verb
permeate
PER-mee-ayt/ˈpɜːrmieɪt/
Spread throughout or pass through something.
The blue dye permeates the water, spreading through it in branching currents.

Etymology
The core image is passing through something, not breaking it open. This fits the selected sense of spreading throughout a substance or reaching every part of it.
In context
there's something about the last 4 days that led to the membranes breaking and air being allowed to permeate through the membranes
More examples
- Rainwater slowly permeates the soil.
- A sense of excitement permeates the entire school.
- Smoke from the campfire permeated our clothes.
Forms
permeate · permeates · permeated · permeating
permeation noun — The process of spreading throughout something.
permeable adjective — Allowing liquids or gases to pass through.