And in answer to your original post, the water will eventually mix in, the same way squirting air freshener in one corner of a still room will still eventually reach the far corner.
There's even a word for it but I can't brain, I have the dumb.
Dumb - D - diffusion. There you go, so maybe I'm not so dumb. It's a molecular motion thing, eventually you'll end up with an even concentration throughout the carboy.
"The main ingredient needed is 'time' followed closely by 'patience'." - The Bishop 2013
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