In the summer of 2020 I started working with colleagues at the University of Bristol to try and better understanding how face coverings/masks filter our potentially infectious droplets. The theory work was done by Josh Robinson and experiments by Ioatzin Rios de Anda, both working in the group of Paddy Royall – who was then at Bristol but is now at ESPCI in Paris. I helped with some Lattice Boltzmann simulations.

Inspired by a really nice Google Sheets by Jose-Luis Jimenez and Zhe Peng, I have done a simple app that plots the Wells-Riley prediction of the probability of becoming infected, as the function of the length of time you spend in a room. Wells-Riley is a simple model for estimating the probability that you will become infected if you spend time in a room with someone who is infected.

The app is hosted by Heroku and it uses Streamlit – an easy way of doing interactive plots using Python.

You can see my blog for latest thoughts on COVID-19 transmission and masks.

Masks/face coverings

The physics of how masks/face-coverings work is a bit complex (see links to preprints below which have the details) but basically they are are air filters that you wear on your face. An air filter is something that allows air through (so you can breathe) but traps particles (in this case droplets that may contain virus) inside it. This means separating out the air and the particles. How this is done depends very sensitively on size of the droplets. The smallest ones (below around 0.3 micrometres) are small enough to just diffuse into the surfaces of the fibres of the mask, and stick. Big ones (a few micrometres or larger) can’t follow the air through the mask because the particles have too much inertia. This inertia means that they crash straight into the fibres and stick. This is illustrated in the little movie below. The movie shows two particles (in red). The first has very little inertia (technically has a small Stokes number), and this particle follows the air around a model of the cross-section of a fibre (green), and is not filtered. The second has much more inertia, can’t follow the air around the fibre and crashes into it — and so is filtered out.

Between the diffusion and inertial mechanisms there is gap for particles around 0.3 to 1 micrometre, which both surgical and cloth masks don’t filter effectively. The more advanced N95/FFP2 respirators worn as part of PPE rely on a third mechanism to filter particles in this size range: electrostatic interactions due to charged up fibres inside the mask. Final comment: masks are only as good as their fit — air that goes round the edges is not filtered! — so please make sure the fit is reasonably good.

We first put a preprint up on arXiv in August 2020, and a greatly revised version was put up in Feb 2021:

Efficacy of face coverings in reducing transmission of COVID-19: calculations based on models of droplet capture

by Joshua F. Robinson, Ioatzin Rios de Anda, Fergus Moore, Jonathan P. Reid, Richard P. Sear, C. Patrick Royall
This is focused on the physics of how masks work.

Also, as of early December 2020 there is another less-physicsy preprint on medRxiv:

How effective are face coverings in reducing transmission of COVID-19?

by Joshua F. Robinson, Ioatzin Rios de Anda, Fergus J. Moore, Florence K. A. Gregson, Jonathan P. Reid, Lewis Husain, Richard P. Sear, C. Patrick Royall

Code written by Joshua Robinson (University of Bristol) and I, that was used for the calculations in this work in these papers is freely available on Github here.

The pdf of the slides of my talk entitled Some simple physics of corona virus transmission at SOFT MATTER: THE UNSEEN SCIENCE ALL AROUND US is here I cover both simple models of person-to-person transmission of SARS-CoV-2, and of masks/face coverings.