Gas absorption in pulmonary airways at low Peclet number

A mathematical model is presented that investigates the mass transport of a diffusible and soluble gas contaminant through a liquid-lined tube when the Peclet number is small. The transport is determined by four dimensionless parameters: lambda, the tube aspect ratio; d, the relative difference in end concentrations; gamma, the radial transport coefficient; and Pe, the Peclet number. The problem is formulated for arbitrary gamma, but in the case of ozone and nitrous oxides the value of gamma is small. An asymptotic analysis for Pe much less than 1 and gamma much less than 1 is presented which yields the concentration field and transport characteristics we seek. It also provides a low Peclet number analysis for the conjugate problem of mass and heat transfer that is not currently available in the literature. The application to transport in the small airways of the lung is discussed, particularly the radial absorption differences in inspiratory and expiratory flow. Depending on the relative sizes of gamma and Pe, fractional uptake decreases with increasing Pe during inspiration but can increase during expiration.