Pseudo-Fickian

This solution is valid for the initially linear portion of the sorption (or desorption) curve when MtIM is plotted against the square root of time. These equations also demonstrate that for Fickian processes the sorption time scales with the square of the dimension. Thus, to confirm Fickian diffusion rigorously, a plot of MJM vs. Vt/T should be made for samples of different thicknesses a single master curve should be obtained. If the data for samples of different thicknesses do not overlap despite transport exponents of 0.5, the transport is designated pseudo-Fickian. ... 

The 75/25 NR/LLDPE blend exhibited the highest amount of Q, of toluene at the temperatures studied. The diffusion, permeation, and sorption coefficients were obtained for toluene in the various blends. The transport of toluene through the 60/40 NR/LLDPE blend was found to be Fickian at 55 °C, pseudo-Fickian at 35 °C, while for the other blends at the temperatures studied, it was anomalous. The calculated activation energies of diffusion and permeation in the rubber blends were all positive, and were found to decrease with an increase in the amount of NR in the blends. The calculated heat of sorptions for the blends were all positive. 

In some cases the Fickian model does not accurately represent moisture uptake in adhesives. This is illustrated in O Fig. 31.12a, which shows the uptake plot for an epoxide immersed in water at SO C. The experimental data appears to indicate Fickian diffusion however, the best fit of the Fickian diffusion equation to the data indicates equilibrium is reached more slowly than predicted by Fickian diffusion. This type of behavior is sometimes termed pseudo-Fickian behavior. In general, anomalous behavior is seen at high temperatures and humidity. 

Wood, J. and Gladden, L.F., Modelling diffusion and reaction accompanied by capillary condensation using three-dimensional pore networks. Part 1. Fickian diffusion and pseudo-first-order reaction... 

By a derivation based on Maxwell-Stefan diffusion, we were able to obtain an advanced formulation, which overcomes this problem and is applicable to any diffusion mechanism, Maxwell-Stefan as well as (pseudo-)binary Fickian diffusion. Contrarily to the old approach, higher moments diffusion is a function of the diffusive polymer flux (a complete derivation is yet to be published) ... 

In some cases, a pseudo-equilibrium stage is reached in the moisture uptake, which is then followed by a secondary uptake process. This is illustrated in O Fig. 31.13a. This type of behavior indicates that the absorbed moisture has triggered an additional moisture uptake mechanism. For example, differential hygroscopic expansion may lead to cracking and moisture uptake by capillary action. In order to model the moisture uptake shown in Fig. 31.13a, Mubashar et al. (2009b) proposed a dual Fickian model with a Heaviside step function. This model was termed the delayed dual Fickian model, where the secondary uptake is modeled by a power law. The mass uptake by a delayed dual Fickian model is, hence, given by ... 

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