Well, I think there might be a way to make it work with pumped oil. But, as
I mentioned before, charge is usually stored on SURFACES. So, if you mixed
air with the oil, so it was a stream of bubbles in the oil, that might
enable it to carry charge. You could use metal screens that the oil/air mix
flowed through to inject/extract the charge.

Interesting thought. It might be possible to create a churning mixture of oil and air.