Yes there are. But not really because of the ink itself, but because of a chemical reaction of chemicals in the ink to cellulose - one of the properties of paper. These permanent inks use cellulose reactive dyes. As the ink companies say, the dyes are water soluble so there is no effect or damage to the pen. When the ink is in the bottle all is normal. But when the dyes react with cellulose in paper and after the ink dries the ink becomes waterproof and permanent.

Tests have been done to a number of the permanent inks by Noodler's Ink and tested how they lasted when held under water. Pretty good. Each had a slightly different amount of "run". Oh yes, there is cellulose in those cotton shirts so when you drop these permanent inks on your clothes, well its permanent!