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The phrase "permeate through" is a valid part of speech that is used in both spoken and written English.
You can use this phrase to describe something that has penetrated or spread throughout an area. For example: "The smell of freshly baked cookies permeated through the house."
Exact(39)
Aminoglycosides severely attenuate the permeation kinetics of K+ and Ca2+ through MET channels while simultaneously slowly permeating through the channel itself [23], [24].
How much more is more is still permeating through the subsurface, contaminating forests and waterways, is unknown.
The inside of the DWT is flushed by helium and collects the tritium permeating through the wall.
We present first the case of a droplet permeating through an individual pore to determine its critical pressure.
Meanwhile, the high speed gas permeating through the sand wall drags the sands of the most downstream layer forward.
Catalytic reduction of N2O was carried out with atomic hydrogen permeating through a palladized Pd sheet electrode.
Similar(21)
"That began to permeate through the club.
But over the years, the marchers' message permeated through.
It did not seem to permeate through to Roy.
The outer membrane is very porous so that the CoA thioesters freely permeate through it.
And thus, it permeates through the most influential facet of their lives — mass media.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com