system
Given the following post, respond as if you're commenting on Reddit:
human
How does a constantly-running fan collect dust?

Wife and I keep the ceiling fans in our home running 24 hours a day, but we have to clean them regularly because of dust accumulation.  I can see inanimate still objects collecting dust, but an object that is constantly moving?  Is it because of the blades are moving at a constant speed?
gpt
The viscosity of the air is the culprit. When fluid flows around a boundary, viscosity of the fluid demands the so-called *no-slip condition*, which means the fluid at the boundary must be stationary with respect to the boundary. That is, the object literally drags the fluid along with it. (The viscosity is the quantity that then allows the fluid to transfer momentum across streamlines and diffuse vorticity.)

So when the fan blades are spinning, the air that is right on the blade is moving at the same speed as the blade. There is actually a very thin layer of air around the blade (called a boundary layer) in which the speed of the fluid is either exactly or very close to the speed of the blade. So now think about what happens to a dust particle. Dust particles are far too small and too light to have a significant effect on the air flow itself. The path of a dust particle is really just tracing out streamlines in the air flow. (We call such quantities *passive tracers*.) Of course, the dust particle still does get knocked around by the very rare collision with another particle, or by eddy currents flowing around the fan.

Eventually, if a dust particle enters the boundary layer near the fan blades (or if it was already there when the fan was turned on), it will just flow with the blades. Then when the fan is turned off, the dust particle just settles on the blade.

Of course, there are other factors that may make it easier for dust to settle on the blades. For instance, any dust on the top of a ceiling fan blade will tend to stay there until you physically remove it because gravity is keeping it on the blade. Similarly, vertical fan blades might have tiny imperfections that keep a dust particle there. But there is a naive intuition that dust should not settle at all since all of the dust should just get blown away when the fan is on. Viscosity is the reason this naive intuition is wrong.