Capillary Alveoli Gas Exchange 1711 Diffusion Across an Interface

In Chapter 16 we discussed how the partial pressure of a gas is defined as the mole fraction of the gas multiplied by the total pressure. If a gas with partial pressure Ps is in contact with a liquid, the steady-state concentration U of gas in the liquid is given by

where a is the solubility of the gas in the liquid. Because of this, we can define the partial pressure of a dissolved gas with concentration U to be U/a.

Now suppose that a gas with partial pressure Pg is brought into contact with a liquid within which that same gas is dissolved with concentration U, and thus partial pressure U/a. If U/a is not equal to Pg, then there will be a net flow of gas across the interface. The simplest model (but not necessarily the most accurate) assumes that the flow is linearly proportional to the difference in partial pressures across the interface,

Diffusion Across Capillaries
Figure 17.2 The alveoli, or air sacs, of the lung are covered by an extensive network of capillaries that form a thin layer of blood for the exchange of gases. (Davis, Holtz, and Davis, 1985, Fig. 19-4, p. 391.)

and thus

where q is the net flux per unit area of the gas (positive when gas is flowing from the gaseous phase to the dissolved phase), and Ds is the surface diffusion constant.

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