Desalination via alternating current

Water flows through a rectangular pipe with some electro magnets on the outside:

electro magnet 
electro magnet 

If you turn on the magnets all the chlorine (and a bunch of water) would go to one side, and sodium (and a bunch of water) to the other.

However if you alternate the current, such that the poles keep switching, I hypothesise that you would get a “stream” of sodium and chlorine ions in the middle, and fresher water near the edges. So essentially to desalinate you have:

electro magnets     fresh water
----------------------/  /
=====> fresh water====  /
=====> salty water=========> back to the sea
=====> fresh water=====  \
-----------------------\  \
electro magnets       fresh water

The reason I think this will work is because of the polarity of the ions and the fact that they will be acted upon despite the orientation of the atom, where as with water being a polar molecule and moving about (spinning), the direction of attraction is going to be pretty much random.

So you run the water through a pipe with an alternating current applying a magnetic field to it and the water in the middle of the pipe is saltier than the water at the edges, stick your outlets on the edges and boom, desalination.

I think you’d have to assume you can produce a laminar flow in the pipe so that eddies and other mixing are taken out of the equation.

So tell me, why doesn’t that work, how come nobody does it? I would be surprised if nobody has tried such a simple idea. Seems low power, no heat needed. Maybe it doesn’t get it desalinated enough? Maybe it just doesn’t work because the water keeps smashing into the ions and they don’t migrate to the middle? Maybe you need a pipe that’s just way too long?

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