# Minimal model of corona virus exposure

Transmission of the corona virus (aka SARS-CoV-2) is very complex, which is basically why it is so poorly understood. But in true theoretical-physicist style, a minimal model has been developed, by a guy called Roland Netz (who is a theoretical physicist in Berlin). It makes a lot of assumptions, and it is clear that there is lot of variability, between one infected individual and another and between one situation and another, so its predictions should be taken with a large pinch of salt. But in this post I will outline this minimal model.

# Sticky droplets and a mask like a spider’s web

The people at Brilliant have done a lovely short (few minutes, last minute is an ad for Brilliant) video explainer on the physics of how masks work. It does a good job of saying why droplets a fraction of a micrometre across are the tough ones to catch, and why you can’t think of a face mask as a simple sieve. It compares a mask to a spider’s web, a comparison I like very much. But one thing it skips over is the physics of why when a droplet hits one of the fibres inside a face mask, we expect the droplet to stick.

# Particles that can’t take corners are filtered out

The picture above shows three trajectories — red, green and orange curves — of particles through a model of a face mask. Face masks are meshes of long thin fibres and the brown discs are cross-sections through these fibres — in a simple model. The blue lines are what are called streamlines, they show the the paths taken by air flowing through the mask, due to the wearer breathing. The trajectories show (at least part of) why masks filter out the bigger droplets from a person’s breath, and it is not because the droplets are too big to fit through holes in the mask.

I am playing around with simple simulations of particles in air flowing through simple models of masks. Masks are made from long thin fibres, so usually people model the flow around cross-sections of long cylinders, which as you can see above are just discs (shown in brown). The air flows between these cylindrical fibres. The air flow is shown above by the blue stream lines that show the paths taken by the flowing air between the fibres. The air flows from bottom to top in the image above. This air carries particles with it, and trajectories of 20 example particles are shown as green and orange curves.

# Going with the flow

Face masks are made of meshes of entangled long thing fibres. Each fibre is around tens of micrometres thick, but much longer than this. So when you breathe through a mask the air flows between these long cylindrical fibres. Above is the result of a simple computer simulation* of flow through a cross section of a few nearby parallel cylindrical fibres. The fibres are the brown discs and the lines with arrows are what are called streamlines. Streamlines are the lines a (light**) particle carried along by the air would follow. The arrows indicate the direction of travel, in the image above the air is flowing from bottom to top.