Surviving under water in an air bubble
physics.stackexchange.com
physics.stackexchange.com
The steps to solve this problem are pretty simple:
1) Find the diffusion coefficient of oxygen in seawater. This can be found from data on ocean waters near the region the guy was trapped (Nigeria), modified to account for the cooler water under the surface. This link (http://www.unisense.com/files/PDF/Diverse/Seawater%20&%20Gas...) has these coefficients for various combinations of salinity and temperature. All of that data is for 1 bar so you'd have to modify those values for the pressure at ~30 m.
2) Set up an oxygen mass balance about a bubble of radius R. We'll assume the bubble is entirely spherical. If you consider the fact that the bubble is centered at a room corner, its radius will need to be sqrt(8) times bigger than the calculated value (since diffusion can only occur at the surface of the bubble that has contact with sea water).
3) The rate of change of O2 concentration (d_C_O2/dt) will be zero (in order for one to persist indefinitely in the bubble), and we know its value must be 15-19 vol % according to this site (http://www.newton.dep.anl.gov/askasci/zoo00/zoo00755.htm).
4) Set up a O2 -> CO2 "reaction" (the lungs) just to get the molar ratios of each. This is the tricky part of the problem because this depends quite a bit on human physiology, and probably varies somewhat by the individual.
5) Plug these values into the radial form of Fick's law of diffusion, and solve the resulting equation for R.
[If I get more time, I'll do this rigorously.]
So as long as the surface area of the trapped bubble-seawater interface was at least that size, perhaps you could survive indefinitely, down to the limit of air-breathing depths.
In smaller bubbles, perhaps you could keep yourself alive by splashing. Like an aquarium bubbler in reverse.
https://en.wikipedia.org/wiki/Pulmonary_gas_pressures
> Following is a list of average partial pressures for a human at rest:
> Lung Capillaries 20-40 pO2 (mmHg)
> Alveolar air 35 pCO2 (Torr)
http://publishing.cdlib.org/ucpressebooks/view?docId=kt167nb... In studies of the distribution of dissolved gases in the sea it is generally assumed that, whatever the location of a water particle, at some time it has been at the surface and in equilibrium with the air. In their studies of the dissolved nitrogen content Rakestraw and Emmel (1938a) have found that the water is virtually saturated (referred to a normal atmosphere), regardless of depth; therefore this assumption appears valid and also indicates that biological activity involving either fixation or production of nitrogen cannot be sufficient to affect significantly the concentration of this gas in the water. As the waters of the oceans appear to have been saturated with oxygen and carbon dioxide at some stage in their history when they were at the surface, the differences between the saturation values (computed from the temperatures and salinities) and the observed contents are measures of the changes which have been effected by biological agencies. The factors influencing the distribution of carbon dioxide are discussed in the following sections, and the distribution of dissolved oxygen will be considered in many places in the ensuing chapters.
For those playing at home, the answer to #4 depends mostly on diet, and for a typical Westerner it will most likely be 0.8. That is, slightly more O2 is used than CO2 is produced, representing a mixed metabolism of carbohydrates and fats.
That's standard air pressure though. As you dive and pressure increases, the metabolized oxygen stays roughly constant (metabolic rate is independent of pressure) but the "amount" of oxygen breathed in shoots up because the inspired volume does not change either (and there's more oxygen in the same volume under pressure). Thus the "extraction efficiency" goes down (you proportionally breathe out more and more oxygen which wasn't metabolized).
This is why closed-circuits rebreathers are so much more efficient than open-circuit cylinders, and the o2 cylinder is so much smaller (excluding safety cylinders): at atmospheric pressure an open circuit may "waste" 75% of the oxygen, at depth it may be >90%. A rebreather or a closed environment (under pressure) will allow much more efficient oxygen use.
Link: Underwater Spider Spins Itself an Aqualung: http://news.sciencemag.org/sciencenow/2011/06/spiders.html
Previous discussion (about the spider): https://news.ycombinator.com/item?id=2643142 (93 points, 734 days ago, 9 comments)
Don't ask a chemistry question on a physics board ;-)
30 meters is just agonizingly close to the surface though, well within what most adults could do horizontally (particularly if their life depended on it.) Being that close to the surface, but still so far away, must be absolutely awful.
Of course if attempting it meant certain but excruciating death, then taking a shot at it would not be the way to go.
If he had swum up right away he would not need decompression.
I imagine in the dark he would have been too scared of not being able to find the way out in the cluttered sunken vessel.
If rescue (and access to a pressure chamber) is available right away, I'd make that ascent immediately even after being down there for a longer time. It beats drowning or CO2 poisoning.
Dive tables illustrate pretty well how the relationship between depth and time works: http://www.naui.org/tables.aspx
I'd have thought you'd feel your lungs expanding and you'd have the reflex to let the air go away. Although on the other hand it's probably not a situation common enough for us to have evolved an inate reaction to it.
No innate reaction - over-inflation would require a positive pressure applied to the lungs - normally as we breathe it's at equilibrium. Your lungs aren't elastic at all - once they are at capacity, over-pressure will rupture them right quick, and you own't feel it coming (but you'll sure feel it happening)
http://en.wikipedia.org/wiki/Submarine_escape_training_facil...
So it must be fairly survivable.... Maybe it's staying for a long time at that pressure that causes the problem?
If you want to have a go, you can go to Nemo33 in Belgium still.
Cf : http://www.worldnavalships.com/forums/showthread.php?t=3787 http://www.subescapetraining.org/History1.html
http://www.adventuresunderthesea.com/scuba-class-information...
The deeper you go, the less time you can stay there before you have to control your ascent.
Even a mild case of the bends can be excruciating, not something you can tough out: http://en.wikipedia.org/wiki/Decompression_sickness
The longer you breathe at pressure, the more time there is for gas (nitrogen, mainly) to saturate your system (until you are at equilibrium, anyway).
Release the pressure, and it's like opening a can of soda... all that dissolved gas can't stay dissolved any longer.
It takes time to get out of your system as you reduce pressure, so a gradual decompression is the only safe way out once you are saturated.
In a typical submarine, air pressure is maintained at standard atmosphere, relying on structural integrity to keep all that pressure from crushing the ship. That means they can surface any time without risk.
Another neat thing when diving is that if you are down at 30 meters, you can take a breath from your regulator, spit it out, open your airway gently (say "AAAAH" quietly to yourslef basically) and then ascend, you feel like you have an endless supply of air, because that breath you took is expanding on your way up. (That's part of recreational diving.. you can ascend from 30 meters on a breath of air and not get stressed out about it)
It's not necessary to get into the chamber instantly - symptoms don't start for 1 to 48 hours.
The problems arise when you breathe in high pressure air down deep and bring that air up with you.
Here's a link that provides a number of references: http://www.thediveforum.com/dive-medicine/3706-long-term-phy...
It's a matter of time and volume - it takes time for nitrogen to dissolve and they are not down there long. And they only have a single lungful of air, so there is not a lot of volume to dissolve.
But, if they do repeated dives, each one will dissolve more and more nitrogen until they do have problems.
The pressure differential, in this case, was three times that between normal pressure and vacuum.
You'll go from feeling fine to acute pain to very dangerous damage pretty much momentarily.
I can assure you, you can exhale upon ascent when inverted. (source: me, who used to log plenty of hours below 150fsw breathing mixed gasses).
... I did wonder how painful a fast ascent from the bottom of the ocean would be once the bends kicked in, but had enough sense not to raise this question with about a quarter of the crew in earshot.
For an approximate simulation, imagine what removing 90% of the air from your lungs might feel like.
I don't have to imagine what removing air from my lungs feels like: that is part of breathing! Anyway, this guy seems to do OK compressing his lungs even more:
http://competition.the-french-job.com/spread-the-world-recor...
Physiological freaks aside, go too deep, and you're dead. Especially when you go from 1 bar to, say, 15 instantly, which is a situation that free divers do not expose themselves to.
You know that pain you get in your sinuses and ears and other air-pockets in your body when you swim to the bottom of the deep-end of the pool? That's from a pressure difference of like .3 bar. Now imagine something 10 times that.
If you are diving you can take a breath of air from your regulator at 30 meters and then, keeping your airway open, ascend to the surface on a single breath. Because you are ascending, the air in your lungs expands as you go up, and you get to the surface with a full breath of air, even though you've been blowing bubbles all the way up.
At 30 meters you limit your dive to 20 minutes... beyond that you risk decompression sickness. At 10 meters the limit is around 3 hours.
In both cases, if you were down for a couple of days, you'd need decompression. The deeper you go, of course, the more dangerous it is as there is more dissolved gas.
Also, he may have been able to stay out of it at least at first, till it rose.
This question assumes the interface between the water and the air is at rest. Think of a bubbler in an aquarium. Would splashing around periodically increase or decrease your survivability? That is, would the increased rate of gas exchange at the air/water interface be greater or less than the increased rate of gas exchange at the air/blood interface?
Double super extra bonus points if you can plot this based on credible data.
Edit: Or alternatively - what if he just breathed out through a tube placed under the water such that his bubbles were recaptured?
Edit 2: I wonder if dehydration due to the salt exposure also played a role in making his situation more survivable. Would dehydration have reduced total air/blood gas exchange in a meaningful way?