It is well known that dust gets deposited on a rotating ceiling fan because formation of a boundary layer over fan blades. The air layer next to blade surface is stagnant due to no-slip condition and the presence of a strong viscous force.
How could I modify the blade design to prevent the blades from accumulating dust? Is it possible to make the blade's surface so smooth as to prevent deposition?
Assuming your explanation of dust accumulation on a blade is correct my suggestion would be to add slots to the blade to create a cascade of aerofoil sections. Doing this would allow you to consistently reenergise your BL and limit its growth, and jumping from this design to a serated TE for turbulent flow wouldn't be a much greater step of complexity.
Frankly I am a tad sceptical of the explanation, since whilst a no-slip condition would be enforced at the blade surface with the air, no such condition exists between the dust and the blade surface, so the shear force acting across the layer of dust is the only force acting on it (yes there is friction with the blade but if the particles are remotely spherical this ought to be small). This shear force becomes significant when you consider the thickness of a layer of dust which a human might notice compared to boundary layer thickness at that Re number.
At any rate your much bigger issue is that when stationary, dust will always settle on your blades. I doubt even a static charge would help you here as you can't easily ionise the dust in the air and you're just as likely to attract dust as repel it if you can't ionise it (which is why old TVs tended to accumulate a layer of dust on the glass).
Alternative solution: design your fan with an absurdly overpowered motor so you can spin it at 1000s RPM and use the centrifugal force to spin the dust off of it. Edit: a couple of other points here, thinking about it, there is also a pressure force encouraging airflow towards the blade tips, and it would be trivial to use the high RPM to produce a high frequency vibration through the blades, indeed this is likely to be a natural side effect, which will help to create turbulence in the BL and also potentially "bounce" the dust particles off of the blades and into faster moving flows. The higher RPM also helps increase Re number, further decreasing BL thickness and encouraging turbulence. Just remember to make sure the blades never ever fail; could be messy. This would actually be a half decent solution to the problem if it weren't so absurd/impractical/expensive/dangerous.
Alternative alternative solution: include a feather duster in the box.
If the blades are conductive, or accommodate a conductive coating, a small static charge should repel dust by imparting a charge to the particles, which would then expel/repel them.
The charge could be periodically alternated since some dust is already ionized and would thus be attracted to one charge, but repelled by the opposite.
The fundamental problem central to the question is the management of dust which is inevitable in any inhabited space as most of the dust consist of shed human skin cells. Although it might seem desirable, rejecting the dust by any means merely decreases the air quality in the space; using charge repulsion results in the deposition of dust elsewhere with potentially equally undesirable results and until it "sticks" to something, it still diminishes the air quality. Thus, managing rather than fighting the problem becomes the only option.
The easiest is to use a cotton/spandex cover such as these (Outer Space Ceiling Fan Blade Covers by Fan Blade Designs -these are mostly polyester so they will hold a static charge unfortunately) and a pillow case. Roll the pillow case (the longer king size work best) like one would a sock and carefully put it over the cover. Remove both but DO NOT SEPARATE and proceed in turn to each blade. Place both items as one into a washing machine and select a long cycle. Stop the cycle when the water has reached the top and separate the two underwater so as to maintain the air quality of the space. A plastic bag can be used temporarily when access to the washer is not direct; however, still place both in the bag, do not separate them.
To further improve the quality of air in the room, a velcro patch may be sown into the portion of the fan blade cover that faces upward and a block shaped ceiling fan air filter such as those made by BestAir can be attached to it. This will capture a great deal of dust and can easily be removed with the previous method without modification. It is my understanding that neither will compromise airflow in the summer and that while the block may disrupt airflow during the winter, it does not do so to such an extent as to alter the basic function of the fan.
I imagine this solution is far from what is desired in as much as it is both low tech and only elegant in appearance rather than substance. Nevertheless, it is effective, inexpensive, and home decor friendly. This last may seem insubstancial to a single person; however, anyone either married or in a long term committed relationship will tell you, it is not an idle consideration.
There are other options; however, these do not involve the fan directly while still only managing the dust in the air albeit in an entirely different manner without eliminating the cleaning. Whilst the cleaning is made more convenient and cleaner in terms of the air in the room, the original condition has not changed; nevertheless, having tried a number of options, I am convinced that no method involving repelling the dust will work without making dust stick unintentionally to other surfaces and making these surfaces harder to clean resulting in no net benefit.
