Wells curve
The Wells curve (or Wells evaporation falling curve of droplets) is a diagram, developed by
A traditional hard size cutoff of 5
Background
Quiet breathing produces few droplets, but forced exhalations such as sneezing, coughing, shouting and singing can produce many thousands or even millions of small droplets. Droplets from healthy people consist of saliva from the mouth and/or the mucus that lines the respiratory tract. Saliva is >99% water, with small amounts of salts, proteins and other molecules.[7] Respiratory mucus is more complex, 95% water with large amounts of mucin proteins and varying amounts of other proteins, especially antibodies, as well as lipids and nucleic acids, both secreted and derived from dead airway cells. Sizes of respiratory droplets vary widely, from greater than 1 mm to less than 1 µm, but the distribution of sizes is roughly similar across different droplet-generating activities.[3]
The Wells curve: the effects of gravity and evaporation
In undisturbed moisture-saturated air, all respiratory droplets fall due to gravity until they reach the ground or another horizontal surface. For all but the largest droplets,
Size of droplet (mm) | Time to fall 2 m |
---|---|
≥1.0 | ≤0.6 sec |
0.1 | 6 sec |
0.01 | 10 min |
0.001 | 16.6 hr |
If the air is not saturated with water vapor, all droplets are also subject to evaporation as they fall, which gradually decreases their mass and thus slows the rate at which they are falling. Sufficiently large droplets still reach the ground or another surface, where they continue to dry, leaving potentially infectious residues called
Wells summarized this relationship graphically, with droplet size on the X-axis and time to evaporate or fall to the ground on the Y-axis. The result is a pair of curves intersecting at the droplet size that evaporates exactly as it hits the ground.[1]
Implications for epidemiology
Wells' insight was widely adopted because of its relevance for the spread of respiratory infections.
Complicating factors
Relative humidity: The effective distinction between 'large' and 'small' droplets depends on the humidity. Exhaled air has become saturated with water vapour during its passage through the respiratory tract, but indoor or outdoor air is usually much less humid. Under 0% humidity, only droplets 125 µm or larger will reach the ground, but the threshold falls to 60 µm for 90% humidity. Since most respiratory droplets are smaller than 75 µm,[2] even at high humidity most droplets will dry out and become airborne.[9]
Movement of exhaled and ambient air: Air that has been violently expelled by a cough or sneeze moves as a turbulent cloud through the ambient air. Such clouds can travel up to several meters, with large droplets falling from the cloud and small ones gradually dispersing and evaporating as they mix with ambient air. The internal turbulence of such clouds may also delay the fall of large droplets, increasing the chance that they will evaporate before reaching the ground. Since exhaled air is usually warmer and thus less dense than the ambient air, such clouds usually also rise. Droplets and dry particles in exhaled air are also dispersed by movement of the ambient air, due to winds and convection currents.[10][11]
Effects of face shields, masks and respirators
A face shield protects the wearer against impacts by large droplets that may be expelled horizontally by an infected person's cough or sneeze or during medical treatments.
References
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- ^ ISBN 978-92-4-154785-7.
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- ^ a b "U.S. Food and Drug Administration. 2020-03-11. Retrieved 2020-03-28". "N95 Respirators and Surgical Masks (Face Masks)". 5 April 2020. Retrieved 2020-05-09.