On the determination of diffusivity and sorption coefficients using different time-lag models

Abstract

Different models have been proposed to fit experimental permeation data in order to obtain membrane transport parameters (sorption capacity and solute diffusivity) when using the time-lag method. Depending on the assumptions, their complexity can vary from a simple linear equation to a more complex non-linear partial differential equation. The applicability, limitations and inaccuracies of these different models are discussed. A numerical procedure to solve the time-lag equation in a membrane slab considering permeate pressure build up is presented. This procedure involves the numerical computation of an inverse Laplace transform using a fast Fourier transform. This is applicable to the full range of the experimental permeation data, provided that both sorption and diffusivity coefficients are constant within the experimental pressure range. Due to its simplicity, the linear time-lag equation is the most commonly used model. However, it does not account for permeate pressure build up. It is shown that this leads to errors in the determination of the permeation parameters which increase with the capacitance parameter (related with the volume available for permeation). For values above a certain threshold (eta > 0.05) these errors are above 5%. Emphasis is put on providing a simple and straight forward way to minimise them.