Permeation whith a double mode of soption.
It may be the case of water molecules. The molecules may be trapped and released step by step by step before crossing the membrane. The stationary concentration profile is reached step by step, is not linear and curved to the bottom. The concentration of the occupied sites (or trapped molecules) is high near the upstream face of the membrane and drops rapidly near the downstream face. The time-lag is long and does not give a proper estimation of the diffusion coefficient if using Fick law and another more complicate formulae should be used.
Example 3, case of strong interaction Langmu´r sites and a rapid kinetics of trapping :