Logistic trajectory maps and aerosol mixing due to asynchronous flow at airway bifurcations

Aerosols too large for significant Brownian transport, and too small for significant inertial transport, are nonetheless known to deposit deep in the lung, and are associated with increased risk of pulmonary disease. Classical models fail to explain such transport. We hypothesized that kinematic irreversibility in ventilation, arising from velocity saddle-points or from flow asynchrony at airway bifurcations, may be the fundamental transport mechanism. Our experimental evidence shows striking trajectory irreversibility in rat lungs ventilated with 2-color polymerizable silicones, representing resident and tidal gas. The striated patterns in small airways, even after one ventilatory cycle, support our hypothesis. Here we analyze bifurcating flow asynchrony in a simplified one-dimensional model. We find: unexpected richness and chaos in particle trajectories; almost all trajectories visit all spatial positions; surprisingly, there is complete mixing-the limiting concentration is spatially uniform. This is a new finding supporting the idea that kinematic irreversibility is a potent mixing and transport mechanism for aerosols deep in the lung.