On coughing and airborne droplet transmission to humans

Abstract

Our understanding of the mechanisms of airborne transmission of viruses is incomplete. This paper employs computational multiphase fluid dynamics and heat transfer to investigate transport, dispersion, and evaporation of saliva particles arising from a human cough. An ejection process of saliva droplets in air was applied to mimic the real event of a human cough. We employ an advanced three-dimensional model based on fully coupled Eulerian-Lagrangian techniques that take into account the relative humidity, turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet-droplet and droplet-air interactions. We computationally investigate the effect of wind speed on social distancing. For a mild human cough in air at 20 °C and 50% relative humidity, we found that human saliva-disease-carrier droplets may travel up to unexpected considerable distances depending on the wind speed. When the wind speed was approximately zero, the saliva droplets did not travel 2 m, which is within the social distancing recommendations. However, at wind speeds varying from 4 km/h to 15 km/h, we found that the saliva droplets can travel up to 6 m with a decrease in the concentration and liquid droplet size in the wind direction. Our findings imply that considering the environmental conditions, the 2 m social distance may not be sufficient. Further research is required to quantify the influence of parameters such as the environment's relative humidity and temperature among others.

FIG. 1.

Initial saliva droplet’s size distribution. The red curve was obtained using Eq. (1). The error is approximately 6%.

FIG. 2.

Human mouth-print during a cough period of 0.12 s captured with a high-speed camera. A rectangular sheet-like mouth-print cross section is observed at 0.07 s, corresponding to the maximum mouth opening.

FIG. 3.

A 2D sketch of the 3D computational domain grid meshed with an advanced technique employing a hexahedral non-uniform structured mesh (≈0.5 × 10⁶ for 2 W). The mesh is very refined at the mouth-print and is gradually coarsened in the streamwise cough flow direction with multilevel refinement. Two computational domains were considered at H = 3 m, W = 1 m, and L = (4 and 6) m. The mouth-print is at z = 1.63 m.

FIG. 4.

Saliva droplet cloud kinematics and dispersion show the carrier fluid flow velocity magnitude from a human cough. Wind speed ≈ 0. The total mass of ejected saliva is 7.7 mg, with 1008 total number of droplets. The environment is at ambient temperature, pressure, and relative humidity of 20 °C, 1 atm, and 50%, respectively, with the ground temperature at 15 °C and mouth temperature at 34°. The saliva droplets reach a horizontal distance of 30 cm from the mouth at t = 250 ms.

FIG. 5.

Saliva droplet cloud kinematics show the diameter of the droplets resulting from a human cough. Larger droplets settle more rapidly than smaller ones due to gravitational forces. Wind speed ≈ 0. The total mass of ejected saliva is 7.7 mg, with 1008 total number of droplets. The environment is at ambient temperature, pressure, and relative humidity of 20 °C, 1 atm, and 50%, respectively, with the ground temperature at 15 °C.

FIG. 6.

Saliva droplet cloud kinematics show the diameter droplet resulting from a human cough. Larger droplets settle more rapidly than smaller ones due to gravity. Wind speed ≈ =0. The total mass of ejected saliva is 7.7 mg, with 1008 total number of droplets. The environment is at ambient temperature, pressure, and relative humidity of 20 °C, 1 atm, and 50% with the ground temperature at 15 °C.

FIG. 7.

A human cough: saliva droplet’s disease-carrier particles cannot travel more than 2 m in space at approximately zero wind speed. The environment is at ambient temperature, pressure, and relative humidity of 20 °C, 1 atm, and 50%, respectively, with the ground temperature at 15 °C and mouth temperature at 34 °C.

FIG. 8.

A human cough: saliva droplet’s disease-carrier particles may travel in the air medium to unexpected considerable distances depending on the environmental conditions. This figure shows the effect of wind speed on the saliva droplet and transport under dispersion and evaporation. Wind blowing from left to right at speeds of 4 km/h (a) and 15 km/h (b). The environment is at ambient temperature, pressure, and relative humidity of 20 °C, 1 atm, and 50%, respectively, with the ground temperature at 15 °C.

FIG. 9.

A human cough: mechanisms of airborne saliva droplet’s transport, breakup, dispersion, and evaporation. This figure shows different cloud kinematics (elongation and rotation) depending on the wind shearing force; the gravitational or settling forces; and the evaporation rates. Wind blowing from left to right at speeds of (a) 4 km/h and (b) 15 km/h. The environment is at ambient temperature, pressure, and relative humidity of 20 °C, 1 atm, and 50%, respectively, with the ground temperature at 15 °C.

FIG. 10.

Variation of saliva droplet diameter, which represents 10% of droplets being smaller than their corresponding initial size.

FIG. 11.

Variation of the maximum saliva droplet diameter, Dp_max, with time.

FIG. 12.

Liquid penetration distance: maximum distance traveled by a saliva liquid droplet made of 95% initial mass.

FIG. 13.

Saliva droplet’s mass reduction with reference to the initial mass.