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

The study addresses how respiratory droplets emitted during a cough disperse, evaporate, and transport viral load, with the goal of informing scientifically grounded social distancing rules. It highlights two unresolved issues: (I1) the need for robust characterization of exhaled droplet size distributions across expiratory activities (coughing, speaking, breathing, sneezing), for which literature reports are inconsistent; and (I2) whether viruses that remain on dry nuclei after droplet evaporation retain full infectivity, which may depend on ambient relative humidity. The authors aim to quantify how uncertainties in initial droplet size distributions and ambient humidity affect predictions of viral-load transport and deposition, using high-fidelity simulations to track droplet motion and evaporation in cough-generated turbulent puffs.

Classical works (Flügge; Wells; Duguid) established the importance of droplet size for airborne transmission. Subsequent experimental studies reported widely divergent droplet size distributions at emission. For cough, Zayas et al. reported approximately 97% of droplets in the sub-micron range, Yang et al. reported less than 4% in that range, and Duguid observed none, reflecting methodological differences, varied ambient conditions, incomplete data reporting, and individual variability. This inconsistency undermines predictive modeling of dispersal. Regarding infectivity post-evaporation, evidence suggests lipid-enveloped viruses can persist longer at low RH, implying enhanced survival on dry nuclei, although counterexamples exist (e.g., discussed by Yang and Marr). These gaps (I1, I2) propagate uncertainty in transmission risk estimates and in the scientific basis for social distancing.

The authors perform direct numerical simulations (DNS) of a cough-generated turbulent airflow coupled with Lagrangian tracking and evaporation of thousands of droplets. The airflow solves the incompressible Navier–Stokes equations and an advection–diffusion equation for supersaturation (s = RH − 1). The computational domain is 4 m (x) × 1.25 m (y) × 2.5 m (z). Air is initially quiescent; a cough is injected through a mouth opening at z = 1.6 m with area 4.5 cm², using a 0.4 s exhalation profile with peak velocity 13 m/s (Re ≈ 9 × 10³), based on Gupta et al. Boundary conditions include no-slip at bottom and inlet, free-slip at top, convective outlet downstream, and periodic lateral boundaries. Exhaled air is saturated (s = 0), ambient supersaturation corresponds to set RH. Droplet dynamics: Droplets are initialized at rest within a 1 cm sphere at the mouth, with sizes sampled from literature distributions. Their motion follows a Lagrangian particle model with Stokes drag, gravity, and Brownian noise; droplet volume fraction is small enough to neglect two-way coupling. Droplets are modeled as salty water (water + NaCl) plus insoluble mucus, with evaporation/condensation governed by a condensational growth model that accounts for Kelvin and Raoult effects and crystallization below efflorescence RH (CRH). In Wet cases (RH = 60%), droplets reach an equilibrium liquid size; in Dry cases (RH = 40%), droplets fully evaporate to dry nuclei with radius about 16% of initial radius. Viral load per droplet is assumed proportional to initial volume and conserved during evaporation (no inactivation modeled), consistent with reports of SARS-CoV-2 persistence in respirable aerosols over many hours. Scenarios: Eight simulations combine two ambient RH levels (Wet: 60%; Dry: 40%) with four initial droplet size distributions: Duguid (Du), Johnson et al. (Jo), Xie et al. (Xi), and Yang et al. (Ya), labeled WetDu, WetJo, WetXi, WetYa, and DryDu, DryJo, DryXi, DryYa. Droplet positions, sizes, and cumulative viral load metrics are tracked over 60 s. Additional analyses include distances to ground upon sedimentation, viral load crossing planes at 1, 2, and 4 m, evaporation time distributions, the center-of-mass (CM) trajectory of airborne viral load, and extrapolated long-range travel in the absence of external flows (using puff decay scaling: puff length ~ t^{1/4}, mean velocity decay ~ t^{-3/4}). Numerical implementation uses a finite-difference DNS solver (Fujin) with second-order Adams–Bashforth time-stepping, FFT-based Poisson solver, MPI parallelization, and uniform grid spacing of 3.5 mm (~0.3 billion grid points). Convergence checks and validation against turbulent puff theory are provided.

- Initial droplet size distribution and ambient RH lead to diametrically opposed predictions for transmission risk and reach. - Sedimentation (ballistic loss): Within the first 1–3 s, viral load reaching the ground varies widely. Wet cases (RH 60%): approximately 99% (Du, Jo), 45% (Xi), and 0% (Ya) of viral load settles; Dry cases (RH 40%): about 94% (Du), 61% (Jo), 12% (Xi), and 0% (Ya). Few large droplets can carry most viral load despite representing a small fraction of droplet count, making droplet-count metrics misleading. - Landing distance of large droplets: For Duguid distribution, large droplets land within ~1 m in Wet conditions vs nearly ~3 m in Dry conditions, demonstrating enhanced spread at lower RH. - Airborne transport (inertial regime): Cumulative viral load crossing planes differs dramatically by scenario. At 4 m within 60 s, up to ~10% of total viral load (DryYa) vs as low as ~0.0001% (WetJo) reaches that distance. Even when considering droplets <10 µm, large uncertainties persist across scenarios. - Evaporation times and cloud dynamics: Evaporation time distributions and droplet cloud expansion rates depend strongly on initial sizes and RH; mean evaporation times differ by ~80% across conditions. At long times, droplets behave as tracers and puff size grows ~ t^{1/4}. - Long-range transmission (tracer regime): Extrapolating the CM trajectory of airborne viral load (no external airflow) indicates small droplets can travel several meters; the CM reaches the floor in about 20 minutes. Estimated horizontal spread ranges from <2.5 m (WetJo) to >7.5 m (DryYa). In Dry conditions, viral load reaches the floor as dry nuclei; in Wet conditions, viruses travel on liquid droplets. - Overall, three contrasting outcomes emerge across plausible inputs: (1) most vs none of the viral content settles within 1–2 m; (2) viruses carried entirely on dry nuclei vs on liquid droplets; (3) small droplets travel less than 2.5 m vs more than 7.5 m.

The findings directly address how uncertainties in droplet size distributions at emission (I1) and infectivity on dry nuclei (I2) impact the scientific basis for social distancing. Simulations show that plausible literature-based size distributions and modest changes in ambient RH can yield opposite conclusions regarding near-field deposition, airborne transport distances, and whether viruses ride on dry nuclei or liquid droplets. Consequently, one-size-fits-all distancing recommendations (e.g., 1–2 m) may be insufficient in certain environments, particularly at low RH where droplets evaporate to nuclei and persist aloft. The results emphasize that reliable infection risk models must integrate accurate droplet size distributions, evaporation physics, and environmental humidity, and should be coupled with virological data on infectivity post-evaporation. The study highlights that airborne transmission risk is highly context-dependent and underscores the need for environment-specific assessments that include ventilation and ambient flows for long-time behavior.

This work uses high-fidelity simulations to quantify how cough-generated droplets disperse and evaporate, demonstrating that current knowledge gaps produce fundamentally different predictions for viral-load deposition and airborne reach. The main contributions are: (i) revealing the decisive role of initial droplet size distribution and ambient RH in determining near-field settling, airborne transport, and long-range travel; and (ii) providing quantitative metrics (e.g., viral load crossing 1–4 m planes, sedimentation fractions, CM travel distances) across eight scenarios. The authors call for urgent experimental efforts to (1) rigorously characterize exhaled droplet size distributions across expiratory activities, and (2) determine the infectious potential of viruses on dry nuclei versus liquid droplets. Future work should incorporate specific environmental airflows and ventilation, extend to longer times, and integrate virological parameters (e.g., infectious dose, viral decay) to refine risk assessments and inform environment-tailored social distancing and mitigation strategies.

- External airflow and ventilation are not modeled; simulations consider only airflow generated by the cough, which is valid at early times but limits long-time predictions in real environments. - Viral load is assumed proportional to initial droplet volume and conserved during evaporation; no viral decay or inactivation dynamics are included. - Infectivity differences between dry nuclei and liquid droplets are unknown and not resolved, contributing to uncertainty in risk interpretation. - Results depend strongly on the chosen initial droplet size distributions from literature, which are inconsistent across studies. - Simulations focus on cough; other expiratory activities (speaking, breathing, sneezing) may have different dynamics and size distributions. - Domain and observation time (60 s) necessitate extrapolation for long-range travel estimates; boundary effects are minimized but not entirely eliminated. - Two-way coupling (droplet feedback on flow) is neglected due to low liquid volume fraction; coagulation and interactions between droplets are not modeled.