Three-dimensional critical points and flow patterns in pulmonary alveoli with rhythmic wall motion

Abstract

The dynamics of airflow in the pulmonary acini are of broad interest in understanding respiratory diseases and the fate of inhaled particles. This study investigates the three-dimensional alveolar flows with rhythmic cavity wall motion, using a finite element method based computational fluid dynamics. This study reports the new research findings on the critical points and associated flow patterns. The locations of critical points are found based on the Brouwer degree theory and Broyden’s method. The phase portrait is used to evaluate the flow patterns around the critical points and the stability (repelling/attracting property) of the critical points on the symmetry plane of the alveolus. Based on the Poincare-Bendixson theorem, the closed orbits on the symmetry plane are found which have the capability to alter the spiral direction of the spiral streamlines. In the three-dimensional space, the alveolar flow is symmetric about the geometric symmetry plane of the alveolus. Different types of three-dimensional critical points, including saddle, spiral, and spiral saddle, are revealed. There are only one saddle point and at least one spiral point or spiral saddle in the alveolar flow. Spiral points and spiral saddles are located on the vortex core line and their number is dependent on the Reynolds number and varies with time. The study of critical points and their evolution helps us to understand the mechanism of irreversible transport of particle tracers from a new perspective.