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 x 10(-5)and 5 x 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.