New compact expressions for concentration-polarization of trace-ions in pressure-driven membrane processes

Oren, Yaeli S.; Freger, Viatcheslav; Nir, Oded

doi:10.1016/j.memlet.2021.100003

Cited by 16 publications

(13 citation statements)

References 34 publications

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“…The formation of concentration boundary layers on the membrane surface impacts the apparent membrane selectivity. 54 To incorporate the concentration polarization effects, the boundary layers were modeled using the method developed by Geraldes and Alves, incorporating diffusive, convective, and electromigrative effects 47,49 (see text B.2 in the SI). Mass transfer coefficients within the concentration boundary layers were calculated using empirical correlations from our prior study.…”

Section: Transport Modelmentioning

confidence: 99%

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration

Foo

Rehman

Bouma

et al. 2023

Environ. Sci. Technol.

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Membranes offer a scalable and cost-effective approach to ion separations for lithium recovery. In the case of salt-lake brines, however, the high feed salinity and low pH of the post-treated feed have an uncertain impact on nanofiltration's selectivity. Here, we adopt experimental and computational approaches to analyze the effect of pH and feed salinity and elucidate key selectivity mechanisms. Our data set comprises over 750 original ion rejection measurements, spanning five salinities and two pH levels, collected using brine solutions that model three saltlake compositions. Our results demonstrate that the Li + /Mg 2+ selectivity of polyamide membranes can be enhanced by 13 times with acid-pretreated feed solutions. This selectivity enhancement is attributed to the amplified Donnan potential from the ionization of carboxyl and amino moieties under low solution pH. As feed salinities increase from 10 to 250 g L −1 , the Li + /Mg 2+ selectivity decreases by ∼43%, a consequence of weakening exclusion mechanisms. Further, our analysis accentuates the importance of measuring separation factors using representative solution compositions to replicate the ion-transport behaviors with salt-lake brine. Consequently, our results reveal that predictions of ion rejection and Li + /Mg 2+ separation factors can be improved by up to 80% when feed solutions with the appropriate Cl − /SO 4 2− molar ratios are used.

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Section: Transport Modelmentioning

confidence: 99%

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration

Foo

Rehman

Bouma

et al. 2023

Environ. Sci. Technol.

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show abstract

“…Yet, we ought to point out that one limitation of our current formulation of the intrapore free energy is that the effect of concentration polarization has been ignored. This may turn relevant when the concentration of solutes such as ions and polymers is high and solutes may condense inside the nanopores or at the interface between membrane and feed solutions, thus leading to a solute concentration drop.…”

Section: Discussionmentioning

confidence: 99%

Connection between Intrapore Free Energy, Molecule Permeation, and Selectivity of Nanofiltration Membranes

Yong

Merlitz

2022

Macromolecules

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Purification and separation by nanofiltration is a fascinating interdisciplinary topic that is being actively studied both in polymer science and nanoscience/nanotechnology. However, a comprehensive understanding of the separation mechanism based on a sound physical foundation for the nanofiltration process of aqueous solutions remains very challenging and not well established. To confront this issue, in this study we developed a physical model that is motivated by classic polymer physics for the permeation of polymer chains in confining channels and based on the physics of Brownian motion in the pressure field, thus generalizing the extensively employed Arrhenius-type equation. Our study showed that the intrapore free energy plays a critical role to separate different species in the process of nanofiltration. One main result of our study is that flux behaviors of molecules are controlled by a characteristic pressure defined as critical pressure. Furthermore, we found that this critical pressure directly connects with a free energy barrier, which has been investigated in depth by the potential of mean force for molecules confined in nanopores in extensive previous studies. Another main result of our research is that we clarified in dilute solutions whether or not the relation between solute retention and pressure drop is a linearly decaying function in the process of nanofiltration. Our study showed that the observed decaying relation depends on the regime of pressure drop: if the pressure drop is on the order of the critical pressure, it is decaying in a nonlinear manner; otherwise, it approaches a linear dependence. Our research demonstrated that these two regimes can be wrapped up into an exponentially decaying relation between solute retention and the critical pressures of solute and water, which in turn are determined by their intrapore free energies. These results are universal for the permeation of both polymer chains and hydrated small molecules and mostly independent of molecular and nanopore details, and they can be applied to determine the confinement free energy barrier of molecule permeation particularly for single polymer permeation in experiments, which is still not fully understood. We expect that these findings will provide a priori insight into the process of designing separation membranes with tailored properties.

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“…We introduce the parameter 𝜃 𝑀 that represents the relative mobility of the two ions [23] in the membrane material, which for symmetry purposes, we define in relation to the membrane charge. Thus, 𝜃 𝑀 expresses the relative mobility of the co-ion vs. the counter ion, rather than the cation vs. the anion:…”

Section: Solution-diffusion-electromigration (Sde) Model For Binary Saltmentioning

confidence: 99%

Solution-Diffusion-Electromigration Approximation Model (Sde-A) for Strongly Charged, Weakly Charged and Effectively Uncharged Reverse Osmosis Membranes

Blankert

Martinez

Vrouwenvelder

et al. 2023

Preprint

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New compact expressions for concentration-polarization of trace-ions in pressure-driven membrane processes

Cited by 16 publications

References 34 publications

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration

Connection between Intrapore Free Energy, Molecule Permeation, and Selectivity of Nanofiltration Membranes

Solution-Diffusion-Electromigration Approximation Model (Sde-A) for Strongly Charged, Weakly Charged and Effectively Uncharged Reverse Osmosis Membranes

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