Slow viscous flow in a lung alveoli model.

Abstract A theoretical analysis of the flow pattern and the law of resistance of blood moving in a model of lung alveoli is presented. The model consists of two parallel flat membranes interconnected by regularly space circular posts. It is structurally an idealization of the internal geometry of the pulmonary alveolar septa. An approximate solution which gives a reasonable representation for flow around a circular post confined between two plates, is extended to construct a periodic solution for the present problem. The solution is found to be adequate when the sheet-thickness-to-post-diameter ratio is not much larger than one. The resistance of the flow as a function of the geometric parameters is computed. It is shown that the posts are very effective in increasing the flow resistance. Numerical results are shown to agree substantially with experimental measurements of the resistance.