Assessing suspension and infectivity times of virus-loaded aerosols involved in airborne transmission

Abstract

Airborne transmission occurs through droplet-mediated transport of viruses following the expulsion of an aerosol by an infected host. Transmission efficiency results from the interplay between virus survival in the drying droplet and droplet suspension time in the air, controlled by the coupling between water evaporation and droplet sedimentation. Furthermore, droplets are made of a respiratory fluid and thus, display a complex composition consisting of water and nonvolatile solutes. Here, we quantify the impact of this complex composition on the different phenomena underlying transmission. Solutes lead to a nonideal thermodynamic behavior, which sets an equilibrium droplet size that is independent of relative humidity. In contrast, solutes do not significantly hinder transport due to their low initial concentration. Realistic suspension times are computed and increase with increasing relative humidity or decreasing temperature. By uncoupling drying and suspended stages, we observe that enveloped viruses may remain infectious for hours in dried droplets. However, their infectivity decreases with increasing relative humidity or temperature after dozens of minutes. Examining expelled droplet size distributions in the light of these results leads to distinguishing two aerosols. Most droplets measure between 0 and 40 µm and compose an aerosol that remains suspended for hours. Its transmission efficiency is controlled by infectivity, which decreases with increasing humidity and temperature. Larger droplets form an aerosol that only remains suspended for minutes but corresponds to a much larger volume and thus, viral load. Its transmission efficiency is controlled by droplet suspension time, which decreases with increasing humidity and decreasing temperature.

Keywords: aerosol; evaporation; infectivity; saliva; virus.

Fig. 1.

Phenomena involved in airborne transmission. Droplet evaporation is a key step of airborne transmission, and it depends on initial droplet size and environmental conditions (such as temperature and RH) but also, on fluid composition. The presence of nonvolatile solutes in respiratory fluid droplets notably sets an equilibrium size and can also impact drying kinetics. Droplet sedimentation, which determines the aerosol suspension time, is thus directly impacted by the evaporation of this complex fluid. Furthermore, viruses’ environment changes during drying, which can also impact their survival.

Fig. 2.

Sorption isotherm and equilibrium droplet size for saliva. (A) Experimentally determined saliva water sorption isotherm. A strong deviation from ideal binary mixtures (red line) is observed, similar to what is observed for polymer aqueous solutions. (B) Calculation of the equilibrium saliva droplet diameter from the sorption isotherm. We observe that the equilibrium size is nearly independent of RH up to 75% RH and corresponds to around 20% of the initial droplet size.

Fig. 3.

Mutual diffusion coefficient in saliva. (A) A schematic of the unidirectional drying setup used to measure concentration gradients building up upon drying saliva at controlled RH. (B) Typical concentration profiles obtained at RH $=$ 0% at two different times, rescaled by the space/time variable x $=$ distance/time${}^{(1/2)}$. (C) Fickian mutual diffusion coefficients obtained numerically from the two above concentration profiles. The orange line represents the best fit of these datasets, which is used in the following for calculations.

Fig. 4.

Evaporation of saliva droplets. (A) Scheme of a droplet drying setup, where a liquid droplet is deposited on a superhydrophobic Teflon-thiolated nanosilver coating and surrounded by an airflow of controlled RH. (B) Ten-milligram droplet drying kinetics for both water and saliva at RH $=$ 0% and numerical calculations using the experimentally determined diffusion coefficient obtained in Fig. 3. The agreement supports the validity of our modeling. (C) Modeled droplet evaporation for water and saliva droplets at different RHs, showing that solutes impact evaporation times only at the end of the process. (D) Evaporation times for water, saliva, and saliva-like fluids at either lower or higher solute concentration for two droplet sizes. Evaporation is increasingly slowed down upon increasing solute concentration, which can be the case in the lower respiratory tract. Still, the effect is mostly observed at the end of the drying process. (E) Evaporation time for water droplets (black lines) and saliva (red dots) at increasing RHs (10, 25, 50, 75%).

Fig. 5.

Sedimentation times of evaporating droplets. Sedimentation times for droplets that do not evaporate (red line), instantly evaporate (green lines), or evaporate as they fall (blue lines) as a function of RH (10, 25, 50, 75%). An intermediate region is observed where sedimentation times increase by an order of magnitude, and its position depends on RH and temperature (SI Appendix, Figs. S4 and S5).

Fig. 6.

Virus survival with RH and temperature (T) in drying aerosols. (A) Two different stages should be considered to evaluate virus survival; the first stage involves water evaporation, while the second stage corresponds to equilibrated droplets that remain suspended in the air. (B) $\varphi$6 survival (percentage of viruses that remain infectious) in dried saliva droplets at RH $=$ 0% at t $=$ 17 and 37 min, which correspond to drying times for droplet diameters of 2.12 and 4.13 mm, respectively. The two orange points represent the means of each data series, with the error bars representing the typical SDs. (C) Drying pathways corresponding to a different stage 1, drying at RH $=$ 0%, and then, equilibration to 60% or direct drying at RH $=$ 60% but the same stage 2. (D) Corresponding virus viability, which shows that the two pathways yield similar results. (E) A general description of the protocol composed of two stages. Stage 1 corresponds to the water evaporation from 5-µL saliva droplets at RH $=$ 0%. In stage 2, once the thermodynamic equilibrium is reached upon evaporation (t $=$ 15 min), the dried droplets are equilibrated at different RHs (0, 60, and 80%). (F) Virus viability was determined as a function of time and RH in stage 2. (G) $\varphi$6 viability in dried saliva droplets of 5 µL at RH $=$ 0% as a function of time at three different temperatures: 1 °C, 22 °C, and 37 °C. (H) $\varphi$6 viability in liquid saliva as a function of time and at three different temperatures: 15 °C, 22 °C, and 37 °C. (I) Summary figure from panels E–H displaying virus survival after 75 min at T $=$ 22 °C. A nonmonotonic RH dependence of virus survival is observed, while survival also overall decreases with increasing temperature.

Fig. 7.

Two distinct aerosols matter for airborne transmission. (A) Volume size distributions recalculated from Johnson et al. (17) using data from Fig. 2 for aerosols emitted through speaking or coughing. (B) Isosedimentation times curves obtained from Fig. 5. Two distinct aerosol populations can be identified: a population of numerous droplets (77% in number) but of a very small overall volume, emitted mainly in the larynx, that can remain suspended for hours (hence, termed hours aerosol) and a population representing a much larger volume emitted in the oral cavity that can remain suspended for minutes (hence, termed minutes aerosol). The gray area recalls that virus viability at longer times is compromised upon increasing RH, as shown in Fig. 6. Note that RH decreases aerosol suspension time, notably for the minutes aerosol over the whole RH range, while the hours aerosol is only impacted at very high RH consistently with the sorption isotherm displayed in Fig. 2.