Short-range exposure to airborne virus transmission and current guidelines

Abstract

After the Spanish flu pandemic, it was apparent that airborne transmission was crucial to spreading virus contagion, and research responded by producing several fundamental works like the experiments of Duguid [J. P. Duguid, J. Hyg. 44, 6 (1946)] and the model of Wells [W. F. Wells, Am. J. Hyg. 20, 611-618 (1934)]. These seminal works have been pillars of past and current guidelines published by health organizations. However, in about one century, understanding of turbulent aerosol transport by jets and plumes has enormously progressed, and it is now time to use this body of developed knowledge. In this work, we use detailed experiments and accurate computationally intensive numerical simulations of droplet-laden turbulent puffs emitted during sneezes in a wide range of environmental conditions. We consider the same emission-number of drops, drop size distribution, and initial velocity-and we change environmental parameters such as temperature and humidity, and we observe strong variation in droplets' evaporation or condensation in accordance with their local temperature and humidity microenvironment. We assume that 3% of the initial droplet volume is made of nonvolatile matter. Our systematic analysis confirms that droplets' lifetime is always about one order of magnitude larger compared to previous predictions, in some cases up to 200 times. Finally, we have been able to produce original virus exposure maps, which can be a useful instrument for health scientists and practitioners to calibrate new guidelines to prevent short-range airborne disease transmission.

Keywords: COVID-19; SARS-CoV-2; airborne; infectious disease; public health.

Fig. 1.

Distance traveled by the front of the jet: comparison between simulations (red dots) and experiments (blue dots). For experiments, data are obtained from seven independent realizations, and error bars corresponding to the SD are also shown. The two stages that characterize the sneezing event, jet (early stage) and puff (late stage), are clearly visible; the scaling laws for the jet, $L\propto t^{1/2}$, and puff phase, $L\propto t^{1/4}$, are reported as reference with black dashed lines. Both simulations and experiments exhibit a very similar behavior and are in excellent agreement. (Insets) Qualitative visualizations obtained from experiments showing the instantaneous tracers concentration (black, high; white, low) at different times ($t=0.25\hspace{0.17em}\text{s}$, $t=0.50\hspace{0.17em}\text{s}$, $t=0.75\hspace{0.17em}\text{s}$, and $t=1.00\hspace{0.17em}\text{s}$) are reported as representative of the jet/puff evolution.

Fig. 2.

Snapshots of the sneezing event at $t=0.25\hspace{0.17em}\text{s}$ (A and C) and $t=0.50\hspace{0.17em}\text{s}$ (B and D), where $t=0$ represents the beginning of the respiratory event. A and B refer to $T=5\hspace{0.17em}°\text{C}$ and $RH=90\%$, while C and D refer to $T=20\hspace{0.17em}°\text{C}$ and $RH=50\%$. The background shows the local value of the relative humidity (white, low; black, high). The respiratory droplets are displayed rescaled according to their size (not in real scale) and are also colored according to their size (red, small; white, large). We can appreciate how most droplets move together with the turbulent gas cloud generated by the sneezing jet. This cloud is characterized by a much larger value of RH with respect to the ambient. In addition, for $T=5\hspace{0.17em}°\text{C}$ and $RH=90\%$ (A and B), a wide region is characterized by supersaturated conditions ($RH>100\%$).

Fig. 3.

(Right) Time required by the respiratory droplets to complete the evaporation process in the four ambient conditions tested: $T=5$ °C and $RH=50\text{to}90\%$ (A and B) and $T=20$ °C and $RH=50\text{to}90\%$ (C and D). (Left) The sample plot on the left provides at-a-glance guidance on how to read A−D. In particular, for any given initial diameter, the leftmost side of the distribution indicates the shortest evaporation time, while the rightmost side of the distribution marks the longest evaporation time observed for droplets with a certain initial diameter. The color of the distribution represents the probability (blue, low; yellow, high) of having a certain evaporation time. Empty black dots represent the mean evaporation time obtained from the simulation data. The predicted evaporation time obtained from the $d^2$ law (12), a model currently employed for the definition of public health guidelines, is reported with a solid red line as a function of the droplet diameter. According to the model prediction, all droplets should evaporate within the time prescribed by the red line; thus the gray-shaded area below the red line should be empty (i.e., droplets should have already evaporated to dry nuclei). Simulations results, however, show a completely different picture, and, for all ambient conditions, droplets evaporate well beyond the predicted time. This reflects the action of turbulence and of moist air released during the sneeze, which largely slows down the evaporation. These effects are very pronounced for the low-temperature/high-humidity case (B), where only a fraction of droplets smaller than $10-\mathrm{\mu }\text{m}$ completely evaporates to a dry nucleus within $2.5\hspace{0.17em}\text{s}$. For the other cases (A, C, and D), small droplets (less than 20 μm to $40\hspace{0.17em}\mathrm{\mu }\text{m}$) complete the evaporation process, and the formation of droplet nuclei can be appreciated.

Fig. 4.

Virus exposure (violet, low; green, high) for the four ambient conditions simulated: $T=5$ °C and $RH=50\text{to}90\%$ (A and B) and $T=20$ °C and $RH=50\text{to}90\%$ (C and D). Exposure is defined as the number of virus copies (virions) that go past a control area in different locations of the domain. The results are shown normalized by the total number of virus copies ejected during a sneeze. The dimensional concentration of virus copies can be obtained by multiplying the normalized exposure data for the viral load and the ejected liquid volume ($\simeq 0.01\hspace{0.17em}\text{mL}$ in the present simulations). We can observe the presence of a core region characterized by a high level of virus exposure, which is mainly determined by the large droplets (100 microns or more). These droplets follow almost ballistic paths and settle to the ground within $\simeq 1.25\hspace{0.17em}\text{m}$. This core region is surrounded by a wider region characterized by a lower level of virus exposure. Although, in this outer region, the value of exposure is smaller, a susceptible individual is still exposed to thousands of virus copies (here we consider an average viral load for SARS-CoV-2 of $7\times 10^6$ copies per mL). According to the independent action hypothesis, the presence of thousands of virus copies in the small droplets and droplet nuclei poses a significant threat on both the short- and long-range airborne transmission routes of SARS-CoV-2.