No more than the weight of a cherry

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.

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Emergence in biology

The beautiful behaviour of this flock of starlings is an example of a class of phenomena variously known as emergent, collective or more-is-different behaviour. The point is that a single starling, or two starlings cannot show this striking phenomenon, you need hundreds or thousands of starlings, to see it. A liquid is a less obviously exciting example of an emergent phenomenon. One or two water molecules aren’t a liquid, you need at least about a hundred to make even a tiny water droplet.

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Biologists arguing over liquids

Balsamoil Protean

Chemical engineers, chemists, physicists and food scientists have been studying coexisting liquids like the (black) balsamic vinegar and (yellow) olive oil above, for over a hundred years. Cell biologists have been busy with other things over this time. But over the last few years at least some cell biologists seem to not only be studying coexisting liquids but arguing over them.

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Sticky droplets and a mask like a spider’s web

Water drop 001

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.

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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.

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Interception by mask fibres

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.

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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.

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Filtering with inertia


The guy with the great sideburns is George Stokes, a 19th physicist who made many contributions to physics, and after whom the Stokes number is named. In this blog post, I’ll show how his work helps us to understand how to filter out corona-virus laden droplets.

The Stokes number* is one of many dimensionless ratios in fluid mechanics. It tells us about the competition between two timescales, and it applies to particles, eg a droplet of mucus containing corona virus, moving in a flowing fluid, eg our breath.

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Cooperation not competition in the time of the corona-virus

Academia can be very competitive. Getting a job is competitive, at least tens of very good people will apply for a job at a reputable university. Fellowships that are stepping stones to academic positions have success rates of around 10% — so 90% of applicants fail. And once you are an academic, it does not ease off. You are under pressure to get grants and again, around 90% of grant applications fail. And government policy has tended to push for more and more competition, between universities and between academics. But, faced with the threat of COVID-19, cooperation is breaking out.

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