Why does dust settle on the moving blades of a fan?
As the air flows across the blades of a fan, the dust particles in it occasionally pierce through the airflow and hit the blades. The same sort of process occurs when a bug hits the windshield of a car; the bug would normally follow the airflow but its inertia prevents it from moving out of the way quickly enough and it hit. Once a dust particle hits the fan blades, there isn’t much to remove it. The air moves remarkably slowly right at the surface of the fan because that surface layer of air experiences lots of viscous drag. Even though the air is moving swiftly only a few millimeters away, the air right on the fan blade is almost stationary. Thus the dust can cling to the blade indefinitely.