Reducing chances of COVID-19 infection by a cough cloud in a closed space

Abstract

The cough of a COVID-19 infected subject contaminates a large volume of surrounding air with coronavirus due to the entrainment of surrounding air in the jet-like flow created by the cough. In the present work, we estimate this volume of the air, which may help us to design ventilation of closed spaces and, consequently, reduce the spread of the disease. Recent experiments [P. P. Simha and P. S. M. Rao, "Universal trends in human cough airflows at large distances," Phys. Fluids 32, 081905 (2020)] have shown that the velocity in a cough-cloud decays exponentially with distance. We analyze the data further to estimate the volume of the cough-cloud in the presence and absence of a face mask. Assuming a self-similar nature of the cough-cloud, we find that the volume entrained in the cloud varies as $V=0.666c^2{d}_c^3$ , where c is the spread rate and d _c is the final distance traveled by the cough-cloud. The volume of the cough-cloud without a mask is about 7 and 23 times larger than in the presence of a surgical mask and an N95 mask, respectively. We also find that the cough-cloud is present for 5 s-8 s, after which the cloud starts dissipating, irrespective of the presence or absence of a mask. Our analysis suggests that the cough-cloud finally attains the room temperature, while remaining slightly more moist than the surrounding. These findings are expected to have implications in understanding the spread of coronavirus, which is reportedly airborne.

FIG. 1.

Schematic of the cough cloud generated by a human subject. The volume of the cloud increases with time due to the entrainment of the surrounding air into it.

FIG. 2.

Front position as a function of time. The front position is compared for the three cases: No mask, surgical mask, and N95 mask.

FIG. 3.

Lateral velocity as a function of the radial coordinate in the cough-cloud at 0.3 m from the origin.

FIG. 4.

Volume of the cloud as a function of distance from the origin. The data for without a face mask are shown in the main plot, while those with the face mask are shown in the inset.

FIG. 5.

Temperature and relative humidity (RH) in the cloud as a function of distance from the origin. The plots of the RH are shown for three different values of RH of the room.