Theoretical gas phase mass transfer coefficients for endogenous gases in the lungs

Gas phase mass transfer coefficients for nitric oxide (NO), ethanol (EtOH), and water vapor (H₂O) were determined for typical conducting airway geometry and tracheal flows (5 × 10^-5 and 5 × 10^-4 m³ s^-1), by solving the steady-state two-dimensional diffusion equation. A constant absolute production rate with first order consumption reactions in pulmonary tissue was assumed for NO. For EtOH and H₂O, constant concentrations were assumed in the blood and tissue, respectively. Results, expressed in terms of the average Sherwood number (Sh), were correlated with the Peclet (Pe_r) number, and the length-to-diameter (L/D) ratio for each airway branch in terms of a lumped variable, Pe_r(L/D)ⁿ. (Sh) increases as the solubility of the gas in tissue and blood increases. In addition, Sh passes through a minimum value at Pe_r(D/L)ⁿ equal to approximately one when axial convection and diffusion have equal but opposite magnitudes. We conclude that Sh is not a monotonic function of Pe_r(L/D)ⁿ within the entire airway tree and that it depends on the physical properties of the gas in the tissue. This conclusion contrasts with previous experimental and theoretical correlations.