Some particles are just the right size to go through a filter, not too small and not too large

Surprisingly, it is easier to filter out (from air) particles tens of nanometres across, than it is to filter particles hundreds of nanometres across. The image above shows why. The orange and green curves show the trajectories of two particles in air flowing through a model mask. The model is a two-dimensional cross section of a mask, with cross-sections through the fibres of which surgical masks are made, shown as reddish brown discs. The blue curves with arrows show the flow of the air through the model mask. The orange trajectory illustrates one of the particles that are hardest to filter out – and so cause us some of the biggest problems when we try and stop COVID-19 transmission.

The particle is so small that it tends to slip between the fibres, but it is large enough that its diffusion or Brownian motion is pretty small. Brownian motion is random motion small particles do due to being bombarded by the surrounding air, and it tends to cause the trajectory of the particle to wobble randomly as it passes through the mask. If you look closely at the orange trajectory it is a little rough and wobbly due to this Brownian motion.

The green trajectory models an even smaller particle than the orange one, and as this particle is smaller its Brownian motion is more violent – seen as a rougher trajectory than the orange one. Ultimately, this random motion causes the particle to crash into a fibre and so be filtered out. Thus the rather counterintuitive result that the smaller particle is easier to filter than the larger one.

It is unfortunate that particles a few hundred nanometres across hard to filter out; SARS-CoV-2 is about a hundred nanometres across so just about small enough to fit into droplets of this size. To combat this the masks used for Personal Protective Equipment (PPE) use charge distributions in the fibres to increase the filtration of particles of this size. These are the masks referred to as FFP2/FFP3 (in EU and UK) or N95 (USA). As David Osborn (a Health & Safety Practitioner) says (eloquently and forcefully I think) these are the sorts of masks healthcare workers caring for COVID-19 patients should be wearing, but often are not (see also previous post).

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