Using plural or singular after "both"

Question

Suppose there are two phases, a water phase and an IL phase, you can use any other name too. We did some calculation between X and each of them. Which of the following is correct:

• Y was calculated between X and both water and IL phases
• Y was calculated between X and both water and IL phase
• Y was calculated between X and each of water and IL phases
• Y was calculated between X and each of water and IL phase

First, I don't know to use "both" or "each of". Secondly, I don't know if I should use "phase" or "phases". I guess "phases" is correct, but then again I think "phase" could be possible too, based on an ellipsis rule, or they may not differ much.

Answer 1

You just listed two phases, so you want the plural. If you repeated the word instead, it would be singular:

...each of water phase and IL phase.

As to both or each of, that is a stylistic matter. I prefer each of, because it appeals to my logical mind - it seems less ambiguous. To me, being prone to look for every possible alternative of things, 'both' could be interpreted as referring to a much more complex and unclear experimental setup. However, there is a big element of taste about that.

Taste aside, I would consider both to be correct uses of English.