How Viruses Survive in Aerosol Droplets

Viruses like flu and SARS-CoV-2 (the cause of COVID) spread across the air in aerosol particles, often of order a micrometre across. To do this the virus needs to survive intact the rather violent process whereby a tiny droplet breaks off from a liquid. In this case the liquid mucus lining our throat and lungs. Violent here includes some rather fast, metres per second, flows as the droplet breaks off from the liquid and rounds up into a sphere. I estimated the shear stresses involved in this process in an earlier blog post as

shear stress in boundary layer σ=η×shear rate∼(η2Γ3ρdD5)1/4∼104Pa      d=1 μm\text{shear stress in boundary layer~} \sigma = \eta \times \text{shear rate} \sim \left(\frac{\eta^2\Gamma^3}{\rho d_D^5}\right)^{1/4}\sim 10^4\text{Pa}~~~~~~d=1~\mu\text{m}

where η is the viscosity (saliva is only a bit more viscous than water, at around 1 mPa s), Γ is the surface tension (about 0.05 N/m), ρ is the mass density (1000 kg/m3) and dD is the droplet diameter.

The basic model for a virus seems to be a soft squidgey core surrounded by a thin protective shell. This shell is elastic with

effective spring constant k∼Eh∼108Pa×10−9m∼10−1N/m\text{effective spring constant}~k\sim Eh \sim 10^8\text{Pa}\times 10^{-9}\text{m}\sim 10^{-1}\text{N/m}

here E is a Young’s modulus for stretching the material the virus’s shell is made of and h is the thickness of this shell. This model seems to be what is used both for enveloped viruses where the shell is based on a fluid (but which resists being stretched) lipid bilayer, or a more solid protein shell (capsid).

In either case if the virus has a diameter dV then

shear force on virus∼σdV2∼(η2Γ3ρdD5)1/4dV2\text{shear force on virus}\sim \sigma d_V^2\sim\left(\frac{\eta^2\Gamma^3}{\rho d_D^5}\right)^{1/4}d_V^2

and the virus should then have a

fractional stretch=δdV∼σdVEh∼dV2∼(η2Γ3ρdD5)1/4dVEh\text{fractional stretch}=\frac{\delta}{d_V}\sim \frac{\sigma d_V}{Eh}\sim d_V^2\sim\left(\frac{\eta^2\Gamma^3}{\rho d_D^5}\right)^{1/4}\frac{d_V}{Eh}

For a 100 nanometre spherical virus (both flu and SARS-CoV-2) in a 1 micrometre (1000 nanometre) droplet, this fractional stretch works out at around 1 %. This looks survivable. Especially as the shear stresses are very transient. The aerosol droplet is formed in much less than a second. Also the stresses are not uniform across the droplet: the above expression is for the stresses near the shearing surfaces, stresses are lower near the centre of the droplet.

But for larger viruses (eg mpox) or long filamentous viruses (eg ebola), maybe the stresses are more of a threat?

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Published by Richard Sear

Computational physicist at the University of Surrey. My research interests are in COVID-19 transmission, especially masks, soft matter & biological physics

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