Above is an aircraft wing which has picked up ice on the leading edge of its wing. This is of course is not ideal, especially for an aircraft in the air. You don’t want large amounts of ice forming along the leading edge of the wing in flight, it will add weight and make the wing less able to generate lift. I think there were particular worries about this during the Second World War, possibly because planes were flying higher and faster as the war drove rapid advances in aircraft design and performance. So the United States Army Air Force turned to the dream team of a Nobel-prize winner, Irving Langmuir, and the first woman to obtain a PhD in physics from the University of Cambridge, Katherine Blodgett. They worked to understand the following problem.
Transmission of COVID-19 likely starts with production of a small droplet that contains one or more SARS-CoV-2 viruses. This occurs somewhere in the lungs, throat, or mouth of an infected person. We have almost no data on this process as it occurs inside the body of an infected person, but we do know how droplets are generally made. One mechanism is named after Lord Rayleigh and Joseph Plateau, and we have all seen it in action. We see it every time we turn a tap a little bit on, and it drips. The stream of water from the tap breaks up into droplets, and the same thing may be happening inside us every time we breath.
I am very struck by this quote from a paper measuring the concentration of corona virus (aka SARS-CoV-2) in swabs taken from infected people
Initial SARS-CoV-2 viral load is widely distributed ranging from 3 to 10 log copies/ml …Jacot et al, medRxiv 2020
Note the log in the first sentence, the range is not from 3 to 10 — about a factor of 3 — it is from 103 to 1010 viruses per millilitre — a range where the top end is 10 million times the bottom end. In other words, some people at some times during their COVID-19 infection have ten million times as much virus as others do. On a log scale, the average is 106.5 ~ 3 million viruses per millilitre but some infected people have thousands of times more, while others have thousands of times less.
Transmission of the corona virus (aka SARS-CoV-2) is very complex, which is basically why it is so poorly understood. But in true theoretical-physicist style, a minimal model has been developed, by a guy called Roland Netz (who is a theoretical physicist in Berlin). It makes a lot of assumptions, and it is clear that there is lot of variability, between one infected individual and another and between one situation and another, so its predictions should be taken with a large pinch of salt. But in this post I will outline this minimal model.
Today I am reading both Calling Bullshit by Jevin West and Carl Bergstrom, and of a “growing crisis” over Scottish Higher results — presumably a similar crisis will happen for A levels when the results are released in a few days. I have got to the bit in Calling Bullshit where West and Bergstrom talk about bullshitting via statements that superficially look rigorous, but in reality are pretty flaky. In this blog post I want to suggest, possibly controversially, that the distinctions at the root of the growing crisis in Scotland, between a grade A and B in a Scottish Higher*, or a B and C, etc, have a slight whiff of bullshit about them.
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.
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.
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.
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.
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.