Is water a good solvent for ink separation?

If the ink is water-soluble it can be.  I suppose you are
experimenting with a form of chromatography, in which you separate the separate pigments
in the ink.  I think most ordinary felt-tip writing pens have this sort of ink, and
you'd be surprised at how many different pigments are in black ink, and how different
they are for different manufacturers.

You can find out by
putting a biggish spot of ink on a strip of paper towel, dipping one end into a glass of
water, and watching while the water percolates up the paper.  As the water climbs past
the ink spot it will carry any water-soluble components along, for a distance that
depends on the component.

Two questions you could think
about:

1) Why does the water crawl up the strip of
paper?

2) (You may have to research this one) Why do
different components show themselves at different places?