Inks that sheen have been around for a while, actually purely by accident. However, sheening inks have become a bit of a trend recently. After all, fountain pens and fountain pen inks offer much more character and style to handwriting anyway so why not step this up a notch with another variable?
So what is sheen?
Some inks, when dry, reflect light in a particular way such as to give the appearance of a different colour. Therefore, some blues and greens show a red sheen, greys can appear blue and blacks can have a purple or brown sheen. This probably isn't due to another colour dye in the mix because sometimes the sheen doesn't appear; it's all dependent on the amount of ink on the paper and the absorbency (well, lack of) of that paper. Instead it's an optical effect, light bouncing off the surface of the ink in a particular way to give the impression of another colour.