many cases. Sea water for instance contains about 20% less oxygen than fresh water (thats a sphere 49 meters across for seawater).

of course it will have the same problem as diving bell spiders, the loss of nitrogen will cause it to deflate, or if rigid allow water to enter as the internal pressure drops. that is why diving spider keep having to bring new air down, not for oxygen but becasue the bubbles slowly lose pressure due to nitrogen loss. This was actually the problem a real oxygenator built by Fuji Systems (it was 'only' roughly the size of a refrigerator but also was not a sphere)

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  • $\begingroup$ Why would rigidity necessarily allow water to enter? What if the plastron is spherical and an airlock is used to enter and exit? $\endgroup$
    – Mike Nichols
    Aug 28, 2018 at 16:00
  • $\begingroup$ @Mike Nichols remember though that 'water entering' in this case means that the water will rise from the level of the bottom of the bell to the new point of equilibrium. That doesn't mean it's going to flood entirely. $\endgroup$
    – Morris The Cat
    Aug 28, 2018 at 16:31
  • $\begingroup$ because as the pressure drops the pressure of the water increases until it exceeds the surface tension. $\endgroup$
    – John
    Aug 28, 2018 at 21:39
  • $\begingroup$ Do you have a source for the claim that water has about 20% of the oxygen of air? In all the other calculations I’ve done with these kind of things it’s been much, much less. See Renan’s answer below. $\endgroup$
    – Dubukay
    Aug 28, 2018 at 23:44
  • $\begingroup$ Glad you asked because that is actually wrong, i have it backwards, or rather I forgot to convert, I will fix that. $\endgroup$
    – John
    Aug 29, 2018 at 3:05
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I will quote a quote from another answer of mine on waterbreathing creatures and lung design:

In fresh water, the dissolved oxygen content is approximately 8 cm3/L compared to that of air which is 210 cm3/L.

The source I got this from elaborates it further:

Water is 777 times more dense than air and is 100 times more viscous. Oxygen has a diffusion rate in air 10,000 times greater than in water. The use of sac-like lungs to remove oxygen from water would not be efficient enough to sustain life.

Insects manage it because they are cold blooded expletives in the literal sense, and because insects are generally tiny[citation needed] (square-cube law strikes again!). Aquatic insects also don't go far from the surface, which is the most oxygen rich part of aquatic ecossystems.

Humans just can't get enough oxygen from water, period. Every other year someone starts a company that is developing a device that will extract oxygen from seawater and allow you to dive for an indefinite amount of time. They usually look like this:

Behold the Triton

And every other year, once they have got enough cash from gullible idiots angel investors and crowdfunding, they disappear in the blink of an eye.

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    $\begingroup$ +1 for "cold-blooded expletives". $\endgroup$
    – Morris The Cat
    Aug 28, 2018 at 18:24
  • $\begingroup$ I'm aware that a human-portable artificial gill that relies purely on diffusion to exchange carbon dioxide for oxygen with the surrounding water is not practical. The surface area will likely have to be much larger. That's why I'm not asking for a portable device but rather an underwater structure with a large enough surface area to keep up with the high metabolic rate of a human. My question is just how large this structure will need to be. $\endgroup$
    – Mike Nichols
    Aug 28, 2018 at 18:26
  • $\begingroup$ @MikeNichols it would have to be so large that the square-cube law would render it unfeasible, that's my point. $\endgroup$
    – The Square-Cube Law
    Aug 28, 2018 at 18:34
  • $\begingroup$ @Renan I'm afraid I still don't understand. What about the square-cube law renders a large air bubble underwater unfeasible? As I increase the surface area of the plastron the effectiveness of the artificial gill continues to increase without end. Moreover, the plastron doesn't have to be a sphere, it could be highly folded sheet that a square-cube relationship wouldn't even necessarily apply to. $\endgroup$
    – Mike Nichols
    Aug 28, 2018 at 18:45
  • $\begingroup$ @MikeNichols from the quote I highlighted - your plastron would have to be 10,000 as volumous as human lungs. That's in an impossible best case scenario, you'd still have to ramjet inject oxygenated water into the system. Imagine a human that is 70kg regular human and a couple tons of lung. If you still think that's feasible then I am out of arguments. $\endgroup$
    – The Square-Cube Law
    Aug 28, 2018 at 19:16
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A pair of functional lungs has a quite large surface area

Estimates of the total surface area of lungs vary from 50 to 75 square metres (540 to 810 sq ft) (ref).

To ensure the same functionality in terms of gas exchange, you should ensure roughly the same surface.

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    $\begingroup$ Moreover, the gas exchange in the lungs is greatly helped by the haemoglobin in the blood... $\endgroup$
    – AlexP
    Aug 28, 2018 at 16:00

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