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Oxygen Flow Through a Concentration Gradient

  1. Mar 11, 2013 #1
    Hi guys

    First things first, I'll lay out the problem. I have a box of volume V containing a constant sink of oxygen (e.g. a candle or an animal); this box is sealed except for a smallish aperture of area, A and depth, L (the L meaning the walls of the box have finite thickness).

    After a significant time has passed from the introduction of the oxygen sink I would expect a dynamic equilibrium to have formed giving a constant, but lower, concentration of oxygen inside the box with oxygen 'flowing' through the hole to sustain this equilibrium - with the outside atmosphere being equivalent to a well mixed infinite reservoir of oxygen at a constant concentration.

    What I am looking for is to be able to find the rate of flow of oxygen through the hole if all of the necessary parameters are known. I have essentially come up with a debauched version of Fick's first law of diffusion to fulfil this and wanted opinions on whether I'm barking up the right tree or if there are any better methods.

    I started with Fick's law, which is: [itex]J=-D\frac{∂\phi}{∂x}[/itex], where J is diffusive flux, D is the diffusion constant, [itex]\phi[/itex] is the concentration and x is position.

    I then reasoned that for small values of x and small differences in concentration that:
    [itex]\frac{∂\phi}{∂x}=\frac{1000(C_{outside}-C_{inside})}{24.5L}[/itex]
    Where C-outside and C-inside are the fractional components of Oxygen in the air outside and inside, L is the length of the hole and 1000/24.5 is the approximate number of moles/m3 of gas at room temp and pressure, thus giving a gradient in moles/m4, which are odd units that cancel down to being just moles/s when multiplied by the diffusion constant (m2/s) and the area of the hole.

    I'm trying to get a practical estimation of what this flow will be, so any help, advice or corrections would be appreciated immensely.

    Thanks,
    Chan
     
  2. jcsd
  3. Mar 11, 2013 #2

    mfb

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    Staff: Mentor

    The approach looks fine, so you get numbers if you add the diffusion constant and some arbitrary concentration difference.
    Diffusion is very slow, however - for a realistic setup, I would expect larger contributions from turbulence and other air movements.

    If L is not much larger than the diameter (or other length scale) of the hole, concentration differences in the box / outside close to the hole could be relevant, too.
     
  4. Mar 11, 2013 #3
    Are the products of combustion expected to vent through the same hole that is feeding the system oxygen?
     
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