filter down
1. (literally) Of a liquid, to slowly seep down through lower substrate levels. The company bottles rainwater that has filtered down through seven layers of volcanic rock, purifying it and enriching it with minerals.
2. (by extension) Of information, resources, communication, etc., to move slowly and in small amounts down to lower levels of people in an organization, population, or group. It always takes a dog's age for any important company information to filter down to me and the other interns. The government has approved a staggering $200 billion stimulus package, but some experts warn it could be years before that money filters down to individuals and smaller businesses.