Permeation with plasticization.
It may be the case of carbon dioxide in oxygenated polymers just under the glass transition. The diffusion coefficients in the dry part of the membrane and in the plasticized part are not very different. The permeation curve likes a fickian permeation curve. The stationary total concentration profile is linear and decreases down to the downstream face. The time-lag gives a rather good estimation of the mean diffusion coefficient using Fick law.
Example 1, case of high dry diffusion speed, moderate speed of relaxation (or plasticization) and short lifetime of plasticized sites :