A single cough can propel as many as 3,000 droplets into the air at a velocity of 6 to 28 m/s. The droplets travel in what classic fluid mechanics calls a “2-stage jet”: the starting jet (when the cough starts) and interrupted jet (when the cough stops). After the original cough ends, a “leading vortex” carries particles forward, but as the momentum slows, particles fall out of the jet according to researchers from the University of Hong Kong and Shenzhen Institute of Research and Innovation, both in China, who studied cough trajectories and the implications for disease transmission in buildings.
Once the penetration velocity drops below 0.01 m/s, environmental factors, such as ventilation and human body temperature, begin to influence the flow. Beyond 1 to 2 m, the exhaled air stream dissolves into the room airflow, and the pathogen-containing droplets or droplet nuclei are dispersed according to the global airflow in the room.
When a cough doesn’t last long, the researchers say, the velocity of fine particles decays significantly after the jet is interrupted. However, even short coughs have consequences: Pathogen-containing droplets as large as ≥ 5 µm in diameter can be directly deposited on the nasal or oral mucosa of a nearby “new host.”
But coughs differ in many ways, including how far and wide they send the droplets. The researchers conducted experiments to help determine spread by discharging dyed or particle-filled water into a water tank. They examined 3 different temporal exit velocity profiles: pulsation, sinusoidal, and real-cough.
The “most striking phenomenon,” the researchers say, is that the particle clouds of all 3 sizes of particles (small [8-14 µm], medium [57-68 µm], large [96-114 µm]) penetrated almost the same distance at different time steps. In other words, large particles can travel as far as fine particles.
The cough flow’s maximum penetration distance was 53.4 to 69.7 opening diameter. That is, for a mouth opening to a diameter of 2 cm, the large particles could penetrate 1 to 1.4 m in a “real cough case,” they note. Cough duration was important in determining the spread range of particles. Their maximum travel distance was “much enhanced” in a long starting jet, especially for small particles.
Wei J, Li Y. PLoS One. 2017;12(1): e0169235.