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.
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.
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.