Nernst–Planck modeling of multicomponent ion transport in a Nafion membrane at high current density

Moshtarikhah, S.; Oppers, N. A. W.; Groot, Matheus T. de; Keurentjes, J.T.F.; Schouten, J.C.; Schaaf, J. van der

doi:10.1007/s10800-016-1017-2

Cited by 36 publications

(31 citation statements)

References 47 publications

(71 reference statements)

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“…Furthermore, a steep decrease of the chloride ion concentration at high current densities makes the contribution of transport of chloride ions inside the membrane lower compared to the other ions. The increase of sodium selectivity with increasing current density is not in line with the observed decreasing trend in our earlier paper [14] in a system with identical sodium hydroxide solution as both anolyte and catholyte. However, it is in line with the observed increasing trend of selectivity in the chlor-alkali experiment carried out in the spinning disc membrane electrolyzer explained in our paper elsewhere [32].…”

Section: Discussioncontrasting

confidence: 84%

“…The diffusivities are calculated based on the temperature-dependent diffusivity in free water [23]. The calculation of the diffusion coefficients inside the membrane taking into account the effect of tortuosity and porosity, together with the calculation of the total porosity of the membrane has been elaborated in our previous paper [1,14,24]. The membrane permselectivity as represented by the sodium transport number is calculated from the ionic fluxes:…”

Section: Model Approach and Assumptionsmentioning

confidence: 99%

“…There are various methods to model ion transport in ion-exchange membranes, and these have been reviewed and modeled by several authors [11][12][13]. In our earlier paper [14], we developed a NernstPlanck model of multicomponent ion transport through a cation-exchange membrane for a monolayer membrane. The model was validated with experiments using same electrolyte solutions with identical anolyte and catholyte concentrations.…”

Section: Introductionmentioning

confidence: 99%

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Multicomponent ion transport in a mono- and bilayer cation-exchange membrane at high current density

et al. 2016

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This work describes a model for bilayer cationexchange membranes used in the chlor-alkali process. The ion transport inside the membrane is modeled with the Nernst-Planck equation. A logistic function is used at the boundary between the two layers of the bilayer membrane to describe the change in the properties of each membrane layer. The local convective velocity is calculated inside the membrane using the Schlögl equation and the equation of continuity. The model calculates the ion concentration profiles inside the membrane layers. Modeling results of mono-and bilayer membranes are compared. The changes in membrane voltage drop and sodium selectivity are predicted. The concentration profile of sodium ions in the bilayer membrane is significantly different from the monolayer membrane. Without the applied current, a linear change in the sodium concentration is observed in the monolayer membrane and in each layer of the bilayer membrane. With an increase in current density, the stronger electromotive force in the carboxylate layer causes a decrease in the sodium concentration in the sulfonate layer, down to the fixed ionic group concentration. This significant decrease of sodium ion concentration in the sulfonate layer results in low concentrations of counter ions and as a consequence a higher permselectivity of the bilayer membrane is obtained when compared to the single-layer membrane. As a drawback, the resistance in the bilayer membrane increases.

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Section: Discussioncontrasting

confidence: 84%

Section: Model Approach and Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multicomponent ion transport in a mono- and bilayer cation-exchange membrane at high current density

et al. 2016

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“…This model has also simplified the calculation of the membrane potential gradient by neglecting the concentration gradient and by using Ohm's law to derive the potential gradient explicitly. The neutrality condition is broken by this simplification, which has been numerically proven during the investigation of the extended Nernst-Planck model [8].…”

Section: Introductionmentioning

confidence: 87%

“…Unfortunately, the information on membrane performance at high current densities remains scarce. Ion transport across a membrane under current load is not completely understood despite the fact that there have been several attempts to model the behavior by either using Maxwell-Stefan (MS) or Nernst-Planck (NP) models [2][3][4][5][6][7][8]. The Nernst-Planck approach assumes an ideal solution and neglects ion-ion interactions.…”

Section: Introductionmentioning

confidence: 99%

Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis

et al. 2019

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A mathematical model based on a generalized Maxwell-Stefan equation has been developed to describe multicomponent ion and water transport inside a cation-exchange membrane. This model has been validated using experimental data and has been used to predict concentration profiles, membrane potential drop, and transport numbers of ions and water for the chlor-alkali process at increased current densities. Several improvements have been made to previously developed Maxwell-Stefan models. In our model, the generalized Maxwell-Stefan equation is written in terms of concentration instead of mole fraction and the fixed group (membrane) concentration is assumed to be constant. We have adapted the Augmented matrix method using the built-in partial differential equation parabolic elliptic (pdepe) solver in Matlab®, and both the concentration and the electrical potential gradients have been solved simultaneously. The boundary conditions are determined with the Donnan equilibrium at the membrane-solution interface. We have also employed semi-empirical correlations to define the Maxwell-Stefan diffusivities inside the membrane. For the bulk diffusivities, we applied the correlations for the concentrated solution instead of the values at infinite dilution. With the diffusivities presented in this work, the model shows a better fit to the experimental data than with previously reported fitted diffusivities. Prediction of the sodium transport number and water transport number is generally good, whereas the deviations with regard to membrane potential might also be related to issues with the experimental data. The model predicts an increase in both sodium and water transport numbers at increased current density operation of chlor-alkali production.

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K⁺ Transport in Perfluorosulfonic Acid Membranes and Its Influence on Membrane Resistance in CO₂ Electrolysis

et al. 2021

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In CO 2 electroreduction it is common to use cation exchange membranes in combination with high-molar electrolytes. In a model polymer electrolyte membrane (PEM) water electrolysis setup, which mimics CO 2 electrolysis in a mixed (mode mix ) and in a separate electrolyte mode (mode sep ), this study investigates how K + -sulfonate interactions increase membrane resistance dependent on the electrolyte concentration. K + -based electrolytes (KHCO 3 , K 2 SO 4 ) are used instead of ultrapure water in the PEM-model electrolyzer. At 1.0 M KHCO 3 , the membrane resistance is increased by 1.7 Ω cm 2 (cathode side only) to 4.2 Ω cm 2 (mode mix ), causing a significant voltage increase that needs to be invested for K + transport over a PFSA membrane. We quantify the underlying ionic interactions to 527-545 mV and observed a further effect, namely a space-charge limitation expressed by a strongly increased voltage, occurring in the case of K + overload when lacking hopping centers for cation transport. Beginning at ca. 300 mA/cm 2 , the current density gets high enough to drive K + back to the cathode side and low enough to prevent large resistive contributions and K + overload. Along with thermodynamic considerations and pHinduced intrinsic operational contributions, the membrane resistance was found to have a significant impact contributing to the total cell voltage V total and proved that current research towards green and scalable CO 2 electrolysis is on a promising way towards broad application.[a] K.

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Nernst–Planck modeling of multicomponent ion transport in a Nafion membrane at high current density

Cited by 36 publications

References 47 publications

Multicomponent ion transport in a mono- and bilayer cation-exchange membrane at high current density

Multicomponent ion transport in a mono- and bilayer cation-exchange membrane at high current density

Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis

K⁺ Transport in Perfluorosulfonic Acid Membranes and Its Influence on Membrane Resistance in CO₂ Electrolysis

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Nernst–Planck modeling of multicomponent ion transport in a Nafion membrane at high current density

Cited by 36 publications

References 47 publications

Multicomponent ion transport in a mono- and bilayer cation-exchange membrane at high current density

Multicomponent ion transport in a mono- and bilayer cation-exchange membrane at high current density

Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis

K+ Transport in Perfluorosulfonic Acid Membranes and Its Influence on Membrane Resistance in CO2 Electrolysis

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K⁺ Transport in Perfluorosulfonic Acid Membranes and Its Influence on Membrane Resistance in CO₂ Electrolysis