Permeation with plasticization.
It may be the case of low solvents like aliphatic solvents in polymers just under the glass transition. The upstream part of the membrane is swelled but the downstream part is dry and then the diffusion decreases strongly from the upstream face to the downstream face on the membrane. The time-lag should not be related to an estimation of the global diffusion coefficient because this one is evoluating greatly with time during the beginning of the permeation kinetics and it is then not easy to found a relation between the time-lag and the stationary global diffusion coefficient. The global permeability of the membrane is low.
Example 2, case of low speed of plasticization, moderate lifetime of plasticized sites and low dry diffusion speed :