4.3.3.P8
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Capillaries are the narrowest elements in the blood transport system of animals. They connect the arteries (the vessels that carry blood away from the heart) to the veins (the vessels that carry blood back to the heart). They are the place where the chemicals that the blood is carrying are taken from source regions (lungs for air, intestines for food, glands for hormones) and delivered to the cells that need them. They are pretty small – about 5 μm in diameter.
One of the interesting questions about this process is: How do oxygen molecules know where to go? For example, Wikipedia says that red blood cells "take up oxygen in the lungs or gills and release it while squeezing through the body's capillaries." In order to consider this let's make a(n oversimplified) model in which oxygen diffuses into the blood stream in the lungs, is carried by fluid flow out to the cells where it diffuses out. (In reality, the oxygen is bound to hemoglobin, carried, and released, but the beginning and end processes are as described here.)
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 Source: Wikimedia commons |
| A. Consider a capillary in an alveolus in the lung. The density of oxygen inside the capillary is 0.3 million molecules/(μm)3 and in the air outside is about 5 million molecules/(μm)3. Which way will the oxygen flow across the membrane? Explain why.
B. Consider an individual molecule in the air outside the alveolus. How is it moving? How does it know how to get into the capillary? |
Source: Wikimedia commons
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C. Now consider a capillary inside a muscle. The muscle has done work and used up its oxygen. The density of oxygen inside the capillary is 1 million molecules/(μm)3 and in the fluid surrounding the muscle is 0.3 million molecules/(μm)3. Which way will the oxygen flow across the membrane? Explain why.
D. Consider an individual molecule in the capillary in part C (after is has been released by the hemoglobin). How is it moving? How does it know how to get out of the capillary into the muscle fluid?
E. Fick's Law tells us how a concentration difference drives flow: J = -D Δn/Δx. If the membrane is 7 nm thick, and the diffusion constant, D, for oxygen through the membrane is 6 x 10-3 (μm)2/s, calculate the rate of flow through the capillary membrane in part C.
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