Comparison of classical hydrodynamic models of transport through porous membranes

• Published in: Separation and purification technology 2025-07, Vol.360, p.131189, Article 131189
• Main Authors: Xiao, Minhao, Wang, Xinyi, Hou, Ziwei, Alan Quezada Renteria, Javier, Dlamini, Derrick S., Jassby, David, Hoek, Eric M.V.
• Format: Article
• Language: English
• Subjects: Darcy equation; Fanning equation; Ferry mechanical sieving model; Hagen-Poiseuille equation; Happel cell model; Kozeny-Carman equation; Microfiltration; Ultrafiltration
• ISSN: 1383-5866
• DOI: 10.1016/j.seppur.2024.131189

[Display omitted] •The Kozeny-Carman permeability model agrees best with experimental data in the lower water permeance range (10 to 200 lmh/bar)•The Hagen-Poiseuille model makes better predictions in the higher permeance range (200 to 3,500 lmh/bar)•The Happel’s cell model predictions most closely match experimental water permeance data over the entire range (10 to 3,500 lmh/bar)•Ferry’s mechanical sieving model predictions aligns well with experimental rejection data after applying the dry-to-wet conversion factors. 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.