A Porous Media Approach for Bifurcating Flow and Mass Transfer in a Human Lung

A porous media approach was proposed to investigate the characteristics of the bifurcating airflow and mass transfer within a lung. The theory of porous media was introduced in order to deal with a large number of bifurcations and a vast scale difference resulting from bifurcations. Upon introducing a two-medium treatment for the air convection and the diffusion in its surrounding wall tissue, the oxygen mass transfer between the inhaling air and the tissue was considered along with the effects of the blood perfusion on the mass transfer within the tissue. The overall mass transfer resistance between the inlet of the trachea and the blood in the capillaries was obtained on the basis of the porous media approach. The analysis reveals that there exists the optimal number of the bifurcation levels, namely, 23, that yields the minimum overall mass transfer resistance for the mass transport from the external air to the red blood cells. The finding is consistent with Bejan’s constructal law, namely, that for a flow system to persist in time, it must evolve in such a way that it provides easier access to its currents.