A POROUS MEDIA MODEL OF ALVEOLAR DUCT FLOW IN THE HUMAN LUNG

Prediction of air flow in the human lung is of great interest for many physiological applications. Recent advances in modeling such flows using computational fluid dynamics have included the development of porous media-based approaches that consider the small-scale airways and alveoli as a porous domain. This article presents a derivation of the governing equations relevant to flow in an alveolated duct based on the theory of volume-averaging as well as their closure. It is shown that the momentum closure problem reduces to that of a steady-state problem which is solved over a representative unit cell of an alveolated duct to predict its permeability. The modeling approach is validated against permeability predictions coming from transient simulations of flow in an expanding and contracting duct. Finally, analytical expressions for the velocity and pressure in an alveolated duct are derived and presented.