Permeation with a double mode of sorption.
Example 1, case of low concentration of Langmu´r sites and weak interactions :

It may be the case of gas molecules such nitrogen or oxygen in olefinic polymers. Strong interaction sites may be induced by some impurities. The kinetic permeation curve likes a fickian kinetics. The concentration of trapped molecules on Langmu´r sites is low, the stationary total concentration profile is linear and decreases down to the downstream face. The time-lag gives a good estimation of the diffusion coefficient using Fick law.