Is it correct and appropriate to omit the subject and verb in the second sentence below?
On the top half of the left face, they injected water. On the bottom half, ethanol.
It is correct and appropriate. This comma is known as a "gapping comma", whereby the comma replaces words used earlier on.
But you should use a semicolon instead of the full stop:
On the top half of the left face, they injected water; on the bottom half, ethanol.
It is similar to the first example in the link I provided. Also have a look at the other comma types and punctuation pages on that site. It is a great resource.