A fan catches dust *because* it is moving.
As fan blades turn, friction with the air causes electron exchange between them. Now electrostatically charged, the fan blades attract neutrally charged dust particles which adhere to the blades.
It’s the same principle that causes helicopter rotors to build significant electrostatic charge during flight.
Even grounded metallic fans collect dust, so it’s not just static electricity like others have mentioned. There is however a point on every fan blade where the airflow splits apart, and if a dust particle gets perched right on the edge, or a hair gets draped reasonably evenly over it, all the force it experiences pushes it harder onto the edge. This doesn’t happen very often, but fans ingest enormous amounts of dust, so every now and then a particle gets a lucky hit and sticks. And dust particles are stickier than metal or plastic, so other particles preferably stick to them, and you’ve got a self-reinforcing cycle.
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