Zone crystallization is a common way to purify silicon rods for use in solar cells, for example. Basically, crystals that form slowly, are pure, and impurities are left behind.
I can only guess -- you have some vinegar, and want to make some glacial acetic acid at home. 'Kay, that sounds a little dangerous, but I'll let it slide. You want the theoretical, or industrial procedure for such a process-- that doesn't exist, no one purifies acetic acid this way.
But if you want to formulate a mathematical theory, I'd work it from the zone crystallization of silicon, or germanium.