Colleagues at the University of Bristol and I are working on trying to understand how masks work. One fundamental aspect of this is that a mask, like any filter, fundamentally involves a trade off. A mask must as permeable as possible to air, but as impermeable as possible to virus-containing droplets. Air must flow through a mask as freely as possible, but droplets should find the mask as close to impenetrable as possible. The problems is that these two design constraints directly contradict each other, and so any mask, any filter in fact, is a compromise.

For example, one obvious way to make a mask better, as far filtering out droplets is concerned, is to make the gaps between the fibres of the mask smaller. This does indeed tend to improve filtration. However, it also makes a mask harder to breath through. It has been known for getting on for two hundred years, that if you force air through gaps, then if you have halve the gap size you have to push four times as hard to push the air through.

So if you shrink and shrink the gaps at some point you can’t breath through the resulting mask. For surgical masks, there is I think a standard, that the maximum total force you have to exert to breathe through them is about the weight of a cherry*.

So one way of stating the design problem for a mask is that it should filter as many virus-containing droplets as possible, while only requiring a force equivalent to the weight of a cherry to breath through.

* The standard unit of force, the Newton, is about the weight of an apple. By extending this fruit-based way of explaining the size of forces, the maximum force to breath through a mask is maybe a twentieth of a Newton or a little less, which is the weight of cherry.

Picture of cherries, from Benson Kua via Wikimedia.

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