Not all inks. This for example withstands pretty much any liquid (yes, including industrial strength solvents -- I've checked): https://www.amazon.com/Noodlers-Black-Waterproof-Fountain-Pe...

Get better pens. There are waterproof ones that I use, they are the anti-fraud ones that they market for use with paper checks.

I use Staedtler pigment liner pens (http://a.co/i0tN5Bz) and they have never run on me. The different widths really help for sketching vs writing vs annotating too.

I was reading through some of my journals that I wrote a few years ago and noticed that the ones written with a pencil are much more readable than the ones written with a fountain pen. I guess picking the right kind of paper and ink is very important for a notebook not to lose its quality.

It may not last for long on the paper, that's why it is suggested to use ink.

I have 20 year old notebooks that are mostly filled with pencil and I refer to them occasionally. They are all perfectly legible still and I used a wide variety of pencils.

For true lab notebooks pencil is unacceptable because of their erasability, not longetivity. A formal lab notebook is used in such a way to provide a nearly immutable record. That's why corrections are done with a single line, blank space is blocked out, the notebook is bound with numbered pages and used chronologically, etc.

In a college chemistry class I took our lab notebooks had carbon(less) copy paper for every page. It made handing work in easier, but it also made an unerasable copy of the original record. Quite handy.

Why are your notebooks wet?

Stuff spills, rain, etc... accidents happen.

Use the cheap bic ballpoints. They don't run or smudge.