Physics of virus transmission by speaking droplets

Roland R. Netz; William A. Eaton

doi:10.1073/pnas.2011889117

New Research In

Edited by Peter B. Moore, Yale University, New Haven, CT, and approved August 15, 2020 (received for review June 11, 2020)

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Table 1.

Theoretical virion emission rates (k), evaporation times (t(R_dn)), and sedimentation times (τ_sed) for initial radii (R₀) and for droplet nuclei radii (R_dn = R₀/3), all for z₀ = 1.5 m, 25 °C, and 50% relative humidity (RH = 0.5)

R₀ (μm)	k^* (virions per min)	t(R_dn)^† (min)	τ_sed(droplet, R₀)^‡ (min)	τ_sed(droplet nuclei,R₀/3)^‡ (min)
1	3	7 × 10⁻⁵	200	2 x 10³
3	80	6 × 10⁻⁴	20	200
5	400	2 × 10⁻³	8	80
10	3 × 10³	7 × 10⁻³	2	20
20	2 × 10⁴	3 × 10⁻²	0.5	5
40	2 × 10⁵	0.1	0.1	1

↵* Calculated from k = (4/3) π R03 ab, a ≈ 10⁵ droplets per min (11, 12), average b = 7 x 10⁻⁶ virions per μm³ (maximum b = 2.35 × 10⁻³ virions per μm³) (16).
↵^† Calculated from t(R_dn) ≈ 7 x 10⁻⁵ R02 min.
↵‡ Calculated from τ_sed = 210 min/R².