Excess pressure in the lungs

If we assume that xs is constant, then an increasing radius would reduce excess pressure, and the alveoli would collapse when the excess pressure fell below a certain value. This kind of instability is not common, since ts does not remain constant in a normal lung but increases with increasing radius such that AP always increases with increasing radius. This behavior of crs is caused by a surface-active agent (phospholipids) in the liquid film. The concentration of the surface-active agent decreases in the interface between liquid and air when the surface of the film distends, and therefore both surface tension and excess pressure increase. The hysteresis of this process is controlled by the diffusion of matter between the free interface and interior of the liquid. 

The surface tension is about 0.06 N/m for water and about 0.05 N/m for blood plasma, and it can vary between 0.002 and 0.04 N/m for the liquid films of alveoli, and the total area changes by a factor of 5. With these data on surface tension and for a maximal area of 100 m2, the total surface energy asA) varies between the values 

Assuming that the hysteresis over a cycle is 25% of the maximal energy, that the power due to surface tension at a respiration frequency of 12 min-1 becomes 

The radii of the —300 million alveoli vary in the interval R = 0.06-0.15 mm. The excess pressures (Eq. (a)) to distend an alveolus and hence surface tensions can vary between 

These relations show the equality between the work of the excess pressure and the increase in surface energy. 

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