
Surviving under water in an air bubble - Xcelerate
http://physics.stackexchange.com/questions/67970/surviving-under-water-in-air-bubble
======
Xcelerate
D'oh! Just realized I was a chemical engineer an hour after I posted this :)

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...](http://www.unisense.com/files/PDF/Diverse/Seawater%20&%20Gases%20table.pdf))
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](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.]

~~~
tiatia
I am not sure how much Fick's law has any influence. Most "mixing" inside and
outside the bubble will be done by convection rather than by diffusion.
Diffusion should have little to no influence on the whole problem. Assuming
that you want to take into account mass transport through the phases
(Air<->Water), you would have to apply Henry's Law.

~~~
Xcelerate
Whoops. You're right. That's what I get for solving a mass transport problem
at 5:00 AM.

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masklinn
> The atmosphere is about 20 percent oxygen. People breathe this in, and
> breathe 15 percent oxygen out

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.

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gus_massa
There is a spider that does something like this. It picks a bubble and uses it
to survive underwater. The bubble exchanges some oxygen from the water, so it
last more time (but not indefinitely).

Link: Underwater Spider Spins Itself an Aqualung:
[http://news.sciencemag.org/sciencenow/2011/06/spiders.html](http://news.sciencemag.org/sciencenow/2011/06/spiders.html)

Previous discussion (about the spider):
[https://news.ycombinator.com/item?id=2643142](https://news.ycombinator.com/item?id=2643142)
(93 points, 734 days ago, 9 comments)

~~~
joshschreuder
There's a Studio Ghibli short that they show at the museum in Japan which
features a spider like this, see here:
[https://en.wikipedia.org/wiki/Mizugumo_Monmon](https://en.wikipedia.org/wiki/Mizugumo_Monmon)

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usaphp
A person can survive in an air bubble but after 13 hours he will start having
a trench foot condition:
[http://en.wikipedia.org/wiki/Trench_foot](http://en.wikipedia.org/wiki/Trench_foot)

~~~
mistercow
According to the article you linked, trench foot occurs in temperatures up to
60°F. The water temperature off the cost of Nigeria this time of year is
closer to 80°F, so I'm guessing trench foot wouldn't be a problem.

~~~
jessaustin
The temperature at a depth of 30m is certainly not 80°F.

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Uchikoma
From the comment that explains a lot, but misses the point completely
(exchange of oxygen between the bubble and the sea to replenish oxygen in the
bubble):

Don't ask a chemistry question on a physics board ;-)

~~~
adamtulinius
And in a comment to that comment: "Using imperial measures in a discussion on
Physics?" hehe :-)

~~~
Uchikoma
:-)

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jlgreco
Does anyone know how survivable rapidly surfacing from 30 meters would be?
Wolfram Alpha has the pressure down there at almost 400 kPa (compared to 100
kPa) so my suspicion is "not at all", but I'm not really familiar with the
tolerances and life expectancies with the bends.

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.

~~~
arethuza
The Royal Navy has a 30m deep "pool" (more of a water filled tower) that they
use for submarine escape training:

[http://en.wikipedia.org/wiki/Submarine_escape_training_facil...](http://en.wikipedia.org/wiki/Submarine_escape_training_facility)

So it must be fairly survivable.... Maybe it's staying for a long time at that
pressure that causes the problem?

~~~
gaius
They no longer use it - too many people were dying in the training, and modern
submarines go much deeper anyway.

If you want to have a go, you can go to Nemo33 in Belgium still.

~~~
Timshel
The too many seems to be 2 death in 60 years with up to 4500 trainee a year
during the 60s/70s.

Cf :
[http://www.worldnavalships.com/forums/showthread.php?t=3787](http://www.worldnavalships.com/forums/showthread.php?t=3787)
[http://www.subescapetraining.org/History1.html](http://www.subescapetraining.org/History1.html)

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chiph
I'm curious how he didn't succumb to hypothermia. Circulating ocean water
would conduct heat away from his body pretty quickly. Granted, he's near the
equator, not the arctic, but still...

~~~
ars
I don't think the water was circulating all the much - it was inside the
vessel. It was rising, but not circulating.

Also, he may have been able to stay out of it at least at first, till it rose.

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benjamincburns
Bonus points:

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?

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inthewind
Related:

[http://www.isracast.com/article.aspx?id=63](http://www.isracast.com/article.aspx?id=63)

~~~
fletchowns
Warning: Audio will start playing on this site. Scared the shit out of me!

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OoTheNigerian
Glad to see Nigeria is on Hacker news for positive news :)

~~~
dia80
Not sure if ship sinking and 10 crew dying and 1 one barely surviving is good
news... :(

