No animal with a high metabolic rate can extract enough oxygen from water to survive. That is the fundamental problem with the artificial gill. Let us suppose a system could be disigned that would extract a normal human’s oxygen needs from seawater. Ignore for a moment the issues of volume changes imposed by pressure at depth. Ignore also that oxygen must be delivered mixed with some other gas because it is toxic in high concentrations. Consider a person floating at the surface with the needed oxygen supplied by this machine and the extra gas somehow recycled so it need not be regenerated.
The resting metabolic rate (energy output) of this relaxed person is about 8 megajoules or 2000 kilocalories per day. It takes about 1 liter of oxygen to aerobically produce 20 Kilojoules of energy, or 400 liters of oxygen per day to stay alive. No problem to obtain this from air since air is about 20% oxygen - this translates to a pretty trivial 2000 liters of air per day. Converting liters to moles so we can easily work in both dissolved and gas phase we get that 400 liters of oxygen is about 18 moles of the gas.
The problem lies in the amount of oxygen that will ‘fit’ into a liter of water. Gasses dissolve in water in different amounts depending on the both the gas and the temperature of the water. Carbon dioxide for example is happy to dissolve in water and 390 micromols will dissolve in a liter at room temperature per kilopascal of pressure. Carbon dioxide is about 30 times more soluble than oxygen so just 14 micromols will dissolve in a liter of water under the same conditions. So far I will admit that this excercise has been no fun, but you need to hang on for a few more steps…it really is better than believing in a biomimetic gill to support a diver.
Assume the oxygen in the water is in equilibrium with the air, that is, there is as much oxygen in the water as will fit given the temperature and oxygen content of air. The pressure of air at the surface of the water is about 100 kPA and about 20% of the pressure is due to oxygen. That means 20 kPa of pressure is due to oxygen and for every kilopascal, about 14 micromols of oxygen will dissolve. OK, that is a grand total of nearly 300 micromols of oxygen. Recall that to stay alive at rest a human uses 18 moles of oxygen - if it were possilbe to completely remove the dissovled oxygen this would be the amount found in 60,000 liters of water.
Sixty thousand liters of water per day, 2500 liters per hour, 41 liters per minute, or 0.7 liters per second. No matter how you look at it this is a large amount of water. Quite apart from the problematic assumption of complete extraction, moving this much water will engender a huge reaction force. The thrust generated by the gill system just by moving the water will be quite substantial. This is simply impractical. It can’t work for humans.
How then does it work for fish? Most fish have very low metabolic rates, they conform to the environmental temperature. Tunas are among the few fish that do have some regional body warmth, and they have most elaborate gills and easily suffocate if prevented from ram ventilating at high speed .
Are artificial gills a total boondoggle? Not at all, there are numerous sensible applications for a device that can transfer gas from one fluid to another with high efficiency. But the motivation for building these devices simply can’t be as a replacement for SCUBA.