Herein, we compare three hydrodynamic models for the water permeance (Hagen-Poiseuille, Kozeny-Carman, and Happel cell) and solute rejection (Ferry, Ferry-Renkin, and Zeman-Wales) of porous microfiltration (MF) and ultrafiltration (UF) membranes. We fabricate a series of porous membranes via nonsolvent induced phase separation (NIPS) comprising different concentrations of polysulfone (PSU), polyvinylidene fluoride (PVDF), and polyethersulfone (PES). Analysis of scanning electron microscope (SEM) images enabled quantification of surface porosity, mean pore size, and skin layer thickness of dry membranes. Water uptake and membrane swelling measurements yield the dry-to-wet conversion factor that allows one to reproduce the fully wetted membrane pore morphology from dry membrane SEM images. Dead-end stirred-cell filtration data establishes the observed water permeance and solute rejection by the membranes. After applying the dry-to-wet conversion factors, Ferry’s mechanical sieving model predictions fit experimental rejection data almost perfectly. The Kozeny-Carman permeability model agreed best with experimental data in the lower water permeance range (10 to 200 lmh/bar), whereas the Hagen-Poiseuille made better predictions in the higher permeance range (200 to 3,500 lmh/bar). That said, Happel’s cell model predictions most closely matched experimental water permeance data over the entire range. A new equation of porous membrane water permeance is proposed based on best fit results from the membranes tested herein, while the original Ferry mechanical sieving model works nearly perfectly for uncharged solutes using SEM derived mean pore size. Our results clearly illustrate the role of porous membrane swelling in aqueous filtration applications and must always be considered in membrane characterization studies.

中文翻译：

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通过多孔膜传递的经典流体动力学模型的比较


在此，我们比较了多孔微滤 （MF） 和超滤 （UF） 膜的透水率（Hagen-Poiseuille、Kozeny-Carman 和 Happel 胞胎）和溶质排斥（Ferry、Ferry-Renkin 和 Zeman-Wales）的三种流体动力学模型。我们通过非溶剂诱导相分离 （NIPS） 制造了一系列多孔膜，其中包含不同浓度的聚砜 （PSU）、聚偏二氟乙烯 （PVDF） 和聚醚砜 （PES）。通过分析扫描电子显微镜 （SEM） 图像，可以量化干膜的表面孔隙率、平均孔径和皮肤层厚度。吸水率和膜溶胀测量产生干湿转换因子，允许从干膜 SEM 图像中重现完全润湿的膜孔形态。死端搅拌细胞过滤数据确定了观察到的膜的透水和溶质截留。在应用干湿转换因子后，Ferry 的机械筛分模型预测几乎完美地拟合了实验废料数据。Kozeny-Carman 渗透率模型与较低透水率范围（10 至 200 lmh/bar）的实验数据最吻合，而 Hagen-Poiseuille 模型在较高渗透率范围（200 至 3,500 lmh/bar）的预测效果更好。也就是说，Happel 的细胞模型预测与整个范围内的实验透水数据最接近。根据本文测试的膜的最佳拟合结果，提出了一种新的多孔膜透水方程，而原始的 Ferry 机械筛分模型使用 SEM 得出的平均孔径几乎完美地适用于不带电的溶质。 我们的结果清楚地说明了多孔膜溶胀在水过滤应用中的作用，在膜表征研究中必须始终考虑。