Going through my loose papers just now I noticed a little comparison of the water-related durability of some assorted inks that I performed a while ago. With a few different pens, I write on a piece of Rhodia notepaper, waited a while for the inks to dry (a couple of hours I think) then cut that page into three columns. The left hand column was not exposed to water at all. The middle was dipped into water, but then removed quickly; the right column was dipped in and enthusiastically slooshed about. Here are the results:
Diamine Grey. Slightly water-resistant, in that it is visible afterwards and almost readable, but not pretty.
Sailor Sei-Boku - the greenish blue "nanocarbon" Sailor ink. As befits an ink by a company called "Sailor" this ink remains identical no matter how much it is dunked into water. Sei-Boku is termed "archival quality" so really should be able to cope with being dunked in a sink.
Waterman South Seas Blue, which is really a turquoise. Here we see the difference between a sailor and the sea. South Seas Blue, when exposed to water, is overjoyed and leaps off the page in ecstasy, to join its brother and sister molecules.
A black Sharpie marker which I happened to have lying around. No nonsense here. Water? Why should it care about water? Try bleach or napalm to erase this sort of thing.
Diamine Monaco Red which surprised me a little (though Diamine inks are not noted for water resistance generally). Monaco Red just vanishes with barely a trace. I'll grant that that example of Monaco Red was likely contaminated with a lot of J Herbin Rouge Caroubier, since it normally dries to a brownish "there's been a murder sir" colour, but even so... evidence has been eradicated.
And then I had run out of inked pens so decided to try a pencil, specifically a 3B lead in a Caran d'Ache clutch pencil. Pencils have something of a reputation (in my mind anyway) for being impermanent, given that they can be erased with a piece of rubber, but graphite particles embedded into the surface layer of paper are apparently entirely non-bothered by the presence of water.