Can a microscopic insect fly by flapping rigid wings?

[Dishsoap]

TL;DR Summary

Are insects at low Reynolds number capable of flying by flapping rigid wings?

While in quarantine, I've been reading a lot about some millimeter-scale flying robots, like DARPA's Nano Hummingbird and others. I'm noticing that a lot of millimeter-scale flying robots flap their wings like a fly, and I'm wondering if it's even possible to use this motion to move if the fly were much smaller (say, 10 microns in size) with rigid wings. In that case, the Reynolds number is much lower, and Purcell's scallop theorem dictates that non-reciprocal motion must be used to have a net motion forward (up, in this case).

That being said, I know virtually nothing about aerodynamics/flight, so I'm curious if there's a reason why the scallop theorem wouldn't apply to upwards motion (lift). Or, if it does, does this mean that flying microscale robots would have to essentially be a helicopter? I notice that this recent Nature paper on untethered flight has the wings flapping in the XY plane (where Z is up), I wonder if this is the reason.

 

[A.T.]

I'm wondering if it's even possible to use this motion to move if the fly were much smaller (say, 10 microns in size) with rigid wings. In that case, the Reynolds number is much lower, and Purcell's scallop theorem dictates that non-reciprocal motion must be used to have a net motion forward (up, in this case).

Rigid wings don't imply reciprocal motion. It depends on how many degrees of freedom they have.

 

[Keith_McClary]

I had to look up the smallest flying insect, Kikiki, 0.15 mm, fuzzy wings.