]]]]]]]]]]]]]]]] (Jesse's comment) I use a plastic coffee filter that is flat on the bottom. I bought mine in the grocery store. You can see it in drawing 3335. If you can't find this kind of filter, you could also strain the ink through two layers of old pantyhose stretched over the mouth of a jar.
I also researched tannin. As I suspected, tannin in plants functions as a protection from predators as well as an aid to decomposition (without which a seed could not get out of the protective hull and have a chance of sprouting). I've made oak gall ink with galls gathered from gall oak trees in parts of Italy and southern France. The tannin in the galls must protect the wasp eggs within the gall and then help the gall decompose so the little insects can escape. Tannin is acidic; hence the bitter taste if you accidentally get a piece of walnut shell in your mouth.