{'fraction_non_alphanumeric': 0.018504240555127217, 'fraction_numerical': 0.0, 'mean_word_length': 5.555555555555555, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Effect of lubrication in the non-Reynolds regime due to the non-negligible gap on the fluid permeation through a membrane

To understand lubrication-induced membrane permeation, the effects of permeability and membrane geometry on lubrication pressure and permeate flux are studied in a range of a wall-membrane gap width wherein the effect of lubrication cannot be resolved using the Reynolds lubrication equation. The unresolvable lubrication effect (referred to as the non-Reynolds lubrication effect) is modelled by including a higher-order effect as the wall-tangential variation of the local Couette–Poiseuille velocity. Analytical prediction of the permeate flux is then validated with the fully validated numerical simulation. The result shows that, while the traditional Reynolds lubrication model underestimates the permeate flux, the permeation with the effect of the non-Reynolds lubrication is effectively improved in a small permeability range. Furthermore, the non-Reynolds lubrication model also enables reproduction of the characteristic variation in the permeate flux along the membrane. The effective range of the permeability for the non-Reynolds permeate model is discussed through the order analysis of the pressure terms in the Reynolds and non-Reynolds lubrication regimes.