Fluid dynamics of respiratory droplets in the context of COVID-19: Airborne and surfaceborne transmissions

Abstract

The World Health Organization has declared COVID-19 a global pandemic. Several countries have experienced repeated periods of major spreading over the last two years. Many people have lost their lives, employment, and the socioeconomic situation has been severely impacted. Thus, it is considered to be one of the major health and economic disasters in modern history. Over the last two years, several researchers have contributed significantly to the study of droplet formation, transmission, and lifetime in the context of understanding the spread of such respiratory infections from a fluid dynamics perspective. The current review emphasizes the numerous ways in which fluid dynamics aids in the comprehension of these aspects. The biology of the virus, as well as other statistical studies to forecast the pandemic, is significant, but they are not included in this review.

FIG. 1.

Schematic of droplet transmission ejected during sneezing and coughing. A typical conical jet flow of droplets during sneezing and coughing has a cone angle in the range of ${22}^{°}-{28}^{°}$.

FIG. 2.

Droplet size distributions during (a) coughing and (b) speaking presented in different studies. Reproduced with permission from Chao et al., “Characterization of expiration air jets and droplet size distributions immediately at the mouth opening,” J. Aerosol Sci. 40(2), 122–133 (2009). Copyright 2009 Elsevier.

FIG. 3.

The kinematics of saliva droplet cloud released from human cough showing the diameter of the droplets. Because of gravity forces, larger droplets settle faster than smaller ones. The entire mass of ejected saliva is 7.7 mg, with a total number of droplets of 1008 in total. The temperature, pressure, and relative humidity in the environment are 20 °C, 1 atm, and 50%, respectively, with the ground temperature at 15 °C. The ambient air is considered to be stationary in this study. Reproduced with permission from T. Dbouk and D. Drikakis, “On coughing and airborne droplet transmission to humans,” Phys. Fluids 32(5), 053310 (2020). Copyright 2020 AIP Publishing.

FIG. 4.

Comparison of the temporal variation of the normalized diameter of different initial size droplets of pure water with the water-salt solution. The initial temperature of the droplets is 36 °C. The values of the ambient temperature, RH, and wind speed are 30 °C, 0.84, and 2 m/s, respectively. Here, D_eq and D₀ represent the equivalent and initial diameter of the droplets, respectively. Reproduced with permission from Li et al., “Dispersion of evaporating cough droplets in tropical outdoor environment,” Phys. Fluids 32(11), 113301 (2020). Copyright 2020 AIP Publishing.

FIG. 5.

The effect of wind speeds of (a) 4 km/h and (b) 15 km/h on the transmission of saliva droplets. The wind is blowing from the left to the right, and the temperature and relative humidity are 20 °C and 50%, respectively. Reproduced with permission from T. Dbouk and D. Drikakis, “On coughing and airborne droplet transmission to humans,” Phys. Fluids 32(5), 053310 (2020). Copyright 2020 AIP Publishing.

FIG. 6.

Temporal variation of the (a) mean saliva droplet diameter D₁₀, (b) maximum saliva droplet diameter D_max and (c) liquid penetration distance, which is defined as the maximum distance a saliva liquid droplet with a 95% initial mass can travel. Reproduced with permission from T. Dbouk and D. Drikakis, “On coughing and airborne droplet transmission to humans,” Phys. Fluids 32(5), 053310 (2020). Copyright 2020 AIP Publishing.

FIG. 7.

Numerical simulations of a breath-generated aerosol plume in a turbulent boundary layer using a large eddy simulation (LES). (a) The transit of breath aerosol puffs is represented by contours of $C/C_o=0.01$, (b) Mean concentration contours for a light plume (warmer than ambient temperature of $0{\hspace{0.17em}}^{°}$C), (c) heavier plume (colder than ambient temperature of $42{\hspace{0.17em}}^{°}$C), and (d) the mean concentration along the streamwise direction at 1.5 m above ground (in meters). The best-fit power laws beyond the near-field region are also shown. The temperature of the exhaled breath was assumed to be $37{\hspace{0.17em}}^{°}$C. Reproduced with permission from R. Mittal, C. Meneveau, and W. Wu, “A mathematical framework for estimating risk of airborne transmission of COVID-19 with application to face mask use and social distancing,” Phys. Fluids 32(10), 101903 (2020). Copyright 2020 AIP Publishing.

FIG. 8.

The effect of ambient temperature and relative humidity on (a) maximum droplet spreading distance, (b) respiratory droplet aerosolization rate, (c) average aerosol particle diameter, and (d) total PM2.5 particle mass. Here, ambient temperature is varied from $0{\hspace{0.17em}}^{°}$C $-42{\hspace{0.17em}}^{°}$C and relative humidity is varied from $0-0.92$. Reproduced with permission from Zhao et al., “COVID-19: Effects of environmental conditions on the propagation of respiratory droplets,” Nano Lett. 20 (10), 7744–7750 (2020). Copyright 2020 American Chemical Society.

FIG. 9.

Filtration efficiency (FE) of an N95 respirator (black), the N95 base fabric (red), a surgical mask (blue), and a twill (magenta) as a function of particle mobility diameter (D_m). The basic sample is represented by solid bold lines, whereas the reneutralized samples are represented by dashing lines. The indigo starts to represent the twill FE as determined by an aerosol particle mass analyzer and reneutralization. In FE, the uncertainty is 5%. Reproduced with permission from Zangmeister et al., “Filtration efficiencies of nanoscale aerosol by cloth mask materials used to slow the spread of SARS-CoV-2,” ACS Nano 14(7), 9188–9200 (2020). Copyright 2020 American Chemical Society.

FIG. 10.

(a) People who use masks reduce respiratory droplet transmission while (partially) isolating themselves from coughing. The findings of a 5 s simulation time for a surgical mask with a 91% initial efficiency are provided. The temperature of the skin of the face is 32 °C, whereas the temperature of the mouth is 34 °C. In this simulation, there is no wind, the ambient temperature is 20 °C, the pressure is 1 atmosphere, and the relative humidity is 50%, (b) Variation of effective dynamic filter efficiency (η) with the number of cycles n of a coughing event, ${\eta }_1=90.4\%$. Reproduced with permission from T. Dbouk and D. Drikakis, “On respiratory droplets and face masks,” Phys. Fluids 32(6), 063303 (2020), Copyright 2020 AIP Publishing.

FIG. 11.

(a) Variation of the lifetime extension by number of factors as compared to the lifetime of a droplet behaving according to the Wells model with the relative humidity. (b) Relative humidity field at 600 ms when the ambient RH is 50% and 90%. Reproduced with permission from Chong et al., “Extended lifetime of respiratory droplets in a turbulent vapor puff and its implications on airborne disease transmission,” Phys. Rev. Lett. 126, 034502 (2021). Copyright 2021 American Physical Society.

FIG. 12.

(a) Concentration fields are displayed on a schematic of the car with a cut plane passing through the center of the interior compartment. (b) The bar graph illustrates the mass fraction of air that reaches the passenger from the driver. Standard deviation of the concentration field around the passenger is represented by the error bars. (c) The heatmaps displaying the concentration field of the species originating from the driver for various window situations. The line segment A–D is at the front of the car cabin, and the flow direction in panel C is from left to right. Open windows are represented by dashed lines, whereas closed windows are represented by solid lines. C₀ is the initial mass percentage of passive scalar at the injection site, with $C/C_0$ = 1. Reproduced with permission from Mathai et al., “Airflows inside passenger cars and implications for airborne disease transmission,” Sci. Adv. 7(1), eabe0166 (2021). Copyright 2021 American Association for the Advancement of Science.

FIG. 13.

Schematic of a sessile saliva droplet on a surface.

FIG. 14.

A comparison of the morphologies of the original droplets (top row) and their corresponding residues (bottom row) on different surfaces. Reproduced with the permission from He et al., “Droplet evaporation residue indicating SARS-CoV-2 survivability on surfaces,” Phys. Fluids 33(1), 013309 (2021). Copyright 2021AIP Publishing.

FIG. 15.

The survival time of various viruses on different surfaces.

FIG. 16.

(a) Variation in the droplet drying time with $\Psi$ at different values of the initial contact angle, θ₀. The rest of the parameters are initial volume, V₀ = 10 nL, T = 30 °C, and RH = 50%. (b) The variation of the normalized mass evaporation rate with the initial mass evaporation rate, $\dot{m}/{\dot{m}}_0$ vs $\Psi$. The rest of the parameters are $T={30}^{°}$C, RH = 50% and ${\theta }_0={50}^{°}$. Reproduced with permission from S. Balusamy, S. Banerjee, and K. C. Sahu, “Lifetime of sessile saliva droplets in the context of SARS-CoV-2,” Int. Commun. Heat Mass Transfer. 123, 105178 (2021). Copyright 2021 Elsevier.

FIG. 17.

(a) Regime maps depicting the droplet's lifetime in the $T-$ RH space. (a) ${\theta }_0={10}^{°}$, (b) ${\theta }_0={90}^{°}$. The colorbar represents the lifetime in second in the logarithmic scale. The rest of the parameters are $V_0=10$ nl, M = 0.154 mol/kg and $\Psi =20$. Reproduced with permission from S. Balusamy, S. Banerjee, and K. C. Sahu, “Lifetime of sessile saliva droplets in the context of SARS-CoV-2,” Int. Commun. Heat Mass Transfer 123, 105178 (2021). Copyright 2021 Elsevier.