In these units: cm³.20μ/m².24hr.atm - (definition) cubic centimeters for a 20 micron film thickness per square meter per 24 hours under a pressure difference of 1 atm.
My question is what does the "Pressure difference of 1 atm" mean?
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One atmosphere pressure difference means the pressure one one face of this membrane is higher than the other face by one atmosphere.
It is the driving force for tests to measure the permeability of membranes for certain gases under constant pressure gradient and constant temperature. check here. Pressure difference is to test static mechanical permeability. Many other test are needed for each chemical or substance.