Experimental observation of nonlinear relation between pressure and water flux is consistent with the solution-diffusion model

Journal Article · Sat Sep 27 00:00:00 UTC 2025 · Journal of Membrane Science

DOI: https://doi.org/10.1016/j.memsci.2025.124756 · OSTI ID:2997741

Reimund, Kevin K.  ^[1]; Sujanani, Rahul  ^[2]; Hernandez, Jorge Marcellino  ^[1]; Gleason, Kristofer L.  ^[1]; Freeman, Benny D.  ^[3]

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1. The University of Texas at Austin, TX (United States)
2. The University of Texas at Austin, TX (United States); University of California, Santa Barbara, CA (United States)
3. The University of Texas at Austin, TX (United States); Monash University, Clayton, VIC (Canada)

In several recent studies, it has been proposed that the fundamental understanding of penetrant transport in dense polymer membranes occurring via the solution-diffusion model, which has been the generally accepted theoretical framework for describing penetrant transport in such materials for the past several decades, is flawed. An alternate mechanistic framework based on the idea of two-phase flow in a porous medium (i.e., pore-flow) has been broadly advanced instead, with proponents of this approach claiming that the pore-flow theoretical framework provides the necessary mechanistic insight to design novel polymeric membrane materials for emerging applications. In this study, we show experimental results for hydraulic permeation of water that are entirely consistent with the solution-diffusion theory, without modification, for three dense polymeric membranes: crosslinked poly(ethylene glycol diacrylate) (XLPEGDA), Nafion 117 ionomer in the sodium counterion form (Nafion 117-Na), and cellulose acetate (CA). By measuring water flux at transmembrane pressures up to 240 bar, we observe a nonlinear relationship between the transmembrane pressure (TMP) and water flux, J_w, for XLPEGDA and Nafion 117-Na, while this relationship is linear for CA. We demonstrate that the behavior of these three materials is described via the solution-diffusion model. According to the solution-diffusion model, flux is, to a good approximation, proportional to the transmembrane concentration difference induced by the pressure difference across the membrane, rather than to TMP itself. Water sorption isotherms are reported for all three materials. They further justify the nonlinear relationship between TMP and J_w observed in XLPEGDA and Nafion 117-Na, emphasizing that the nonlinearity in the flux/TMP relationship stems from nonlinearities in the sorption isotherm with pressure. Additionally, the relationship between water flux and TMP can be predicted, a priori, with no adjustable parameters when a predictive model for the diffusion coefficient of water is employed in conjunction with the experimental water sorption isotherms in the solution-diffusion model. Furthermore, our results demonstrate the validity of the solution-diffusion model to describe transport of penetrants in dense polymer membranes, while highlighting the sensitivity of the solution-diffusion model to the many physical and mathematical simplifications commonly applied to the theory in literature.

• Research Organization: The University of Texas at Austin, TX (United States); University of California, Santa Barbara, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0019272
• OSTI ID: 2997741
• Journal Information: Journal of Membrane Science, Journal Name: Journal of Membrane Science; ISSN 0376-7388
• Publisher: Elsevier BVCopyright Statement
• Country of Publication: United States
• Language: English