[martin_a]

They probably won't.

After a flap has passed the upper lip, which is kind of holding it back to have a precise "flipping point", gravity will take care of moving it down.

No gravity, no flap. ;-)

[amelius]

You could use suction or flow of air to overcome this. Or perhaps even a spring.

[martin_a]

Or just some kind of display that does not rely on gravity, yes.