This water drop isn't falling through air. It's moving through oil. But why is it bouncing endlessly between the top and bottom of the frame, instead of combining with the rest of the water below?
The curve at the bottom of the frame is called the meniscus, marking a boundary between the oil and more water. Water molecules have a weak attraction for each other, so when the water drop hits the meniscus, it should combine with the water. Instead it is repelled, and goes shooting upwards again.
This is happening because the black cylinder at the top of the frame is an electrode. The drop is moving through a strong electric field. Researchers learned, by observing these drops, that above a certain strength, water droplets go from "join" to "bounce" -- provided those droplets are oppositely charged. The paper describes the phenomenon thus:
We observe that appropriately positioned and oppositely charged drops migrate towards one another in an applied electric field; but whereas the drops coalesce as expected at low field strengths, they are repelled from one another after contact at higher field strengths. Qualitatively, the drops appear to 'bounce' off one another.
They hope this will help with industrial applications, unmixing mixed-up solutions. It's also possible that it will help us understand certain weather phenomena. Rainstorms often involve water moving through an electric field.
In the meantime, here are two droplets bouncing off each other, the electrode, and the meniscus.
[Source: Non-coalescence of oppositely-charged drops.]