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?