Soft manageable hair and protection from SARS-CoV-2

The physics of how masks work is a bit complex. Masks/face covering are air filters you wear on your face. They filter out droplets from the air you breathe in, or out. The mechanism for filtration is different for small and for large droplets. For small droplets it relies on diffusion of the droplets into contact with the fibres inside the mask, where the droplets stick and are filtered out of the air. Droplets in air are constantly bombarded with air molecules and this pushes them around at random: this random motion is called diffusion. For small enough droplets, these pushes are enough to cause significant numbers of the droplets to diffuse into contact with the fibres of a mask, during the short time the air and droplets spend crossing the thickness of the mask.

We want to understand how this happens, to understand and so hopefully maximise filtration of these small droplets. The bad news here is that until 2020, the physics of air filtration was a rather neglected area, so little work was done. The good news is that the global market for hair conditioners must be billions a year. And at least some hair conditioners work by depositing small droplets of gunk onto the surface of hairs – hairs are a few times thicker than the typical fibres in a surgical mask*. So the scientists studying how to make soft, shiny yet manageable hair have a very similar problem to those studying how masks work. They also want as many as possible of the droplets to hit the surfaces (here of the hair strands) as the droplets that don’t are wasted. Motivated by this large market, there has been work on how to make better hair conditioners.

The result of this work is that for droplets in air or water that is flowing past obstacles, there is what is called a “diffusive boundary layer” surrounding these obstacles. Droplets inside this boundary layer can diffuse across the layer and into contact with the obstacles, while droplets outside this layer can’t and so go straight past the obstacle. So only droplets that enter this boundary layer have a chance of being filtered out, or of coating the hair to make it soft and shiny.

For air flowing at a few centimetres per second past a fibre a few tens of micrometres thick, the thickness of the boundary layer is very roughly ~ 1/a1/3 micrometres thick, with the a the droplet diameter in micrometres. So for droplets a micrometre across, the boundary layer where filtration occurs is only about a tenth of the diameter of the fibres. This is not really enough for much filtration.

But for smaller droplets, the layer is thicker. So for droplets not much bigger than a single virus, which is about a tenth of a micrometre across, the filtering boundary layers are several micrometres across and there is a fair amount of filtration. These very small droplets are so small, most will not contain even a single virus, but they may be important in some (possibly) rare cases.

These are cases are when the infected person is producing a lot of virus, such people are called superreplicators. Some infected people have a billion times as much virus as others, and superreplicators may produce enough virus that even very small droplets contain virus. These small droplets also can persists in the air for a long time, as they are so light. So very small droplets look like something to worry about when a superreplicator is sharing a poorly ventilated room with others. In that case, we may need to learn from hair-care scientists.

* We live in a capitalist economy, and as many have said, such economies tend to give us what we want (shiny hair), not what need (less COVID-19 transmission). At least that is the pessimistic viewpoint. The optimistic viewpoint is that if you have been buying hair conditioner your money has contributed in small part to preparation to the viral pandemic**.

** It is only a small contribution, so does not excuse voting for politicians who don’t prepare for anything, if you have done that.

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