ABSTRACT
This study aimed at estimating the transport dynamics of a single severe acute respiratory syndrome corona-virus 2 (SARS-CoV-2)-laden droplet of 1 to 500 µm in diameter at a wind speed from 1 to 4 m/s. Motion dynamics of SARS-CoV-2-laden respiratory droplets under calm or turbulent air conditions were quantified using a combined model. Dalton's law was implemented to estimate their evaporation. One-factor-at-a-time procedure was applied for the sensitivity analysis of model of deposition velocity. The transport distance of the single virus ranged from 167 to 1120 m as a function of the droplet size, wind speed, and falling time. The evaporation times of the droplets ≤ 3 and ≤ 14 µm in diameter were shorter than their settling times from 1.7 m in height at midnight and midday, respectively. Such droplets remained in the air for about 5 min as the droplet nuclei with SARS-CoV-2. The minimum transport distance of the respiratory droplets of 1-15 µm varied between 8.99 and 142 m at a wind speed range of 1-4 m/s, based on their deposition velocity. With their short transport distance, the larger droplet (30 to 500 µm) was not suspended in the air even under the windy conditions. The deposition velocity was found most sensitive to the droplet diameter. The droplets < 15 µm in diameter completely evaporated at midday and the droplet nuclei with the single virus can travel a minimum distance of 500 m under a horizontal wind speed of 3 m/s.
ABSTRACT
A simplified model has been devised to estimate the falling dynamics of severe acute respiratory syndrome corona-virus 2 (SARS-CoV-2)-laden droplets in an indoor environment. Our estimations were compared to existing literature data. The spread of SARS-CoV-2 is closely coupled to its falling dynamics as a function of respiratory droplet diameter (1 to 2000 µm) of an infected person and droplet evaporation. The falling time of SARS-CoV-2 with a respiratory droplet diameter of about 300 µm from a height of 1.7 m remained almost the same among the Newtonian lift equation, Stokes's law, and our simplified model derived from them so as to account for its evaporation. The evaporative demand peaked at midday which was ten times that at midnight. The evaporating droplets [Formula: see text] 6 µm lost their water content rapidly, making their lifetimes in the air shorter than their falling times. The droplets [Formula: see text] 6 µm were able to evaporate completely and remained in the air for about 5 min as droplet nuclei with SARS-CoV-2.
Subject(s)
Aerosols , Air Microbiology , Environmental Monitoring , SARS-CoV-2 , Humans , SARS-CoV-2/isolation & purificationABSTRACT
PURPOSE: The purpose of this study is to quantify the motion dynamics of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). METHODS: Three physical models of Newton's and Stokes's laws with(out) air resistance in the calm air are used to determine the falling time and velocity regimes of SARS-CoV-2 with(out) a respiratory water droplet of 1 to 2000 micrometers (µm) in diameter of an infected person of 0.5 to 2.6 m in height. RESULTS: The horizontal distance travelled by SARS-CoV-2 in free fall from 1.7 m was 0.88 m due to breathing or talking and 2.94 m due to sneezing or coughing. According to Newton's laws of motion with air resistance, its falling velocity and time from 1.7 m were estimated at 3.95 × 10-2 m s-1 and 43 s, respectively. Large droplets > 100 µm reached the ground from 1.7 m in less than 1.6 s, while the droplets ≥ 30 µm fell within 4.42 s regardless of the human height. Based on Stokes's law, the falling time of the droplets encapsulating SARS-CoV-2 ranged from 4.26 × 10-3 to 8.83 × 104 s as a function of the droplet size and height. CONCLUSION: The spread dynamics of the COVID-19 pandemic is closely coupled to the falling dynamics of SARS-CoV-2 for which Newton's and Stokes's laws appeared to be applicable mostly to the respiratory droplet size ≥ 237.5 µm and ≤ 237.5 µm, respectively. An approach still remains to be desired so as to better quantify the motion of the nano-scale objects.