Short-range airborne route dominates exposure of respiratory infection during close contact

Abstract

AbstractA susceptible person experiences the highest exposure risk of respiratory infection when he or she is in close proximity with an infected person. The large droplet route has been commonly believed to be dominant for most respiratory infections since the early 20th century, and the associated droplet precaution is widely known and practiced in hospitals and in the community. The mechanism of exposure to droplets expired at close contact, however, remains surprisingly unexplored. In this study, the exposure to exhaled droplets during close contact (< 2 m) via both the short-range airborne and large droplet sub-routes is studied using a simple mathematical model of expired flows and droplet dispersion/deposition/inhalation, which enables the calculation of exposure due to both deposition and inhalation. The short-range airborne route is found to dominate at most distances studied during both talking and coughing. The large droplet route only dominates when the droplets are larger than 100 μm and when the subjects are within 0.2 m while talking or 0.5 m while coughing. The smaller the exhaled droplets, the more important the short-range airborne route. The large droplet route contributes less than 10% of exposure when the droplets are smaller than 50 μm and when the subjects are more than 0.3 m apart, even while coughing.Practical implicationsOur simple but novel analysis shows that conventional surgical masks are not effective if most infectious viruses are contained in fine droplets, and non-conventional intervention methods such as personalised ventilation should be considered as infection prevention strategies given the possible dominance of the short-range airborne route, although further clinical evidence is needed.NomenclatureSubscripti Droplets of different diameter groups (i = 1, 2, …, N)LD Large droplet routeSR Short-range airborne routeSymbolsA0 Area of source mouth [m2]AE Aspiration efficiency [-]Ar0 Archimedes number [-]bg Gaussian half width [m]bt Top-hat half width [m]CD Drag coefficient [-]CI Specific heat of liquid [J•kg-1•K-1]Cs Specific heat of solid [J•kg-1•K-1]CT Correction factor for diffusion coefficient due to temperature dependence [-]dd Droplet diameter [m]dd0 Droplet initial diameter [m]de1 Major axis of eye ellipse [m]de2 Minor axis of eye ellipse [m]dh Characteristic diameter of human head [m]dm Mouth diameter [m]dn Nostril diameter [m]D∞ Binary diffusion coefficient far from droplet [m2•s-1]DE Deposition efficiency [-]eLD Exposure due to large droplet route [μL]eSR Exposure due to short-range airborne route [μL]g Gravitational acceleration [m•s-2]Iv Mass current [kg•s-1]IF Inhalation fraction [-]Kc Constant (=0.3) [-]Kg Thermal conductivity of air [W•m-1•K-1]LS Exposure ratio between large droplet and short-range airborne [-]Lv Latent heat of vaporization [J•kg-1]md Droplet mass [kg]mI Mass of liquid in a droplet [kg]ms Mass of solid in a droplet [kg]M0 Jet initial momentum [m4•s-2]MW Molecular weight of H2O [kg•mol-1]MF Membrane fraction [-]n Number of droplets [n]n0 Number of droplets expelled immediately at mouth [n]Nin Number of droplets entering the inhalation zone [n]Nm Number of droplets potentially deposited on mucous membranes [n]Nt Total number of released droplets [n]Nu Nusselt number [-]p Total pressure [Pa]pv∞ Vapour pressure distant from droplet surface [Pa]pvs Vapour pressure at droplet surface [Pa]Qjet Jet flow rate [m3•s-1]r Radial distance away from jet centreline [m]rd Droplet radius [m]R Radius of jet potential core [m]Rg Universal gas constant [J•K-1•mol-1]s Jet centreline trajectory length [m]Sin Width of region on sampler enclosed by limiting stream surface [m]Sh Sherwood number [-]Stc Stokes number in convergent part of air stream [-]Sth Stokes number for head [-]Stm Stokes number for mouth [-]t Time [s]T0 Initial temperature of jet [K]T∞ Ambient temperature [K]Td Droplet temperature [K]u0 Initial velocity at mouth outlet [m•s-1]ud Droplet velocity [m•s-1]ug Gaussian velocity [m•s-1]ugas Gas velocity [m•s-1]ugc Gaussian centreline velocity [m•s-1]uin Inhalation velocity [m•s-1]ut Top-hat velocity [m•s-1]vp Individual droplet volume considering evaporation [m3]x Horizontal distance between source and target [m]z Jet vertical centreline position [m]ρ0 Jet initial density [kg•m-3]ρ∞ Ambient air density [kg•m-3]ρd Droplet density [kg•m-3]ρg Gas density [kg•m-3]Δρ Density difference between jet and ambient air [kg•m-3]μg Gas dynamic viscosity [Pa•s]φ Sampling ratio in axisymmetric flow system [-]αc Impaction efficiency in convergent part of air stream [-]