Gradual process of assimilation (7)
I believe the answer is:
osmosis
'gradual process of assimilation' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for osmosis that I've seen before include "Passage of bodily fluid through porous partition" , "Becoming absorbed" , "Diffusion of liquid through porous barrier" , "Miss Soo? (anag)" , "absorbing process" .)