Evaluation of diffusivity in dense polymeric membranes by statistical moment analysis

A robust procedure to estimate vapor diffusion coefficients from unsteady state measurements is proposed. The permeate flux is measured for a step change in the inlet. The method is based on the interpretation of the normalized permeate flux over time as an integral distribution function. Under the assumption that Fickʹs second law is valid, a relation between the first two statistical moments and the diffusion coefficient was found. The resulting expressions are surprisingly short, convenient to use and robust against errors in determining the actual starting time of an experiment. Furthermore, a ratio involving the first two statistical moments yields a constant number. The comparison with the same ratio obtained from the experimental data shows whether an unsteady permeation process described above obeys Fickʹs second law with constant diffusion coefficient.