Hydrostatic pressure gradients in ion exchange membranes during mass and charge transfer

Holt, Torleif; Kjelstrup, Signe; Førland, Katrine Seip; Østvold, Terje

doi:10.1016/s0376-7388(00)85118-2

Cited by 10 publications

(5 citation statements)

References 5 publications

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“…First of all, hydrostatic pressure, though zero at both pore mouths, makes a steep excursion within the pore, as also observed in ref. [78], reaching a maximum value of p h,v ∼ 82 kPa, corresponding to the osmotic pressure of a 17 mM salt solution. The electric potential, φ v (x), is virtually unchanging for most of the pore (0 < x < 0.8) before steeply increasing at the very end of the pore.…”

Section: Pore-averaged Fluxesmentioning

confidence: 99%

Analysis of electrolyte transport through charged nanopores

et al. 2016

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We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

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Section: Pore-averaged Fluxesmentioning

confidence: 99%

Analysis of electrolyte transport through charged nanopores

et al. 2016

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“…The simplified calculation for WR in eq can be problematic should there be water exchange between the brackish stream and flow electrodes. In regard to water diffusion across the IEMs, four mechanisms have been proposed, − including (i) hydrostatic water transfer induced by the difference in flow velocities of the brackish stream and the flow electrodes, (ii) an osmotic mechanism ascribed to the ion concentration difference across the membranes, (iii) electroosmosis, that is, concomitant water transfer with ions according to the Maxwell–Stefan (MS) theory, and (iv) water molecules associated with the hydrated ions. Undesirable water diffusion not only reduces FCDI productivity but also dilutes the concentration of active materials in the flow electrode.…”

Section: Introductionmentioning

confidence: 99%

Water Recovery Rate in Short-Circuited Closed-Cycle Operation of Flow-Electrode Capacitive Deionization (FCDI)

Zhang

et al. 2019

Environ. Sci. Technol.

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While flow-electrode CDI is a promising desalination technology that has major advantages when the electrodes are operated in the short-circuited closed-cycle (SCC) mode, little attention has been paid to the water recovery rate, which, in the SCC mode, is determined by the need for partial replacement of the saline electrolyte of the flow electrodes. Results of this study show that an extremely high water recovery rate of ∼95% can be achieved when desalting a 1000 mg NaCl L–1 brackish influent to a potable level of 150 mg L–1. The improved performance with regard to the electrical cost is related, at least in part, to the alleviated concentration polarization at the membrane/electrolyte interface during electrosorption. In effect, the current efficiency decreases with an increase in the water recovery rate. This finding is ascribed to inevitable co-ion leakage since the flow electrodes reject ions with the same charge. In addition, water transport across the ion exchange membranes also influences the water recovery rate. The effect of partial replacement of the saline electrolyte during (semi-)continuous operation requires particular consideration because the associated dilution of the carbon content in the flow electrodes results in a decrease in process performance.

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“…Water transport through ion-exchange membranes has been addressed in the literature both experimentally [3][4][5] and theoretically [6][7][8]. Four mechanisms are often considered to cause water transport: I.…”

Section: Introductionmentioning

confidence: 99%

Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

Tedesco¹,

Hamelers²,

Biesheuvel³

2017

Journal of Membrane Science

136

121

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Transport of water through ion-exchange membranes is of importance both for electrodialysis (ED) and reverse electrodialysis (RED). In this work, we extend our previous theory [J. Membrane Sci., 510, (2016) 370-381] and include water transport in a two-dimensional model for (R)ED. Following a Maxwell-Stefan (MS) approach, ions in the membrane have friction with the water, pore walls, and one another. We show that when ion-ion friction is neglected, the MS-approach is equivalent to the hydrodynamic theory of hindered transport, for instance applied to nanofiltration. After validation against experimental data from literature for ED and RED, the model is used to analyze single-pass seawater ED, and RED with highly concentrated solutions. In the model, fluxes and velocities of water and ions in the membranes are self-consistently calculated as function of the driving forces. We investigate the influence of water and coion leakage under different operational conditions.

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Hydrostatic pressure gradients in ion exchange membranes during mass and charge transfer

Cited by 10 publications

References 5 publications

Analysis of electrolyte transport through charged nanopores

Analysis of electrolyte transport through charged nanopores

Water Recovery Rate in Short-Circuited Closed-Cycle Operation of Flow-Electrode Capacitive Deionization (FCDI)

Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

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