Question: There are no capillaries in the outer surface of your skin, presumably because they would be too easily damaged when you scratch or...
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# Question:There are no capillaries in the outer surface of your skin, presumably because they

would

be too easily damaged when you scratch or otherwise damage your skin. Cells in the outer

400 micrometers of your skin receive oxygen passively, through diffusion from the skin

surface. We will look at this process quantitatively, estimate the effective diffusion

coefficient of oxygen through human skin, and show that transdermal oxygen uptake is

small compared to total oxygen uptake, which occurs primarily through the lungs.1

Below is a list of facts that I gathered from the internet and a couple of articles from the

1950s:

• The density of the atmosphere at STP (basically at room temperature and at sea

level) is 44.6 moles/m3, of which 21% is oxygen.

• The typical oxygen concentration in your internal body tissue is 2.3 moles/m3.

• Over the outer 0.4 mm of your skin, oxygen concentration falls linearly from

atmospheric levels to internal tissue levels. This concentration gradient causes

oxygen to diffuse inward from the skin surface.

• The total oxygen uptake per area through the surface of your skin is

3.7 ⨉ 10-7 moles/m2/s.

• Your total body oxygen utilization is around 1.7 ⨉ 10-4 moles/s.

• A typical human has 1.7 m2 of skin.

• The diffusion coefficient of oxygen in water is 2.10 ⨉ 10-9 m2/s

1. Compare oxygen uptake through skin to total oxygen usage:

(a) Calculate how much oxygen you absorb through your skin, in moles/s, based on the

total uptake rate per square meter, and the size of your skin.

(b) What fraction of your total body oxygen usage comes through dermal transpiration?

2. Diffusion through the skin:

(a) Use the given numbers in Fick's law to calculate the effective diffusion coefficient of

oxygen in skin, Dskin, in m2/s.

(b) Compare the diffusion of oxygen in skin to its diffusion in water (that is, compare Dskin

and Dwater). Why do you think they are so different?

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