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.

It is because bigger particles have more inertia, which means they cannot follow the stream of air as it slaloms past the fibres. The orange curve above shows a particle with little inertia that follows the streamlines and so slaloms between the fibres and is not caught. This particle avoids the surfaces of the fibres and so is not filtered out.

The green curve is the trajectory of a particle with more inertia, and this just about manages to get past the first two fibres, but is caught by a third. Finally, the red curve is for a particles with a lot of inertia, and it just plows straight into the first fibre and is filtered.

This effect of inertia is captured by what is called the Stokes number, and I discuss this number a bit in an earlier post. But I have now got a code working to simulate trajectories with varying amounts of inertia, and I pleased with the results. The effect of varying the inertia shows up very clearly from some simple plots like the one above.

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