Transmission of airborne virus through sneezed and coughed droplets

Abstract

The spread of COVID19 through droplets ejected by infected individuals during sneezing and coughing has been considered a matter of key concern. Therefore, a quantitative understanding of the propagation of droplets containing the virus assumes immense importance. Here, we investigate the evolution of droplets in space and time under varying external conditions of temperature, humidity, and wind flow by using laws of statistical and fluid mechanics. The effects of drag, diffusion, and gravity on droplets of different sizes and ejection velocities have been considered during their motion in air. In still air, we found that bigger droplets traverse a larger distance, but smaller droplets remain suspended in air for a longer time. Therefore, in still air, the horizontal distance that a healthy individual should maintain from an infected one is based on the bigger droplets, but the time interval to be maintained is based on the smaller droplets. We show that in places with wind flow, the lighter droplets travel a larger distance and remain suspended in air for a longer time. Therefore, we conclude that both temporal and geometric distance that a healthy individual should maintain from an infected one is based on the smaller droplets under flowing air, which makes the use of a mask mandatory to prevent the virus. Maintenance of only stationary separation between healthy and infected individuals is not substantiated. The quantitative results obtained here will be useful to devise strategies for preventing the spread of other types of droplets containing microorganisms.

FIG. 1.

The horizontal distance, L(t), traveled by the ejecta of mass 4186 ng (nano-g) from the source of infection as a function of time for different ejection velocities has been shown here. The droplets are ejected at a height of 1.7 m from the ground. The change in the height, H(t), with time of the droplet for initial velocity 21 m/s has also been depicted.

FIG. 2.

Variation in H with L for a droplet of 4186 ng mass and 100 μm radius for different ejection velocities.

FIG. 3.

The variation in the maximum horizontal distance (L_max) traveled by droplets as a function of radius for different ejection velocities.

FIG. 4.

The variation in the maximum time the droplets take to reach a height of 1 m from the ground (dashed line) and to hit the ground (solid line).