Verb
Of a liquid; to move slowly down to lower substrate levels.
(idiomatic) (by extension) Of information, or resources; to move slowly down to lower levels of an organisation, or population.
They might say that the economy is improving, but it is taking a long time for any money to filter down to the poorer classes.
In the long run, much public opinion is made in the universities; ideas generated there filter down through the teaching profession and the students into the general public. B. Carroll Reece