Wells curve

Last updated
The Wells curve demonstrates that respiratory droplets rapidly dry out or fall to the ground after being exhaled. The Wells falling and evaporation curve of droplets (The Wells Curve).png
The Wells curve demonstrates that respiratory droplets rapidly dry out or fall to the ground after being exhaled.

The Wells curve (or Wells evaporation falling curve of droplets) is a diagram, developed by W. F. Wells in 1934, which describes what is expected to happen to small droplets once they have been exhaled into air. [1] Coughing, sneezing, and other violent exhalations produce high numbers of respiratory droplets derived from saliva and/or respiratory mucus, with sizes ranging from about 1 μm to 2 mm. [2] [3] Wells' insight was that such droplets would have two distinct fates, depending on their sizes. The interplay of gravity and evaporation means that droplets larger than a humidity-determined threshold size would fall to the ground due to gravity, while droplets smaller than this size would quickly evaporate, leaving a dry residue that drifts in the air. Since droplets from an infected person may contain infectious bacteria or viruses, these processes influence transmission of respiratory diseases. [4] [5]

Contents

A traditional hard size cutoff of 5 μm between airborne and respiratory droplets has been criticized as a false dichotomy not grounded in science, as exhaled particles form a continuum of sizes whose fates depend on environmental conditions in addition to their initial sizes. However, it has informed hospital based transmission based precautions for decades. [6]

Background

Each histogram shows the size distribution of 3000 respiratory droplets produced by the specified activity. Data from Duguid 1946 Sizes of respiratory droplets.png
Each histogram shows the size distribution of 3000 respiratory droplets produced by the specified activity. Data from Duguid 1946

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, Stokes Law predicts that falling speeds quickly reach a limit set by the ratio of mass to cross-sectional area, with small droplets falling much more slowly than large ones. [8]

Falling times of droplets in water-saturated air (data from Duguid 1946 [2] )
Size of droplet (mm)Time to fall 2 m
≥1.0≤0.6 sec
0.16 sec
0.0110 min
0.00116.6 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 fomites. However, the high surface area to volume ratios of small droplets cause them to evaporate so rapidly that they dry out before they reach the ground. The dry residues of such droplets (called 'droplet nuclei' or 'aerosol particles') then cease falling and drift with the surrounding air. Thus, the continuous distribution of droplet sizes rapidly produces just two dichotomous outcomes, fomites on surfaces and droplet nuclei floating in the air. [1]

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. [5] The efficiency of transmission of specific viruses and bacteria depends both on the types of droplets and droplet nuclei they cause and on their ability to survive in droplets, droplet nuclei and fomites. Diseases such as measles, whose causative viruses remain highly infectious in droplet nuclei, can be spread without personal contact, across a room or through ventilation systems and are said to have airborne transmission. [4] Although later studies demonstrated that the droplet size at which evaporation outpaces falling is smaller than that described by Wells, and the settling time is longer, his work remains important for understanding the physics of respiratory droplets. [3]

Wells curves for different relative humidities Droplet falling-evaporation curves for different humidities.png
Wells curves for different relative humidities

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. [12] Since the shield is an impermeable barrier that air must travel around, it provides little protection against small droplets and dry particles that travel with the air. Surgical masks and home-made masks can filter out large and small droplets, but their pores are too large to block passage of small aerosol particles. They are thought to be more effective when worn by an infected person, preventing release of infectious droplets, than when worn by an uninfected person to protect against infection. Air that travels around a poorly fitting mask is not filtered, nor is violently expelled air produced by a cough or sneeze. [13] [14] N-95 respirator masks are designed to filter out even small dry particles, but they must be individually fitted and checked to prevent leakage of air around the sides. [14]

Related Research Articles

<span class="mw-page-title-main">Common cold</span> Common viral infection of the upper respiratory tract

The common cold or the cold is a viral infectious disease of the upper respiratory tract that primarily affects the respiratory mucosa of the nose, throat, sinuses, and larynx. Signs and symptoms may appear fewer than two days after exposure to the virus. These may include coughing, sore throat, runny nose, sneezing, headache, and fever. People usually recover in seven to ten days, but some symptoms may last up to three weeks. Occasionally, those with other health problems may develop pneumonia.

In medicine, public health, and biology, transmission is the passing of a pathogen causing communicable disease from an infected host individual or group to a particular individual or group, regardless of whether the other individual was previously infected. The term strictly refers to the transmission of microorganisms directly from one individual to another by one or more of the following means:

<span class="mw-page-title-main">Surgical mask</span> Mouth and nose cover against bacterial aerosols

A surgical mask, also known by other names such as a medical face mask or procedure mask, is a personal protective equipment used by healthcare professionals that serves as a mechanical barrier that interferes with direct airflow in and out of respiratory orifices. This helps reduce airborne transmission of pathogens and other aerosolized contaminants between the wearer and nearby people via respiratory droplets ejected when sneezing, coughing, forceful expiration or unintentionally spitting when talking, etc. Surgical masks may be labeled as surgical, isolation, dental or medical procedure masks.

<span class="mw-page-title-main">Natural reservoir</span> Type of population in infectious disease ecology

In infectious disease ecology and epidemiology, a natural reservoir, also known as a disease reservoir or a reservoir of infection, is the population of organisms or the specific environment in which an infectious pathogen naturally lives and reproduces, or upon which the pathogen primarily depends for its survival. A reservoir is usually a living host of a certain species, such as an animal or a plant, inside of which a pathogen survives, often without causing disease for the reservoir itself. By some definitions a reservoir may also be an environment external to an organism, such as a volume of contaminated air or water.

Aerosolization is the process or act of converting some physical substance into the form of particles small and light enough to be carried on the air i.e. into an aerosol. Aerosolization refers to a process of intentionally oxidatively converting and suspending particles or a composition in a moving stream of air for the purpose of delivering the oxidized particles or composition to a particular location.

<span class="mw-page-title-main">Influenza</span> Infectious disease

Influenza, commonly known as "the flu" or just "flu", is an infectious disease caused by influenza viruses. Symptoms range from mild to severe and often include fever, runny nose, sore throat, muscle pain, headache, coughing, and fatigue. These symptoms begin one to four days after exposure to the virus and last for about two to eight days. Diarrhea and vomiting can occur, particularly in children. Influenza may progress to pneumonia from the virus or a subsequent bacterial infection. Other complications include acute respiratory distress syndrome, meningitis, encephalitis, and worsening of pre-existing health problems such as asthma and cardiovascular disease.

<span class="mw-page-title-main">Airborne transmission</span> Disease transmission by airborne particles

Airborne transmission or aerosol transmission is transmission of an infectious disease through small particles suspended in the air. Infectious diseases capable of airborne transmission include many of considerable importance both in human and veterinary medicine. The relevant infectious agent may be viruses, bacteria, or fungi, and they may be spread through breathing, talking, coughing, sneezing, raising of dust, spraying of liquids, flushing toilets, or any activities which generate aerosol particles or droplets.

Influenza prevention involves taking steps that one can use to decrease their chances of contracting flu viruses, such as the Pandemic H1N1/09 virus, responsible for the 2009 flu pandemic.

<span class="mw-page-title-main">Sneeze guard</span> Acrylic or glass screen designed to protect people or food from exposure to respiratory droplets

A sneeze guard, sneezeguard, or cough shield is an acrylic or glass screen designed to protect food or people from the exposure to respiratory droplets, which are dispensed when coughing, sneezing, or speaking. Sneeze guards have been in use in restaurants for decades. With the rise of the COVID-19 pandemic, sneeze guards have been installed in public places like offices, schools and retail stores to reduce the risk of infection through respiratory droplets.

<span class="mw-page-title-main">Respiratory droplet</span> Type of particle formed by breathing

A respiratory droplet is a small aqueous droplet produced by exhalation, consisting of saliva or mucus and other matter derived from respiratory tract surfaces. Respiratory droplets are produced naturally as a result of breathing, speaking, sneezing, coughing, or vomiting, so they are always present in our breath, but speaking and coughing increase their number.

A toilet plume is the dispersal of microscopic particles as a result of flushing a toilet. Normal use of a toilet by healthy individuals is considered unlikely to be a major health risk. However this dynamic changes if an individual is fighting an illness and currently shedding out a virulent pathogen in their urine, feces or vomitus. There is indirect evidence that specific pathogens such as norovirus or SARS coronavirus could potentially be spread by toilet aerosols, but as of 2015, no direct experimental studies had clearly demonstrated or refuted actual disease transmission from toilet aerosols. It has been hypothesized that dispersal of pathogens may be reduced by closing the toilet lid before flushing, and by using toilets with lower flush energy.

<span class="mw-page-title-main">Dental aerosol</span> Hazardous biological compound

A dental aerosol is an aerosol that is produced from dental instrument, dental handpieces, three-way syringes, and other high-speed instruments. These aerosols may remain suspended in the clinical environment. Dental aerosols can pose risks to the clinician, staff, and other patients. The heavier particles contained within the aerosols are likely to remain suspended in the air for relatively short period and settle quickly onto surfaces, however, the lighter particles may remain suspended for longer periods and may travel some distance from the source. These smaller particles are capable of becoming deposited in the lungs when inhaled and provide a route of diseases transmission. Different dental instruments produce varying quantities of aerosol, and therefore are likely to pose differing risks of dispersing microbes from the mouth. Air turbine dental handpieces generally produce more aerosol, with electric micromotor handpieces producing less, although this depends on the configuration of water coolant used by the handpiece.

<span class="mw-page-title-main">Cloth face mask</span> Mask made of common textiles worn over the mouth and nose

A cloth face mask is a mask made of common textiles, usually cotton, worn over the mouth and nose. When more effective masks are not available, and when physical distancing is impossible, cloth face masks are recommended by public health agencies for disease "source control" in epidemic situations to protect others from virus laden droplets in infected mask wearers' breath, coughs, and sneezes. Because they are less effective than N95 masks, surgical masks, or physical distancing in protecting the wearer against viruses, they are not considered to be personal protective equipment by public health agencies. They are used by the general public in household and community settings as protection against both infectious diseases and particulate air pollution.

An aerosol-generating procedure (AGP) is a medical or health-care procedure that a public health agency such as the World Health Organization or the United States Centers for Disease Control and Prevention (CDC) has designated as creating an increased risk of transmission of an aerosol borne contagious disease, such as COVID-19. The presumption is that the risk of transmission of the contagious disease from a patient having an AGP performed on them is higher than for a patient who is not having an AGP performed upon them. This then informs decisions on infection control, such as what personal protective equipment (PPE) is required by a healthcare worker performing the medical procedure, or what PPE healthcare workers are allowed to use.

Lydia Bourouiba is an Esther and Harold E. Edgerton Professor, an Associate Professor in the Civil and Environmental Engineering and Mechanical Engineering departments, and in the Institute for Medical Engineering and Science at the Massachusetts Institute of Technology. She is also a Harvard-MIT Health Sciences and Technology Faculty, and Affiliate Faculty of Harvard Medical School. She directs the Fluid Dynamics of Disease Transmission Laboratory at MIT.

Human-to-human transmission (HHT) is an epidemiologic vector, especially in case the disease is borne by individuals known as superspreaders. In these cases, the basic reproduction number of the virus, which is the average number of additional people that a single case will infect without any preventative measures, can be as high as 203.9. Interhuman transmission is a synonym for HHT.

<span class="mw-page-title-main">Source control (respiratory disease)</span> Strategy for reducing disease transmission

Source control is a strategy for reducing disease transmission by blocking respiratory secretions produced through speaking, coughing, sneezing or singing. Surgical masks are commonly used for this purpose, with cloth face masks recommended for use by the public only in epidemic situations when there are shortages of surgical masks. In addition, respiratory etiquette such as covering the mouth and nose with a tissue when coughing can be considered source control. In diseases transmitted by droplets or aerosols, understanding air flow, particle and aerosol transport may lead to rational infrastructural source control measures that minimize exposure of susceptible persons.

William Firth Wells was an American scientist and sanitary engineer. In his early career, he pioneered techniques for the aquaculture of oysters and clams. He is best known for his work on airborne infections. Wells identified that tuberculosis could be transmitted through air via the nuclei of evaporated respiratory droplets, and developed the Wells curve to describe what happens to respiratory droplets after they have been expelled into the air.

<span class="mw-page-title-main">Transmission of COVID-19</span> Mechanisms that spread coronavirus disease 2019

The transmission of COVID-19 is the passing of coronavirus disease 2019 from person to person. COVID-19 is mainly transmitted when people breathe in air contaminated by droplets/aerosols and small airborne particles containing the virus. Infected people exhale those particles as they breathe, talk, cough, sneeze, or sing. Transmission is more likely the closer people are. However, infection can occur over longer distances, particularly indoors.

Droplet nuclei are aerosols formed from the evaporation of respiratory droplets. They are generally smaller than 5 μm in diameter. Droplet nuclei are formed by the "dried residua of larger respiratory droplets". These particles are "the vehicle for airborne respiratory disease transmission, which are the dried-out residual of droplets possibly containing infectious pathogens". Diseases such as tuberculous and COVID-19 can be transmitted via droplet nuclei.

References

  1. 1 2 3 Wells, W. F. (1934-11-01). "On Air-Borne Infection". American Journal of Epidemiology. 20 (3): 611–618. doi:10.1093/oxfordjournals.aje.a118097. ISSN   0002-9262.
  2. 1 2 3 4 Duguid, J. P. (September 1946). "The size and the duration of air-carriage of respiratory droplets and droplet-nuclei". Epidemiology & Infection. 44 (6): 471–479. doi:10.1017/S0022172400019288. ISSN   1469-4409. PMC   2234804 . PMID   20475760.
  3. 1 2 3 Gralton, Jan; Tovey, Euan; McLaws, Mary-Louise; Rawlinson, William D. (January 2011). "The role of particle size in aerosolised pathogen transmission: A review". Journal of Infection. 62 (1): 1–13. doi:10.1016/j.jinf.2010.11.010. ISSN   0163-4453. PMC   7112663 . PMID   21094184.
  4. 1 2 Kutter, Jasmin S; Spronken, Monique I; Fraaij, Pieter L; Fouchier, Ron AM; Herfst, Sander (2018-02-01). "Transmission routes of respiratory viruses among humans". Current Opinion in Virology. Emerging viruses: intraspecies transmission • Viral Immunology. 28: 142–151. doi:10.1016/j.coviro.2018.01.001. ISSN   1879-6257. PMC   7102683 . PMID   29452994.
  5. 1 2 World Health Organization; Y. Chartier; C. L Pessoa-Silva (2009). Natural Ventilation for Infection Control in Health-care Settings. World Health Organization. p. 79. ISBN   978-92-4-154785-7.
  6. ↑ Environmental Health Matters Initiative; National Academies of Sciences, Engineering, and Medicine (2020-10-22). Shelton-Davenport, Marilee; Pavlin, Julie; Saunders, Jennifer; Staudt, Amanda (eds.). Airborne Transmission of SARS-CoV-2: Proceedings of a Workshopâ€"in Brief. Washington, D.C.: National Academies Press. doi:10.17226/25958. ISBN   978-0-309-68408-8. PMID   33119244. S2CID   236828761.{{cite book}}: CS1 maint: multiple names: authors list (link)
  7. ↑ Humphrey, Sue P.; Williamson, Russell T. (February 2001). "A review of saliva: Normal composition, flow, and function". The Journal of Prosthetic Dentistry. 85 (2): 162–169. doi:10.1067/mpr.2001.113778. PMID   11208206.
  8. ↑ Stokes, George Gabriel (1901). "On the Effect of the Internal Friction of Fluids on the Motion of Pendulums". Mathematical and Physical Papers. Vol. 3. Cambridge: Cambridge University Press. pp. 1–10. doi:10.1017/cbo9780511702266.002. ISBN   978-0-511-70226-6.
  9. ↑ Xie, X.; Li, Y.; Chwang, A. T. Y.; Ho, P. L.; Seto, W. H. (June 2007). "How far droplets can move in indoor environments ? revisiting the Wells evaporation?falling curve". Indoor Air. 17 (3): 211–225. doi: 10.1111/j.1600-0668.2007.00469.x . ISSN   0905-6947. PMID   17542834.
  10. ↑ Bourouiba, Lydia; Dehandschoewercker, Eline; Bush, John W. M. (April 2014). "Violent expiratory events: on coughing and sneezing". Journal of Fluid Mechanics. 745: 537–563. Bibcode:2014JFM...745..537B. doi:10.1017/jfm.2014.88. hdl: 1721.1/101386 . ISSN   0022-1120. S2CID   2102358.
  11. ↑ Pica, Natalie; Bouvier, Nicole M (2012-02-01). "Environmental factors affecting the transmission of respiratory viruses". Current Opinion in Virology. Virus entry/Environmental virology. 2 (1): 90–95. doi:10.1016/j.coviro.2011.12.003. ISSN   1879-6257. PMC   3311988 . PMID   22440971.
  12. ↑ Roberge, Raymond J. (2016-04-02). "Face shields for infection control: A review". Journal of Occupational and Environmental Hygiene. 13 (4): 235–242. doi:10.1080/15459624.2015.1095302. ISSN   1545-9624. PMC   5015006 . PMID   26558413.
  13. ↑ Tang, Julian W.; Liebner, Thomas J.; Craven, Brent A.; Settles, Gary S. (2009-12-06). "A schlieren optical study of the human cough with and without wearing masks for aerosol infection control". Journal of the Royal Society Interface. 6 (suppl_6): S727-36. doi:10.1098/rsif.2009.0295.focus. ISSN   1742-5689. PMC   2843945 . PMID   19815575.
  14. 1 2 "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.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.