Synonyms for Filter (same or very similar meaning)
WordNet sense 1 (run or flow slowly, as in drops or in an unsteady stream):
dribble, trickle
WordNet sense 2 (remove by passing through a filter):
filtrate, strain, filter out, separate out
WordNet sense 3 (pass through):
percolate, permeate, sink in
From the ODE community, based on WordNet
add/edit