This is a picture of a mechanical water softener unit.
http://www.softwaterdeals.com/howwatersoftwork.html
Every once in a while these beads need to be resaturated with sodium, so there is another tank that holds a brine solution (a solution with a lot of sodium in it). This solution gets flushed back through the system forcing sodium back onto the beads by the sheer number of Na ions. The solution that now carries Ca and Mg instead of Na goes into the drain. Now the softener is ready to make more soft water. This whole procedure is shown here.
http://www.ianr.unl.edu/pubs/housing/g946.htm
Mechanical water softeners are units that can be installed into a plumbing system so that it will always work to remove the calcium and magnesium out of the water. The first step is that the hard water goes into a mineral tank that is filled with small little beads that are saturated with sodium ions. The water is pushed though these beads. As it passes by, the beads which have a negative charge, attract the magnesium and calcium ions, which have positive charges. As the water flows through the beads and the magnesium and calcium ions are attracted to the beads, the Mg and Ca ions are replaced in their molecules by sodium ions. The beads are able to give up the Na ions because they have less of a positive charge. This leaves water that only has NaCO3 in it to be ready to use without hurting things that it is being used for.
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