Materials science

Aerosol

Physics

Settling

Meteorology

Computer science

Algorithm

Thermodynamics

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

By modelling the evaporation and settling of droplets emitted during respiratory releases and using previous measurements of droplet size distributions and SARS-CoV-2 viral load, estimates of the evolution of the liquid mass and the number of viral copies suspended were performed as a function of time from the release. The settling times of a droplet cloud and its suspended viral dose are significantly affected by the droplet composition. The aerosol (defined as droplets smaller than 5 μ m) resulting from 30 s of continued speech has O(1 h) settling time and a viable viral dose an order-of-magnitude higher than in a short cough. The time-of-flight to reach 2 m is only a few seconds resulting in a viral dose above the minimum required for infection, implying that physical distancing in the absence of ventilation is not sufficient to provide safety for long exposure times. The suspended aerosol emitted by continuous speaking for 1 h in a poorly ventilated room gives 0.1–11% infection risk for initial viral loads of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>8</mml:mn> </mml:msup> <mml:mtext>–</mml:mtext> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> <mml:mo> </mml:mo> <mml:msubsup> <mml:mrow> <mml:mtext>copies ml</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">l</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">l</mml:mi> </mml:mrow> </mml:mrow> </mml:msubsup> </mml:math> , respectively, decreasing to 0.03–3% for 10 air changes per hour by ventilation. The present results provide quantitative estimates useful for the development of physical distancing and ventilation controls.

Evolution of spray and aerosol from respiratory releases: theoretical estimates for insight on viral transmission