permeate through (something)
To pass or seep through something that is not entirely solid, such as a mesh or porous material. The store said this jacket was waterproof, but I can feel moisture starting to permeate through it. The fungus permeated through the thin walls, eventually contaminating every room in the house.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
permeate through something
to seep in and saturate something. The coffee spilled on the desk and permeated through all the papers and stuff. The strong odor permeated through the walls and nearly suffocated us.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.