Wall Kinematics and Pulsatile Inertia in Low-Reynolds-number Alveolar Chaotic Mixing

The complex dynamics and chaotic behavior within pulmonary alveoli significantly influence particle deposition and transport. However, the mechanisms governing alveolar chaos and its specific effects on material transport remain poorly understood. This study establishes four distinct alveolar boundary conditions: fixed walls, self-similar expanding walls (including expandable and fixed ducts), and non-self-similar expanding walls, to examine how various parameters affect chaotic alveolar flows. Using Dynamic Mode Decomposition and Lagrangian particle tracking, we construct Poincaré maps to identify periodic points and, additionally, compute finite-time Lyapunov exponent (FTLE) ridges to provide supplementary visualization of Lagrangian stretching. The results demonstrate that increasing the Reynolds number enhances flow chaos, while expansion ratio has negligible impact. Increasing the Womersley number weakens chaotic mixing in alveolar flows. The Poincaré map exhibits distinct patterns: island structures dominate the alveolar central region, while chaotic seas characterize the periphery. Elliptical periodic points form the centers of islands, whereas hyperbolic periodic points and their manifolds are distributed throughout chaotic region. FTLE ridges also appear primarily within the chaotic region. Wall conditions significantly influence chaotic mixing by modifying the spatial distribution and quantity of periodic points. The saddle points in the velocity field are not as representative of chaos in alveolar flows as previously thought. The observed chaotic behavior promotes particle transport from chaotic regions into alveolar ducts, effectively transforming the alveolar cavity into an efficient mixer. These findings advance our fundamental understanding of dynamics in alveolar flow and provide a theoretical framework for optimizing scalar transport systems.