Mathematical Modelling of Dynamic Behavior of Droplets of Saliva as a Vehicles for Respiratory Pathogens Transmission
Keywords:
Droplets, Dynamic Behavior, Respiratory Pathogens, Virus, COVID-19, CoronavirusAbstract
This study performs an analytical description of the dynamic behavior of the droplets and the effect of the environmental air temperature on their drop time and horizontal velocity to highlight some aspects that improve the fight against the spread of the respiratory pathogens, such as the COVID-19, between humans. According to this study, when the droplet exits the human body, its horizontal velocity reduces drastically. The smaller the size of the droplets, the higher is the rate of this decay. The droplets achieve its largest horizontal range instantaneously. Thus, the horizontal displacement for droplets with less than 100 µm in diameter does not exceed 380 mm. However, droplets with larger than 300 µm in diameter have a horizontal range that can reach distances greater than 1600 mm, without significant reduction of their heights to the ground. This can invalid the current rule of social distance (least 1.5 m — 2 m between people). Because of this, if a person is within the horizontal displacement range of a droplet he will be hit in the face which can increase the contagion. The droplets with less than 1 µm in diameter remain airborne for at least 15 hours, which can further increase of contagion by inhalation. The temperature of the environment has a negative influence on droplets drop time. Faced with this, the people in warmer countries can inhale more virus of suspension than those in colder countries. Finally, the higher the environmental air temperature, the lower the horizontal range achieved by the droplets.
References
. J. Yan et al.; EMIT Consortium, “Infectious virus in exhaled breath of symptomatic seasonal influenza cases from a college community” in Proc. Natl. Acad. Sci. U.S.A. 115, 2018, pp.1081–1086.
. L. Liljeroos, J. T. Huiskonen, A. Ora, P. Susi, S. J. Butcher, “Electron cryotomography of measles virus reveals how matrix protein coats the ribonucleocapsid within intact virions”, in Proc. Natl. Acad. Sci. U.S.A. 108, 2011, pp.18085–18090.
. K. P. Fennelly et al., “Variability of infectious aerosols produced during coughing by patients with pulmonary tuberculosis”. Am. J. Respir. Crit. Care Med. 186, pp.450–457, 2012.
. J. F.-W. Chan et al., “Improved molecular diagnosis of COVID-19 by the novel, highly sensitive and specific COVID-19-RdRp/Hel real-time reverse transcription-polymerase chain reaction assay validated in vitro and with clinical specimens”. J. Clin. Microbiol. 58, pp.310-320, 2020.
. R. Wölfel et al., “Virological assessment of hospitalized patients with COVID-2019”. Nature, pp. 2020.
. P.K. Dutta, “Spread of Coronavirus Infection and Science of Cough and Sneeze”, IndiaTODAY, 2020.
. S. Zhu, “Study on Transport Characteristics of Saliva Droplets Produced by Coughing in a Calm Indoor Environment”. Building and Environment, 41(12), 2006.
. L. Marr, “Mechanistic Insights into the Effect of Humidity on Airborne Influenza Virus Survival Transmission and Incidence”, Journal of the Royal Society Interface, 16, pp.1-10, 2019.
. V. Stadnytskyi, C. E. Bax, A. Bax, P. Anfinrud, “The airborne lifetime of small speech droplets and their potential importance in SARS-CoV-2 transmission”, in Proc. of the National Academy of Sciences, 2020, pp.1-3.
. C.Y.H. Chaoam, M.P. Wanb, L. Morawskac, G.R. Johnsonc, Z.D. Ristovskic, M. Hargreavesc, K. Mengersend, S. Corbette, Y. LifX.Xief and D. Katoshevski, “Characterization of expiration air jets and droplet size distributions immediately at the mouth opening”. Journal of Aerosol Science, 40, issue 2, pp.122-133, 2009.
. S. Asadi et al., “Aerosol emission and superemission during human speech increase with voice loudness”. Sci. Rep. 9, 2348, 2019.
. W.F. Wells, “On-airborne infection - study II droplets and droplet nuclei”. Amer.J.Hyg, 20, pp.611-618, 1934.
. J. P. Duguid, “The size and the duration of air-carriage of respiratory droplets and droplet-nuclei”. J. Hyg. (Lond.), 44, pp.471–479, 1946.
. P. Bahl, C, Doolan, C. de Silva, A. A. Chughtai, L. Bourouiba, and C. R. MacIntyre. “Airborne or Droplet Precautions for Health Workers Treating Coronavirus Disease 2019?”. Journal of Infectious Diseases, pp.1-8, 2020.
. L. Bouroubia, “Turbulent Gas Clouds and Respiratory Pathogen Emissions – Potential Implications for Reducing Transmission of COVID-19”. Journal of American Medical Association, 323, 18, pp.1837-1838, 2020.
. J. Wei, and Y. Li, “Human Cough as Two-Jets and its Role in Particle Transport”. PL.SONE 12, 1, pp.1-15, 2017.
. F.M. White. Fluid Mechanics. University of Rhode Island: McGraw-Hill Higher Education, 2016, pp.59-85.
. P.J. Pritchard and J.W. Mitchell. Introduction to Fluid Mechanics. Kendallville: Wiley &Sons, Inc., 2015, pp.374-378.
. P.P Wegener, What makes airplanes fly?. New York: Springer-Verlag, 1991, pp.87-108.
. D.R.J Owen, C.R. Leonardi, and Y.T. Feng, Y. T. “An efficient framework for fluid-structure interaction using the lattice Boltzmann method and immersed moving boundaries”. International Journal for Numerical Methods in Engineering, 87 (1–5), pp.66–95, 2011.
. D.F. Griffths and D.J. Higham. Numerical methods for ordinary differential equations – initial value problems. New York: Springer-Verlag, 2010, pp.19-31.
. W. Sutherland. “LII. The viscosity of gases and molecular force”. Philosophical Magazine Series 5, 36:223, pp.507-531, 1893.
Downloads
Published
How to Cite
Issue
Section
License
Authors who submit papers with this journal agree to the following terms.
