Double mode of sorption.
It may be the case of solvent molecules at low vapor pressures. Energy of sorption on strong interaction sites is strongly higher than in the other parts of the membrane. At the beginning of the kinetics, most of the molecules are absorbed in the membrane without being trapped and strong interaction sites become to be more and more occupied very slowly. The sorption kinetic curve tends to a equilibrium plateau only after a very long time. The measurement of the initial slope of the sorption kinetic curve cannot give a good estimation of the diffusion coefficient because the estimation of the equilibrium sorbed mass is bad and then, one should obtain only a pseudo diffusion coefficient. The concentration profile becomes to be rather rapidly flat and continues to rate slowly to a final equlibrium profile wich sould be in fact the same as in example 3.
Example 4, case of strong interaction sites and a low kinetics of trapping :