Solution-diffusion-imperfection model revised
Abstract
The traditional version of solution diffusion imperfections (SDI) model does not take into account solute diffusion through imperfections. Although the mechanism of transport through imperfections is a non-separative viscous flow, the solute concentration at the exit of an imperfection is decreased due to solute diffusion along the membrane towards the surrounding perfect regions, hence, solute diffusion through imperfections. The SDI model was revised by including this phenomenon in it. It was found that the plots in the {, ) coordinates become non-linear. Small and numerous imperfections produce large deviations from linearity than large and scarce ones. The non-linearity may give rise to errors in extrapolation to the limiting rejection.
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In the past few decades, organic solvent nanofiltration (OSN) has attracted numerous researchers and broadly applied in various fields. Unlike conventional nanofiltration, OSN always faced a broad spectrum of solvents including polar solvents and non-polar solvents. Among those recently developed OSN membranes in lab-scale or widely used commercial membranes, researchers preferred to explore intrinsic materials or introduce nanomaterials into membranes to fabricate OSN membranes. However, the hydrophilicity of the membrane surface towards filtration performance was often ignored, which was the key factor in conventional aqueous nanofiltration. The influence of surface hydrophilicity on OSN performance was not studied systematically and thoroughly. Generally speaking, the hydrophilic OSN membranes performed well in the polar solvents while the hydrophobic OSN membranes work well in the non-polar solvent. Many review papers reviewed the basics, problems of the membranes, up-to-date studies, and applications at various levels. In this review, we have focused on the relationship between the surface hydrophilicity of OSN membranes and OSN performances. The history, theory, and mechanism of the OSN process were first recapped, followed by summarizing representative OSN research classified by surface hydrophilicity and types of membrane, which recent OSN research with its contact angles and filtration performance were listed. Finally, from the industrialization perspective, the application progress of hydrophilic and hydrophobic OSN membranes was introduced. We started with history and theory, presented many research and application cases of hydrophilic and hydrophobic OSN membranes, and discussed anticipated progress in the OSN field. Also, we pointed out some future research directions on the hydrophilicity of OSN membranes to deeply develop the effect made by membrane hydrophilicity on OSN performance for future considerations and stepping forward of the OSN industry.
Role of imperfections in transfer of organic micro-pollutants through RO/NF membranes: Numerical study
2023, DesalinationDue to relatively low diffusivities, the rejection of organic micro-pollutants in pressure-driven membrane processes is more affected by Concentration Polarization (CP) than that of typical inorganic ions. On the other hand, it can be more sensitive to various membrane imperfections because the rejection of these solutes by intact membranes can be expected to be quite high. This makes necessary simultaneous accounting for membrane imperfections and Concentration Polarization in Reverse Osmosis and/or Nanofiltration of organic micro-pollutants. This study, for the first time, explores this problem numerically for the model of a single circular opening in a selective layer (the porous support is assumed to remain undamaged). The solute accumulated due to the CP close to the surrounding intact active layer “spills over” to the imperfection, which leads to an enhanced transmembrane solute passage as compared to the classical solution-diffusion-imperfection model assuming this passage to be controlled by the feed concentration. Our analysis reveals that the extent of this “spill-over” depends primarily on the size of imperfection (we studied the range between 0.2 μm and 20 μm) as well as on the ratio of hydraulic resistances of selective and support layers. Smaller imperfections in active layers of membranes with less permeable porous supports have larger impact. The extent of CP away from the imperfection is also important. Contrary to the trend expected for imperfection-free membranes (a better rejection of larger solutes due to a stronger steric exclusion and hindrance), the solute passage through imperfections is demonstrated to be larger for solutes with smaller diffusion coefficients, so in future experiments this can be considered a signature feature of a noticeable impact of imperfections. Quantifying their impact is important for understanding membrane aging, rational selection of membrane cleaning procedures as well as development of better membranes.
Two-dimensional model of ion transport in composite membranes active layers with TEM-scanned morphology
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Interplay between membrane imperfections and external concentration polarization
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Deep learning meets quantitative structure–activity relationship (QSAR) for leveraging structure-based prediction of solute rejection in organic solvent nanofiltration
2022, Journal of Membrane ScienceCitation Excerpt :The solution–diffusion model governs dialysis, reverse osmosis, gas permeation, pervaporation, or, more broadly, permeation through dense media [22]. The solution–diffusion–imperfection model can accurately estimate solvent flux or solute permeance for nanofiltration, particularly for OSN [23,24]. Hildebrand and Hansen's solubility parameters have been employed in the modeling of solvent and solute permeation in OSN [14,20].
Methods for determining solute rejection in organic solvent nanofiltration (OSN) are time-consuming and expensive and still rely on wet-lab measurements, resulting in the slow development of membrane processes. OSN, similar to other membrane technologies, requires precise and comprehensive predictive models that can function on various solutes, membranes, and solvents. We present two prediction methods based on the quantitative structure–activity relationship (QSAR) using traditional machine learning (ML) and deep learning (DL) models. The partial least-squares regression model combined with the variable importance in projection and genetic algorithm achieves a slightly lower root-mean-square error score (8.04) than the DL-based graph neural network (10.40). For the first time, we visualize the effect of different solute functional groups on rejection, providing a new platform for a more in-depth investigation into the membrane–solute interactions, potentially enabling the design of membranes with improved selectivity. Our ML model is freely accessible on the OSN database website (www.osndatabase.com) for everyone.
Influence of Solute Molecular Diameter on Permeability-Selectivity Tradeoff of Thin-Film Composite Polyamide Membranes in Aqueous Separations
2021, Water ResearchFundamental understanding of the reverse osmosis (RO) transport phenomena is necessary for quantitative prediction of contaminant rejection and development of more selective membranes. The solution-diffusion (S-D) model predicts a tradeoff relationship between permeability and selectivity, and this tradeoff trend was recently reported for RO. But the first principles governing the relationship are not well understood for aqueous separation membranes. This study presents a framework to elucidate the underlying factors of the permeability-selectivity tradeoff relationship in thin-film composite polyamide (TFC-PA) membranes. Water and solute permeabilities of membranes with a range of selectivities are examined using six nonelectrolyte solutes of various sizes and dimensions. The permeability-selectivity tradeoff trend, as defined by S-D, was observed for all six solutes. Crucially, the slopes of the tradeoff lines, λ, are found to be related to the solute and solvent (i.e., water) diameters, ds and dw, respectively, by λ = (ds/dw)2 – 1, consistent with the S-D framework established for gas separation membranes. Additionally, the intercepts of the tradeoff lines are shown to be also influenced by ds. These results highlight that solute molecular diameter is a primary influence on the permeability-selectivity tradeoff for the permeants investigated in this study. Furthermore, a transport regime where solute permeation is only very weakly coupled to water transport, in addition to the conventional S-D, is identified for the first time. We demonstrate that the boundary delineating the two transport regimes can be determined by the solute diameter. The relationship between characteristic features of the “additional regime” and solute dimensions are analyzed. The study shows that the general principles of the S-D framework are applicable to TFC-PA membranes and the analysis quantified the principal role of solute size in governing RO transport. The experimental and analytical evidence suggest that nonelectrolyte solute transport can, in principle, be a priori predicted using molecular diameter. Findings of this investigation provide new insights for understanding the transport mechanisms in osmotic membrane processes.