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Abstract
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This study presented a comprehensive gas permeation model to predict the skin parameters of a complex system,
specifically a hollow fiber membrane with an asymmetric structure consisting of two external and internal skin
layers. According to the work of Haefer for n segments of pores connected in series as in hollow fiber membranes,
applying the Wakao et al. model, a comprehensive model for the transition regime was derived. The model was
examined against the various fabricated PES and PEI hollow fiber membranes. Unlike conventional models, the
proposed method predicted the mean pore size and mean pore length independent of surface porosity for each
skin layer. The study revealed valuable insights into i) the middle pressure, ii) the difference between the skin
parameters of the two membrane skins, and iii) the impact of the feeding direction on gas permeation behavior. It
was shown that the dependency of permeation behavior on the feeding direction is linked to the influence of
middle pressure on viscous flow, which is closely related to surface porosities of each side. It is evident that even
the slightest variations in the fabrication parameters can result in different structures. Furthermore, it is evident
that the assumption of neglecting slip flow was reasonable within the experienced Knudsen number range. The
model also highlighted that the skin parameters of the two skin layers may not be identical, a distinction not
captured by the current models. The traditional approach of setting the middle pressure as the average of the
upstream and downstream pressures has been improved by expressing it as a linear function of both pressures. In
the feed side, higher pressures led to dominant viscous flow, whilst the permeate side was more influenced by the
free molecular regime due to lower pressures. There existed a competition between the Knudsen flow and the
viscous flow at a specific Knudsen number for the feeding side pores, whether it was the inner or outer surf
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