Fluid dynamics of COVID-19 airborne infection suggests urgent data for a scientific design of social distancing

The COVID-19 pandemic underscored the critical role of airborne transmission in disease spread. While social distancing is a key mitigation strategy, its scientific basis remains inadequately defined. The dispersal of virus-containing respiratory droplets during coughing, sneezing, speaking, and breathing is a complex process involving fluid dynamics, evaporation, and the infectivity of the virus. This study addresses the significant uncertainties in predicting the reach and infectious potential of these droplets. The lack of consistent data regarding the initial size distribution of exhaled droplets and the infectiousness of viruses residing on dried nuclei presents a major hurdle in developing robust social distancing strategies. This research aims to quantify the impact of these uncertainties on predictions of airborne viral transmission and proposes two key areas requiring urgent attention: (1) a precise characterization of the initial size distribution of exhaled droplets, and (2) an understanding of how viral infectivity changes depending on whether the virus is carried on a liquid droplet or a dry nucleus. The implications of resolving these knowledge gaps are far-reaching, as they are fundamental to the establishment of evidence-based social distancing rules globally, potentially influencing billions of individuals.

Existing literature on respiratory droplet size distributions reveals significant inconsistencies. Studies using different experimental techniques and ambient conditions report vastly different percentages of submicron droplets following a cough event. For example, while some studies report a predominance of submicron droplets (97%), others show a much smaller percentage (less than 4%), and some even fail to detect any droplets within this size range. This discrepancy is attributed to incomplete understanding of respiratory droplet formation physics, diverse experimental setups, and variations in reporting practices. Similarly, research on the infectious potential of viruses carried on dried nuclei shows conflicting evidence. While some studies suggest that viruses with lipid membranes, like SARS-CoV-2, retain infectivity longer at lower humidity, others present counterexamples. This ambiguity concerning both the initial droplet size and the infectivity of dry versus wet droplets creates substantial uncertainty in predicting the effectiveness of disease transmission mitigation strategies.

This study employs advanced direct numerical simulations (DNS) of airflow and humidity to track the position and evaporation of thousands of respiratory droplets emitted during a cough. The airflow is modeled using the incompressible Navier-Stokes equations, while the supersaturation field is modeled with an advection-diffusion equation. A Lagrangian model tracks the position and evaporation of individual droplets using a stochastic model, incorporating Brownian motion, gravity, and droplet evaporation based on the surrounding humidity. The droplets are assumed to be composed of salty water and an insoluble solid component, reflecting the composition of real respiratory droplets. The simulations consider eight scenarios, combining two ambient relative humidity levels (60% and 40%) with four initial droplet size distributions from the literature. The computational domain is discretized using a high-resolution finite-difference method, with approximately 0.3 billion grid points. The researchers track both the cumulative viral load (assuming it is proportional to initial droplet volume) carried on liquid droplets versus dry nuclei, and the number of droplets that reach the ground. The simulations are validated against theoretical predictions for turbulent puff growth, and grid resolution convergence is also verified.

The simulations reveal striking differences in predictions based on initial droplet size distributions and ambient humidity. Specifically: 1. **Sedimentation:** For some initial conditions, almost all viral load settles to the ground within 1–3 seconds, while for others, none settles during the simulation time. The amount of viral load lost to sedimentation varies dramatically depending on both humidity and the initial size distribution. Drier conditions result in greater spreading of larger droplets. 2. **Airborne Transport:** The distance traveled by airborne droplets varies widely, ranging from less than 2.5 meters to more than 7.5 meters depending on initial conditions. The distribution of evaporation times also varies significantly across scenarios, indicating that the cloud of droplets expands at different rates. The amount of viral load reaching distances of 1, 2, and 4 meters differs substantially across the various conditions, even when only considering droplets smaller than 10 µm in diameter. These smaller droplets are of particular concern due to their potential to reach the pulmonary alveoli. 3. **Long-Range Transmission:** Even without external airflow, small droplets travel several meters, with the extent of travel depending strongly on the initial conditions. Extracting the trajectory of the viral load's center of mass, a simple extrapolation in the absence of external airflow estimates the distance traveled by small droplets; variations ranged from less than 2.5 m to more than 7.5 m. The study quantifies these observations by tracking the relative viral load carried by each droplet and determining the cumulative viral load reaching specific distances. These data highlight the substantial uncertainty in current predictions. For example, the percentage of viral load reaching 4 meters or more varies from as much as 10% to as little as 10⁻⁴%.

The findings challenge the current 1–2 meter social distancing guidelines, as the simulations demonstrate that predictions vary drastically depending on poorly understood factors such as initial droplet size distribution and ambient relative humidity. The results underscore the critical need for more precise experimental data to address the two key uncertainties: the precise characterization of the initial size distribution of exhaled droplets and the infectious potential of viruses on dry versus wet nuclei. While this study focuses on the fluid mechanics of droplet dispersion, further research must integrate this knowledge with epidemiological and virological data to create more accurate models of transmission risk. Factors such as the total viral load emitted per individual, and the infectious dose of SARS-CoV-2 are essential for connecting the relative viral load computed in this study with actual infection probabilities. The environment's impact on droplet transport and evaporation is also crucial, requiring environmental factors (such as ventilation) to be included in more refined models. This comprehensive approach could lead to more tailored social distancing recommendations that consider the specific environments involved.

This study reveals significant uncertainties in predicting COVID-19 airborne transmission risk due to incomplete knowledge of exhaled droplet size distributions and the infectiousness of viruses carried on dry versus wet nuclei. The results strongly suggest that a single social distancing guideline may not be sufficient across various environments and conditions. Future research should prioritize refining experimental measurements of droplet size distributions, understanding the infectivity of dry nuclei, and integrating the findings with epidemiological data. This will pave the way for scientifically grounded social distancing strategies.

The simulations assume a simplified cough model and do not account for external airflows, which become significant in the long term. The model also assumes that viral load is proportional to initial droplet volume and neglects any viral degradation. While a significant number of particles are simulated, the inherent variability in individual coughs and the complexity of real-world environments mean that these results represent a range of possibilities rather than a definitive answer. This study focuses on a single type of expiratory event (coughing); further studies investigating other modes of expulsion (e.g. sneezing and breathing) will be necessary to gain a complete understanding of airborne transmission dynamics.