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.
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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.