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Thomas Gimmi - One of the best experts on this subject based on the ideXlab platform.
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Solving the Nernst‐Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces
Water Resources Research, 2020Co-Authors: Christophe Tournassat, Carl I Steefel, Thomas GimmiAbstract:Molecular diffusion of dissolved species is a fundamental mass transport process affecting many environmental and technical processes. Whereas diffusive transport of single tracers can be described by Fick's law, a multicomponent approach based on the Nernst‐Planck Equation is required for charge‐coupled transport of ions. The numerical solution of the Nernst‐Planck Equation requires special attention with regard to properties that are required at interfaces of numerical cells when using a finite difference or finite volume method. Weighted arithmetic and harmonic averages are used in most codes that can solve the Nernst‐Planck Equation. This way of averaging is correct for diffusion coefficients but inappropriate for solute concentrations at interfaces. This averaging approach leads to charge balance problems and thus to numerical instabilities near interfaces separating grid volumes with contrasting properties. We argue that a logarithmic‐differential average should be used. Here this result is generalized, and it is demonstrated that it generally leads to improved numerical stability and accuracy of concentrations computed near material interfaces. It is particularly relevant when modeling semipermeable clay membranes or membranes used in water treatment processes.
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solving the nernst planck Equation in heterogeneous porous media with finite volume methods averaging approaches at interfaces
Water Resources Research, 2020Co-Authors: Christophe Tournassat, Carl I Steefel, Thomas GimmiAbstract:Molecular diffusion of dissolved species is a fundamental mass transport process affecting many environmental and technical processes. Whereas diffusive transport of single tracers can be described by Fick's law, a multicomponent approach based on the Nernst‐Planck Equation is required for charge‐coupled transport of ions. The numerical solution of the Nernst‐Planck Equation requires special attention with regard to properties that are required at interfaces of numerical cells when using a finite difference or finite volume method. Weighted arithmetic and harmonic averages are used in most codes that can solve the Nernst‐Planck Equation. This way of averaging is correct for diffusion coefficients but inappropriate for solute concentrations at interfaces. This averaging approach leads to charge balance problems and thus to numerical instabilities near interfaces separating grid volumes with contrasting properties. We argue that a logarithmic‐differential average should be used. Here this result is generalized, and it is demonstrated that it generally leads to improved numerical stability and accuracy of concentrations computed near material interfaces. It is particularly relevant when modeling semipermeable clay membranes or membranes used in water treatment processes.
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simulating donnan equilibria based on the nernst planck Equation
Geochimica et Cosmochimica Acta, 2018Co-Authors: Thomas Gimmi, Peter AlteppingAbstract:Abstract Understanding ion transport through clays and clay membranes is important for many geochemical and environmental applications. Ion transport is affected by electrostatic forces exerted by charged clay surfaces. Anions are partly excluded from pore water near these surfaces, whereas cations are enriched. Such effects can be modeled by the Donnan approach. Here we introduce a new, comparatively simple way to represent Donnan equilibria in transport simulations. We include charged surfaces as immobile ions in the balance Equation and calculate coupled transport of all components, including the immobile charges, with the Nernst-Planck Equation. This results in an additional diffusion potential that influences ion transport, leading to Donnan ion distributions while maintaining local charge balance. The validity of our new approach was demonstrated by comparing Nernst-Planck simulations using the reactive transport code Flotran with analytical solutions available for simple Donnan systems. Attention has to be paid to the numerical evaluation of the electrochemical migration term in the Nernst-Planck Equation to obtain correct results for asymmetric electrolytes. Sensitivity simulations demonstrate the influence of various Donnan model parameters on simulated anion accessible porosities. It is furthermore shown that the salt diffusion coefficient in a Donnan pore depends on local concentrations, in contrast to the aqueous salt diffusion coefficient. Our approach can be easily implemented into other transport codes. It is versatile and facilitates, for instance, assessing the implications of different activity models for the Donnan porosity.
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incorporating electrical double layers into reactive transport simulations of processes in clays by using the nernst planck Equation a benchmark revisited
Applied Geochemistry, 2018Co-Authors: Peter Altepping, Thomas Gimmi, Paul Wersin, Andreas JenniAbstract:Abstract Owing to their low permeability clay formations are considered as potential host rocks for nuclear waste or as seals capping permeable reservoirs for storing unconventional gases. Clay materials such as bentonite are considered as backfill or buffer material in nuclear waste repositories forming barriers to fluid flow owing to their hydraulic and swelling properties. The low permeability of clays implies that solute transport in the pore water is dominated by diffusion. Another important characteristic of clays is the negative surface charge of clay minerals which affects transport and the distribution of ions in the pore space: cations are attracted to while anions are repelled from clay mineral surfaces. Models of reactive transport need to consider these electrostatic effects to be able to accurately simulate the transport of ions through clay. Here we use a new approach which is entirely based on the solution of the Nernst-Planck Equation to incorporate the effect of diffuse layers (DLs) into reactive transport simulations. A simulation benchmark is used to validate this new approach. In variants of this benchmark problem the impact of different activity models on the pore water composition, Donnan equilibrium versus a kinetic exchange between the DL and free pore water and the effect of diffusive transport in the DL are explored.
Takashi Kakiuchi - One of the best experts on this subject based on the ideXlab platform.
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a theory of voltammetry of ion transfer across a liquid membrane in the absence of supporting electrolytes using the nernst planck Equation and electroneutrality assumption
Electrochimica Acta, 1998Co-Authors: Takashi KakiuchiAbstract:A theory of cyclic voltammetry of ion transfer across a liquid membrane has been presented based on the Nernst–Planck Equation and the electroneutrality assumption. The initial conditions are given by the partition equilibrium of ions between the membrane and the two bathing solutions. Current–potential curves are calculated for the case of reversible transfer of Na+ across the membrane/solution boundary and the complete dissociation of electrolytes in the membrane, taking account of time-dependent solution resistance and the diffusion potential. The peaks appear only in the limited range of the scan rate at a given thickness of the membrane. The model explains wide peak separation which has been reported in the voltammetry of ion transfer in the presence of lipophilic ions. Upon imposing the voltage across the membrane, the phase-boundary potential at each side of the membrane varies with time and, hence, the ion partitioning at the membrane/bathing solution interface is a time-dependent process.
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A theory of voltammetry of ion transfer across a liquid membrane in the absence of supporting electrolytes using the Nernst–Planck Equation and electroneutrality assumption
Electrochimica Acta, 1998Co-Authors: Takashi KakiuchiAbstract:A theory of cyclic voltammetry of ion transfer across a liquid membrane has been presented based on the Nernst–Planck Equation and the electroneutrality assumption. The initial conditions are given by the partition equilibrium of ions between the membrane and the two bathing solutions. Current–potential curves are calculated for the case of reversible transfer of Na+ across the membrane/solution boundary and the complete dissociation of electrolytes in the membrane, taking account of time-dependent solution resistance and the diffusion potential. The peaks appear only in the limited range of the scan rate at a given thickness of the membrane. The model explains wide peak separation which has been reported in the voltammetry of ion transfer in the presence of lipophilic ions. Upon imposing the voltage across the membrane, the phase-boundary potential at each side of the membrane varies with time and, hence, the ion partitioning at the membrane/bathing solution interface is a time-dependent process.
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current potential characteristic of ion transfer across the interface between two immiscible electrolyte solutions based on the nernst planck Equation
Journal of Electroanalytical Chemistry, 1992Co-Authors: Takashi KakiuchiAbstract:Abstract A current—potential characteristic for ion transfer across the polarized interface between two immiscible electrolyte solutions (ITIES) is derived using a Goldman-type approximation to solve the Nernst—Planck Equation which describes ion transfer across the inner part of the double layer. The proposed model can predict salient features of the current—potential characteristic experimentally observed in monovalent ion transfer across ITIES. The nonlinearity in the current—overpotential characteristic, i.e. the Goldman-type rectification, provides a new way of studying charge transfer kinetics at ITIES.
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Current—potential characteristic of ion transfer across the interface between two immiscible electrolyte solutions based on the Nernst—Planck Equation
Journal of Electroanalytical Chemistry, 1992Co-Authors: Takashi KakiuchiAbstract:Abstract A current—potential characteristic for ion transfer across the polarized interface between two immiscible electrolyte solutions (ITIES) is derived using a Goldman-type approximation to solve the Nernst—Planck Equation which describes ion transfer across the inner part of the double layer. The proposed model can predict salient features of the current—potential characteristic experimentally observed in monovalent ion transfer across ITIES. The nonlinearity in the current—overpotential characteristic, i.e. the Goldman-type rectification, provides a new way of studying charge transfer kinetics at ITIES.
Peter Altepping - One of the best experts on this subject based on the ideXlab platform.
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simulating donnan equilibria based on the nernst planck Equation
Geochimica et Cosmochimica Acta, 2018Co-Authors: Thomas Gimmi, Peter AlteppingAbstract:Abstract Understanding ion transport through clays and clay membranes is important for many geochemical and environmental applications. Ion transport is affected by electrostatic forces exerted by charged clay surfaces. Anions are partly excluded from pore water near these surfaces, whereas cations are enriched. Such effects can be modeled by the Donnan approach. Here we introduce a new, comparatively simple way to represent Donnan equilibria in transport simulations. We include charged surfaces as immobile ions in the balance Equation and calculate coupled transport of all components, including the immobile charges, with the Nernst-Planck Equation. This results in an additional diffusion potential that influences ion transport, leading to Donnan ion distributions while maintaining local charge balance. The validity of our new approach was demonstrated by comparing Nernst-Planck simulations using the reactive transport code Flotran with analytical solutions available for simple Donnan systems. Attention has to be paid to the numerical evaluation of the electrochemical migration term in the Nernst-Planck Equation to obtain correct results for asymmetric electrolytes. Sensitivity simulations demonstrate the influence of various Donnan model parameters on simulated anion accessible porosities. It is furthermore shown that the salt diffusion coefficient in a Donnan pore depends on local concentrations, in contrast to the aqueous salt diffusion coefficient. Our approach can be easily implemented into other transport codes. It is versatile and facilitates, for instance, assessing the implications of different activity models for the Donnan porosity.
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incorporating electrical double layers into reactive transport simulations of processes in clays by using the nernst planck Equation a benchmark revisited
Applied Geochemistry, 2018Co-Authors: Peter Altepping, Thomas Gimmi, Paul Wersin, Andreas JenniAbstract:Abstract Owing to their low permeability clay formations are considered as potential host rocks for nuclear waste or as seals capping permeable reservoirs for storing unconventional gases. Clay materials such as bentonite are considered as backfill or buffer material in nuclear waste repositories forming barriers to fluid flow owing to their hydraulic and swelling properties. The low permeability of clays implies that solute transport in the pore water is dominated by diffusion. Another important characteristic of clays is the negative surface charge of clay minerals which affects transport and the distribution of ions in the pore space: cations are attracted to while anions are repelled from clay mineral surfaces. Models of reactive transport need to consider these electrostatic effects to be able to accurately simulate the transport of ions through clay. Here we use a new approach which is entirely based on the solution of the Nernst-Planck Equation to incorporate the effect of diffuse layers (DLs) into reactive transport simulations. A simulation benchmark is used to validate this new approach. In variants of this benchmark problem the impact of different activity models on the pore water composition, Donnan equilibrium versus a kinetic exchange between the DL and free pore water and the effect of diffusive transport in the DL are explored.
S J Judd - One of the best experts on this subject based on the ideXlab platform.
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characterisation of zirconium poly acrylic acid low pressure dynamically formed membranes by use of the extended nernst planck Equation
Journal of Membrane Science, 1998Co-Authors: C Diaper, V M Correia, S J JuddAbstract:The rejection of a single electrolyte solution, by a hydrous zirconium oxide/poly(acrylic acid) (Zr/PAA) dual layer dynamically formed membrane (DFM), has been investigated. A flat sheet titania-coated sintered stainless steel (IMAS UK) was used as a substrate for DFM formation. Flux and rejection were recorded for a series of experiments at different transmembrane pressures, feed solution cross-flow rates and salt concentration. Experimental data was interpreted using a model based on the extended Nernst-Planck Equation. This interpretation allows characterisation of the membrane in terms of two parameters, the effective membrane charge density and a structural parameter which combines porosity and membrane thickness. Good correlation between experimental data and theory has been obtained. Calculation of the effective membrane charge density and the structural parameter at pH 6.7 and 9.0 for a range of salt concentrations provides conclusive evidence that membrane pore size decreases with increasing salt concentration and that the degree of ionisation of the PAA contained within the membrane increases with increasing pH and salt concentration.
Muhammad Bilal - One of the best experts on this subject based on the ideXlab platform.
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electrokinetic viscous rotating disk flow of poisson nernst planck Equation for ion transport
Journal of Molecular Liquids, 2020Co-Authors: Muhammad Shuaib, Rehan Ali Shah, Imranzeb Durrani, Muhammad BilalAbstract:Abstract The main features of the present numerical model is to explore the behavior of an ionic transport electroviscous boundary layer flow over a rotating disk. For this purpose, the Nernst-Planck Equation and Poisson's Equation together with the traditional Navier Stokes Equations are simulated for the conservation of ionic species. The Poisson-Nernst-Planck (PNP) Equation neglects sterile effects and ion-ion interactions, which is widely recognized by the electro-chemists community, leading to advancement of various mathematical models. The modeled governing Equations of the fluid flow are transformed to dimensionless ordinary differential Equations under Von Karman's approach. The Parametric Continuation Method (PCM) is applied, in order to analyzed the numerical simulation of the problem. For validity of the method the results are compared with another numerical method (bvp4c) and some previous published work, seem to be in a very good agreement to each other. It is found that the potential gradient becomes smaller as Debye length parameter K increases and exposing more counter-ions to the flow which results an increase in the fluid velocity. The physical constraints impact on radial, axial and tangential velocity and on both positive and negative charge profile are sketched and briefly discussed.