Breathing at high Reynolds number
Birds such as this black-headed gull rely on their unique lung structures for efficient oxygen uptake, particularly when they fly for long distances or at high altitudes.
Kornel Mizdalski/pexels.com
When a human inhales and exhales, the direction of flow through the airways alternates. Blood circulation, on the other hand, uses the heart’s rhythmic pumping to drive flow in one direction, out from the heart through arteries and back through veins. Bird respiration is somewhere in the middle: Air flows both in and out through an upper airway, but it flows in a single direction around loops in the lungs. That design helps birds efficiently extract oxygen from the air by getting oxygen-rich air into the lungs during both inhalation and exhalation.
Although researchers have long known that bird lungs employ unidirectional flows, how they generate those flows remains unclear. Circulatory systems use valves to enable an alternating pump to direct flow in one direction, but no valve-like structures have been found in bird lungs. Also absent are complicated geometries, like sawtooth corrugations, that create direction-dependent hydraulic resistance in fluidic diodes. Now Quynh Nguyen and coworkers at New York University and the New Jersey Institute of Technology have shown through experiments and simulations that the topology and connectivity of the airway network are sufficient to generate valveless unidirectional flows.
In the researchers’ simplified bird-lung model (left), air enters the primary bronchus through the mouth, travels clockwise around an airway loop, and exits back through the primary bronchus. An air sac provides an alternating forcing by expanding and contracting, akin to a diaphragm.
Q. M. Nguyen et al., Phys. Rev. Lett. 126, 114501 (2021)
As a further simplification, the researchers used a piston (right) whose back-and-forth motion mimics breathing. The piston connects the primary bronchus (yellow) and air sac (orange) to the airway loop (green). They tracked the flow in their setup with tracer particles, as shown in the demonstration video, and confirmed that the oscillatory flows in the orange and yellow sections did in fact become unidirectional flows once they reached the green sections.
Three crucial factors underlie the behavior: a high Reynolds number, the presence of loops, and asymmetric junctions. Flows at high Reynolds number are dominated by inertial forces. When the fluid in the setup encountered a T junction where it could either continue straight or turn, the fluid preferentially continued straight. The orange tube in the figure therefore fed primarily into the upper light-green path. But when the flow in the orange section reversed, it pulled fluid equally from the dark and light green segments. That flow irreversibility sustained the one-directional flows.
Simulations agreed, and they also showed that vortices formed at junction corners—another consequence of flows at high Reynolds number. The vortices served as valves and “plugged” the junction’s orthogonal branch. Further study could shed light on the range of Reynolds numbers and the variety of junction geometries that can produce flow rectification. (Q. M. Nguyen et al., Phys. Rev. Lett. 126, 114501, 2021 .)
