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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A scalable DG solver for the electroneutral Nernst-Planck equations

The robust, scalable simulation of flowing electrochemical systems is increasingly important due to the synergy between intermittent renewable energy and electrochemical technologies such as energy storage and chemical manufacturing. The high Péclet regime of many such applications prevents the use of off-the-shelf discretization methods. In this work, we present a high-order Discontinuous Galerkin scheme for the electroneutral Nernst-Planck equations. The chosen charge conservation formulation allows for the specific treatment of the different physics: upwinding for advection and migration, and interior penalty for diffusion of ionic species as well the electric potential. Similarly, the formulation enables different treatments in the preconditioner: AMG for the potential blocks and ILU-based methods for the advection-dominated concentration blocks. Here we evaluate the convergence rate of the discretization scheme through numerical tests. Strong scaling results for two preconditioning approaches are shown for a large 3D flow-plate reactor example.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗
DOE OSTI2021

Water and Solute Activities Regulate CO 2 Reduction in Gas-Diffusion Electrodes

Electrolysis of CO 2 at gas-diffusion electrodes (GDEs) has typically been limited by the supply of gas to the electrocatalyst, overshadowing the importance of the supply of water. However, at high current densities that approach 1 A cm –2 , where the electrolyte becomes highly concentrated in the catalyst layer of a GDE, the activity of water and solutes deviate from their bulk dilute solution values, potentially slowing reaction rates and changing reaction equilibrium potentials. In addition, as flow plates for the gas stream are introduced to enable larger electrodes and high single pass conversion of CO 2 to product, variations in the gas composition will become important. By drawing upon literature for the oxygen reduction reaction (ORR), here we explain how to account for these effects in future modeling and experimental work, with particular attention to accurate use of the Nernst equation for electrode potentials and the Arrhenius equation for reaction rates. Specifically, using measurements of KOH solvent and solute activity reported in literature, and assuming the second protonation of CO 2 by water as the rate-determining step, we show the Nernst equation dilute-solution approximation of the CO 2 to CO equilibrium potential to be accurate below 5 M KOH, but it has a 74 mV error when increasing the concentration up to 10 M KOH. Finally, a simple one-dimensional model of a serpentine flow-field on a GDE demonstrated that a reactor with constant pressure of 1 bar and 1 A cm –2 at the inlet had only ~0.3 A cm –2 at the outlet for a conversion in CO 2 partial pressure from 0.90 to 0.48 bar, showing the significant practical implications of this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Effect of electrode rinse solutions on the electrodialysis of concentrated salts

The data presented indicate that modest attention to the chemistry of the electrode rinse solution can yield as much as 56% improvement in process efficiency. When operating electrodialysis (ED) with salt concentrations greater than 10,000 mg/l (as NaCl) the amperage can be relatively high even at low voltages. To maximize the overall rate of ion transport from diluate to concentrate, there is a need to minimize resistances in the electrode cells since these can represent as much as 30% of the total resistances in the entire process and in this particular ED unit, represented resistance roughly equivalent to that within the membrane stack. This work describes the performance of a 10-cell pair, 200 cm 2 (0.02 m 2 ) per membrane, pilot ED unit operated in batch mode at 5 V potential. The feedstock to the stack was varied from 0.5% to 6% NaCl. Results from Volt-amp profiles (2.0–15 V) were used as the rationale for choosing the preferred electrode rinse solution, 90 g/l (kg/m 3 ) disodium sulfate at pH 12.5. The recommended solution of 30 g/l (kg/m 3 ) disodium sulfate at neutral pH was tested against stronger solutions (60, 90, and 120 g/l (kg/m 3 ) disodium sulfate) at neutral pH and with 1 g/l (kg/m 3 ) sodium hydroxide added to yield solutions at pH 12.5. There were stark differences in the performance of the ED unit between the solutions at pH 7 and those at pH 12.5. The slopes of the Volt-amp profiles improved indicating less resistance to ion flow at pH 12.5. Most of the difference can be attributed to the greater conductivity of sodium hydroxide compared to disodium sulfate, where even a modest addition of 1 g/l (kg/m 3 ) sodium hydroxide increased the conductivity of the solution between 8 and 20% depending on the concentration of disodium sulfate. Most notably, the initiation voltage was 2.39 ± 0.08 V with solutions at pH 7 and 1.99 V ± 0.04 V when the rinse solutions were around pH 12.5, a difference of around 0.42 V. Since the full batch runs were performed at 5.0 V, this 0.42 V differential represented a loss of 8% in process efficiency. A series of tests showed a shift in initiation voltage occurred between pH 11.5 and 12.5. Nernst equations for water electrolysis are coupled with a simple flux model that estimates the concentration of hydroxide and hydronium ions at the electrode surfaces. This model indicates that the potential demanded by the electrodes is directly linked to the current. Furthermore, there is a steep drop in the potential demanded by the anode when there is sufficient hydroxide available to generate oxygen from hydroxide as opposed to generation from water. The voltage demand is minimal at pH 12.5 and reflective of the reference standard voltage (just over 1.23 V predicted at 0.1 amps). However, the flux model predicts that the voltage demanded by the electrodes at pH 7 is 1.61 V at 0.1 amps (the lowest amperage measurable with the power pack). In conclusion, comparing this result to the reference standard (E 0 = -1.23 V) yields a satisfactory explanation for the observed difference below reference standard of 0.42 V.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Ni/NiO Reference Electrode Potential Measurements in Molten CaCl 2 –CaO

A direct oxide reduction (DOR) process is used to reduce PuO 2 to Pu metal via Ca metal. Molten CaCl 2 is commonly used as the electrolyte for this reaction. As the DOR reaction proceeds, CaO accumulates in the salt and must be measured in real-time to know when the reaction has gone to completion. Open circuit potential (OCP) was measured in this report between a reference electrode consisting of Ni/NiO contained in a MgO tube and a tungsten working electrode. Two methods of CaO additions were performed over several experiments, and both methods correlated to a 0.11 to 0.23 V decrease in OCP up to 14.4 wt% CaO. CaO concentrations were separately measured via sampling and acid-base titration. A plot of OCP versus concentration of CaO fits the Nernst equation with the CaO powder additions up to 5.2 wt% and also at the higher end of the CaO pellet concentration range. While the MgO tubes were observed to be structurally stable in the molten salt, scanning electron microscopy and energy dispersive X-ray spectroscopy showed that Mg in the tubes had been partially replaced with Ca.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of Metal Chloride Impurities on Equilibrium Potential of Fe/FeCl 2 in Eutectic LiCl-KCl

In this study, interaction of dilute metal chloride solutes in molten eutectic LiCl-KCl was studied via equilibrium potential measurements. Open circuit potential (OCP) was measured between a pure iron rod and a Ag/AgCl reference electrode with concentration of FeCl 2 varying from 0.2–1 mol% at 530 °C. The Nernst equation was used to calculate activity coefficient of FeCl 2 based on OCP. Measurements were made in LiCl-KCl-FeCl 2 with and without additions of 0.5 mol% CsCl, NaCl, and LaCl 3 . The activity coefficient of FeCl 2 was found to be unaffected by these small concentrations of CsCl, LaCl 3 , and NaCl. However, there was observed evidence that the activity coefficient of FeCl 2 , above 0.8 mol% Fe, may be affected by the presence of LaCl 3 at higher concentrations beginning around 0.5 mol% La. Over the full range of conditions tested, the activity coefficient of FeCl 2 in molten LiCl-KCl ranged from 2.95 × 10 −5 to 1.01 × 10 −4 .

Electrochemistry↗
DOE OSTI2020

Principles of Corrosion in Nuclear Systems: Theory and Analytical Methods

This article is meant to provide the reader with the fundamental electrochemistry necessary to critically evaluate the data and discussions in the articles on corrosion that follow. As such it has two main sections, theory and analytical methods. In the section on theory, a review of half cell reactions, cell potentials and the Nernst equation, and reference electrodes in nuclear systems are discussed. In addition, a review of the thermodynamics from room temperature to the PWR and kinetics of dissolution and passive film formation is also presented. In the section on analytical methods, we review the principles of potentiodynamic polarization, electrochemical impedance spectroscopy, and we introduce a more seldom used technique, Mott-Schottky analysis.

Lillard, R Scott↗
DOE OSTI2024

Simplified Universal Equations for Ionic Conductivity and Transference Number

Nernst-Einstein equation can provide a reasonable estimate of the ionic conductivity of dilute solutions. For concentrated solutions, alternate methods such as Green–Kubo relations and Einstein relations are more suitable to account for ion-ion interactions. Such computations can be expensive for multicomponent systems. Simplified mathematical expressions like the Nernst-Einstein equation do not exist for concentrated multicomponent mixtures. Newman’s treatment of multicomponent concentrated solutions yields a conductivity relation in terms of species concentration and Onsager phenomenological coefficients. However, the estimation of these phenomenological coefficients is not straightforward. Here, mathematical formulations that relate the phenomenological coefficients with the friction coefficients are developed, leading to simplified, ready-to-use expressions of conductivity and transference numbers that can be used for a wide range of ionic mixtures. This approach involves spectral decomposition of the matrix of Onsager phenomenological coefficients. The general analytical expressions for conductivity and transference number are simplified for binary electrolytes, and numerical solutions are provided for ternary and quaternary mixtures with ion dissociation.

Electrochemistry↗
DOE OSTI2025

Validating corrosion models: A comparison of governing equations

Experimental validation of Finite Element Method (FEM) models varying electrochemical governing equations, inclusion of chemical reactions, and time on the resultant damage profile for two galvanic couples is explored. Two anode materials (Magnesium AZ31 and Carbon Steel) in contact with a cathode (Stainless Steel 304 L) were modeled in/exposed to NaCl (1 and 0.1 M respectively for the anode materials) for up to one week. The physics approach, inclusion of chemical reactions, and the boundary conditions required to accurately represent the damage profile in FEM models depended on the galvanic couple materials and, ultimately, the corrosion rate. For high rates of corrosion (i.e., magnesium anode), the Nernst-Planck equation with Electroneutrality was sufficient to describe the damage, while, for low rates of corrosion (i.e., carbon steel anode), the Laplace equation was sufficient. In all cases, the most complete governing equation (Nernst-Planck-Poisson Equation) was not necessary to accurately describe the damage. Precipitation reactions in solution also played a critical role in the predicted damage profile, especially for high corrosion rate systems. Finally, for short time periods (< 6 h), the choice of governing equations does not significantly influence damage profile results. Overall, the choice of physics to reduce error in simulations relies on the boundary conditions, geometry, conductivity of the solution, electrochemical potential differences, and time of exposure. The above results are discussed with regard to accuracy and computational savings.

Carbon steel↗
DOE OSTI2022

Finite Element Method for Electrochemical Transport

This code provides Finite Element solvers for Electrochemical Transport. A few examples from the literature are reproduced, with a focus on CO2 electrolysis. The Discontinuous Galerkin scheme for the electroneutral Nernst-Planck equations is from Roy, T., Andrej, J. and Beck, V.A., 2021. A scalable DG solver for the electroneutral Nernst-Planck equations. arXiv preprint arXiv:2112.09271. This work also includes a scalable preconditioner.

Beck, VictorA↗
DOE OSTI2020

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗
DOE OSTI2026

Validating corrosion models: Influence of physical properties

In chloride containing environments, two metals in physical contact can undergo galvanic corrosion limiting the lifetime of components. Being able to accurately predict galvanic corrosion damage distributions over time has not been widely presented in literature. Therefore, Finite Element Method (FEM) corrosion models were experimentally validated for two galvanic couples as a function of governing equations, environment, anode material, anode:cathode ratio, and time. Carbon steel/stainless steel (CS/SS) and zinc/stainless steel (Zn/SS) galvanic couples were exposed to NaCl solutions at room temperatures for up to 14 days. For the galvanic couples and environments, the Laplace equation with variable conductivity and reactions was sufficient to model the experimental corrosion damage. Increasing the chloride concentration for the CS/SS galvanic couple, regardless of the anode:cathode ratio, decreased the observed and modeled corrosion damage. Decreasing the anode:cathode ratio (i.e., increasing the cathode length), increased the experimentally observed and modeled corrosion damage. For small anode:cathode ratios, the governing equations deviate over long time periods with the Nernst-Plank equation being conservative. For the Zn/SS galvanic couple, the cathode length controls the dominant cathodic reduction reaction. For small cathode lengths, the hydrogen evolution reaction is dominant. For larger cathode lengths, the oxygen reduction reaction is dominant. The results are discussed with regard to the influence of solution chemistry, ohmic drop, and governing reactions. Overall, validated FEM models were presented, and the resultant models, physics, and mechanisms can be applied to other corrosion scenarios with confidence.

Carbon steel↗
DOE OSTI2022

Numerical modeling of ion transport and adsorption in porous media: A pore-scale study for capacitive deionization desalination

In this report a pore-scale model is presented to simulate the dynamic ion transport and adsorption processes in porous electrodes used for capacitive deionization (CDI). The Stokes equation governing water flow is solved using the lattice Boltzmann method and Nernst-Planck equation describing ion transport is solved using the finite volume method. The ion adsorption process is considered at the surface of carbon electrodes. After validation against analytical solutions and published results, the model is used to study the coupled water flow, ion transport and adsorption in both two-dimensional and three-dimensional porous CDI electrodes at the pore scale. The effect of electrode microstructure, electrical potential and flow velocity on the adsorption processes is quantitatively investigated, and the relative importance of various parameters is determined. The presented model can be a powerful numerical tool to quantitatively analyze ion transport and adsorption in porous electrodes, and may provide useful information for the design and optimization of CDI electrodes and operating conditions for desired desalination efficiency, water throughput and cost.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

An integrated approach to optimizing concentration shock wave electrodialysis using 2D multicell simulation and response surface models

Shock wave electrodialysis (SWED) is a highly promising technique for energy-efficient ion separation in the context of a circular economy. This paper presents a approach way of modeling and improving SWED using a two-dimensional multicell model combined with the COMSOL program and response surface methodology. The model integrates the Nernst-Planck equation, Darcy's law, and first-order electroosmosis to examine the local concentration, flux of ionic species, distribution of current, and velocity of flow in SWED cells under various operating conditions. We first illustrate the clear depiction of concentration, velocity, and electric potential distribution through contours which aids in identifying optimal operating conditions and designing scalable SWED systems. The results emphasize the significance of surface charge density and voltage in influencing the features of shock waves for obtaining effective ion separation while optimizing energy consumption and improving current efficiency by controlling the retention time of feed flow. Here, this study defines two crucial characteristics of shock waves, namely the length of the flat depletion zone of a fully developed shock wave (shock wave height) and the distance of shock wave propagation (shock wave length). These properties significantly impact separation performance, as determined by the simulation results. Additionally, the response surface methodology is incorporated with the COMSOL models to develop predictive models and graph responses, enabling a more comprehensive understanding of the interactions between parameters and performance indicators, such as removal ratio, energy consumption, and water recovery. Finally, this work suggests design tactics for expanding SWED processes and outlines potential areas for further research. This research provides valuable insights into the prospective applications, design optimization, and scalability of SWED in the field of electrokinetic separation technologies for green chemistry and a circular economy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Opportunities and challenges in process modeling and simulation of electrochemical systems

Electrochemical technologies have garnered intense interest in both academic research and industrial applications due to their potential to increase energy efficiency and reduce carbon footprint. However, electrochemical process fundamentals have been absent from the chemical process simulators available to millions of chemical engineers worldwide. To expedite process research and development of electrochemical technologies in the chemical industry, it is imperative that essential electrochemical process fundamentals be incorporated into process simulators to support modeling and simulation of electrochemical processes. Here, this study examines three process fundamentals key to the research and development of electrochemical processes: electrochemical reaction kinetics, electrolyte thermodynamics, and heat and mass transfer. It further illustrates application of these process fundamentals with a case study modeling an electrochemical process for the conversion of acrylonitrile to adiponitrile. The modeling example highlights the roles of applied voltage on reaction rates, and electron flow rates on the performance of electrochemical processes. It suggests that the applied voltage and electron flow rates are two unique concepts that should be included in simulators for electrochemical processes.

09 BIOMASS FUELS↗
DOE OSTI2020

Onsager Transport Coefficients and Transference Numbers in Polyelectrolyte Solutions and Polymerized Ionic Liquids

Electrolytes featuring negatively charged polymers, such as nonaqueous polyelectrolyte solutions and polymerized ionic liquids, are currently under investigation as potential high cation transference number (t+) electrolytes for lithium-ion batteries. Herein, we use coarse-grained molecular dynamics simulations to characterize the Onsager transport coefficients of polyelectrolyte solutions as a function of chain length and concentration. For all the systems studied, we find that the rigorously computed transference number is substantially lower than that approximated by the ideal solution (Nernst-Einstein) equations typically used to characterize these systems due to the presence of strong anion-anion and cation-anion correlations. None of the polyelectrolyte solutions achieve t+ greater than that of the conventional binary salt electrolyte, with some solutions having negative t+. Overall, this work demonstrates that the Nernst-Einstein assumption does not provide a physically meaningful estimate of the transference number in these solutions and calls into question the expectation of polyelectrolytes to exhibit a high cation transference number.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗