Falling Dynamics of SARS-CoV-2 as a Function of Respiratory Droplet Size and Human Height

Abstract

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.