Sticky droplets and a mask like a spider’s web

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.

Try and imagine a tiny droplet in your breath hitting an almost equally tiny fibre in a face mask. There are two forces you need to consider. The first is the inertia of the droplet, this force tends to make the droplet keep on going, so it opposes sticking. It is the second force that makes the droplet stick, and this is the force of surface tension. When the surface of a droplet touches the surface of fibre, the water and the fibre attract each other and it is this force that drives the stickiness

The physics of why we expect the droplets in your breath to just stick to a fibre in mask, like a fly to a spider’s web, is pretty straightforward. We can understand it with aid of one of the many named numbers found in fluid mechanics. One I actually give as an example in in my final year course. This is the Weber number.

The Weber number is just the ratio of the inertial force to the surface tension force. If you put the numbers in, the Weber number is about 0.01 for a droplet about 10 micrometres across in our breath. The air we breath in and out is typically move at around 10 centimetres per second. A Weber number of 0.01 means the force of inertia is 100 times weaker than the force of surface tension, so we expect that in at at least 99% of cases surface tension will win and the droplet will stick. Simple.

Incidentally, the opposite limit where inertia wins over surface tension is common in our kitchens. We know that big fast moving droplets splash when they hit a surface, this happens when the Weber number is much larger than one, and inertia overcomes surface tensions, causing fun stuff like that shown in the picture at the top of this post.