MathBench > Cellular Processes

Diffusion

Diffusion is efficient in small organisms, but not big ones

So even a huge amoeba can diffuse oxygen through its body in about 5 seconds. If I could do that, I probably wouldn’t bother with lungs either. A similar calculation shows that carbon dioxide can also be diffused out of the cell without the need for lungs or gills.

Lots of other, larger animals do gas exchange without lungs – but they tend to be large in only 1 or two dimensions, so that gases can diffuse through the smaller third dimension. Thus, flatworms, nematodes, and many other kinds of worm-like animals don’t need complicated respiratory systems.


mouseHow long would it take for oxygen to diffuse from the outside to the middle of a mouse if its body has a 1 cm radius? (Just ignore that the mouse is more irregularly shaped than a cylinder and contains numerous barriers to diffusion - PLEASE!!)

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I think I have the answer: T = X 2 / 2D =
(1cm)2 / (2*10-5cm2/sec ) =
50 000 sec =
13 hours


rhinoHow about a rhino whose body had a radius of 75 cm?

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I think I have the answer: T = X 2 / 2D =
(75cm)2 / (2*10-5cm2/sec ) =
2.8*108 sec =
78,125 hours =
8.9 years

Yikes, even this very tiny mouse cannot survive on diffusion alone, and with a rhinoceros, the question is clearly preposterous!