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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Superionic iron oxide–hydroxide in Earth’s deep mantle

Water ice becomes a superionic phase under the high pressure and temperature conditions of deep planetary interiors of ice planets such as Neptune and Uranus, which affects interior structures and generates magnetic fields. The solid Earth, however, contains only hydrous minerals with a negligible amount of ice. Here we combine high pressure and temperature electrical conductivity experiments, Raman spectroscopy and first-principles simulations to investigate the state of hydrogen in the pyrite-type FeO 2 H x (x ≤ 1), which is a potential H-bearing phase near the core–mantle boundary. We find that when the pressure increases beyond 73 GPa at room temperature, symmetric hydroxyl bonds are softened and the H + (or proton) becomes diffusive within the vicinity of its crystallographic site. Increasing temperature under pressure, the diffusivity of hydrogen is extended beyond the individual unit cell to cover the entire solid, and the electrical conductivity soars, indicating a transition to the superionic state, which is characterized by freely moving protons and a solid FeO 2 lattice. Furthermore, the highly diffusive hydrogen provides fresh transport mechanisms for charge and mass, which dictate the geophysical behaviours of electrical conductivity and magnetism, as well as geochemical processes of redox, hydrogen circulation and hydrogen isotopic mixing in Earth’s deep mantle.

58 GEOSCIENCES↗
DOE OSTI2024

Biopolymer-supramolecular polymer hybrids for photocatalytic hydrogen production

Solar generation of H 2 is a promising strategy for dense energy storage. Supramolecular polymers composed of chromophore amphiphile monomers containing perylene monoimide (PMI) have been reported as crystalline light-harvesting assemblies for aqueous H 2 -evolving catalysts. Gelation of these supramolecular polymers with multivalent ions creates hydrogels with high diffusivity but insufficient mechanical stability and catalyst retention for reusability. We report here on using sodium alginate (SA) biopolymer to both induce supramolecular polymerization of PMI and co-immobilize them with catalysts in a robust hydrogel with high diffusivity that can also be 3D-printed. Faster mass transfer was achieved by controlling the material macrostructure by reducing gel diameter and microstructure by reducing biopolymer loading. Optimized gels produce H 2 at rates rivaling solution-based PMI and generate H 2 for up to 6 days. The PMI assemblies in the SA matrix create a percolation network capable of bulk-electron transfer under illumination. These PMI–SA materials were then 3D-printed on conductive substrates to create 3D hydrogel photoelectrodes with optimized porosity. The design of these versatile hybrid materials was bioinspired by the soft matter environment of natural photosynthetic systems and opens the opportunity to carry out light-to-fuel conversion within soft matter with arbitrary shapes and particular local environments.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Observed volatilization behavior of silicon carbide in flowing hydrogen above 2000 K

In this work, the intrinsic compatibility of silicon carbide (SiC) and hydrogen (H 2 ) at high temperatures (2000-2473 K) and pressure near one atmosphere was evaluated through a combination of thermodynamic calculations and hot hydrogen exposure testing. Thermodynamic calculations predict the decomposition of SiC in a hydrogen environment to form free silicon (Si) and free carbon (C). Free Si is predicted to vaporize from the surface as a volatile species, while free C may interact with H 2 to form the hydrocarbons CH 4 (T < 2100 K) or C 2 H 2 (T > 2100 K). Coupons of high purity chemical vapor deposition (CVD) β-SiC were exposed to slowly flowing hydrogen at temperatures ranging between 2000 and 2473 K. SiC experienced active attack as the result of H 2 exposure, exhibiting linear weight loss kinetics and an Arrhenius dependence of weight loss on exposure temperature. The linear volatilization constant was experimentally evaluated to correspond with an activation energy of 370 ± 18 kJ/mol. Due to the dependence of observed corrosion rates on gas velocity, corrosion of SiC in flowing H 2 was determined to be governed by external mass transfer of volatile Si species through the boundary layer. Experimentally derived mass losses were in good agreement with mass losses predicted by a boundary layer limited gas diffusion model.

36 MATERIALS SCIENCE↗
DOE OSTI2023

An Analytic Formula for Entraining CAPE in Midlatitude Storm Environments

Abstract This article introduces an analytic formula for entraining convective available potential energy (ECAPE) with an entrainment rate that is determined directly from an environmental sounding, rather than prescribed by the formula user. Entrainment is connected to the background environment using an eddy diffusivity approximation for lateral mixing, updraft geometry assumptions, and mass continuity. These approximations result in a direct correspondence between the storm-relative flow and the updraft radius and an inverse scaling between the updraft radius squared and entrainment rate. The aforementioned concepts, combined with the assumption of adiabatic conservation of moist static energy, yield an explicit analytic equation for ECAPE that depends entirely on state variables in an atmospheric profile and a few constant parameters with values that are established in past literature. Using a simplified Bernoulli-like equation, the ECAPE formula is modified to account for updraft enhancement via kinetic energy extracted from the cloud’s background environment. CAPE and ECAPE can be viewed as predictors of the maximum vertical velocity w max in an updraft. Hence, these formulas are evaluated using w max from past numerical modeling studies. Both of the new formulas improve predictions of w max substantially over commonly used diagnostic parameters, including undiluted CAPE and ECAPE with a constant prescribed entrainment rate. The formula that incorporates environmental kinetic energy contribution to the updraft correctly predicts instances of exceedance of by w max , and provides a conceptual explanation for why such exceedance is rare among past simulations. These formulas are potentially useful in nowcasting and forecasting thunderstorms and as thunderstorm proxies in climate change studies. Significance Statement Substantial mixing occurs between the upward-moving air currents in thunderstorms (updrafts) and the surrounding comparatively dry environmental air, through a process called entrainment. Entrainment controls thunderstorm intensity via its diluting effect on the buoyancy of air within updrafts. A challenge to representing entrainment in forecasting and predictions of the intensity of updrafts in future climates is to determine how much entrainment will occur in a given thunderstorm environment without a computationally expensive high-resolution simulation. To address this gap, this article derives a new formula that computes entrainment from the properties of a single environmental profile. This formula is shown to predict updraft vertical velocity more accurately than past diagnostics, and can be used in forecasting and climate prediction to improve predictions of thunderstorm behavior and impacts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Low Temperature Water-Gas Shift: Enhancing Stability through Optimizing Rb Loading on Pt/ZrO 2

Recent studies have shown that appropriate levels of alkali promotion can significantly improve the rate of low-temperature water gas shift (LT-WGS) on a range of catalysts. At sufficient loadings, the alkali metal can weaken the formate C–H bond and promote formate dehydrogenation, which is the proposed rate determining step in the formate associative mechanism. In a continuation of these studies, the effect of Rb promotion on Pt/ZrO 2 is examined herein. Pt/ZrO 2 catalysts were prepared with several different Rb loadings and characterized using temperature programmed reduction mass spectrometry (TPR-MS), temperature programmed desorption (TPD), diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), an X-ray absorption near edge spectroscopy (XANES) difference procedure, extended X-ray absorption fine structure spectroscopy (EXAFS) fitting, TPR-EXAFS/XANES, and reactor testing. At loadings of 2.79% Rb or higher, a significant shift was seen in the formate ν(CH) band. The results showed that a Rb loading of 4.65%, significantly improves the rate of formate decomposition in the presence of steam via weakening the formate C–H bond. However, excessive rubidium loading led to the increase in stability of a second intermediate, carbonate and inhibited hydrogen transfer reactions on Pt through surface blocking and accelerated agglomeration during catalyst activation. Optimal catalytic performance was achieved with loadings in the range of 0.55–0.93% Rb, where the catalyst maintained high activity and exhibited higher stability in comparison with the unpromoted catalyst.

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

Methods of controllable interstitial oxygen doping in niobium

A method for vacuum heat treating Nb, such as is used in superconducting radio frequency cavities, to engineer the interstitial oxygen profile with depth into the surface to conveniently optimize the low-temperature rf surface resistance of the material. An example application is heating of 1.3 GHz accelerating structures between 250-400° C. to achieve a very high quality factor of 5×1010 at 2.0 K. With data supplied by secondary ion mass spectrometry measurements, application of oxide decomposition and oxygen diffusion theory was applied to quantify previously unknown parameters crucial in achieving the oxygen alloy concentration profiles required to optimize the rf surface resistance. RF measurements of vacuum heat treated Nb superconducting radio frequency cavities confirmed the minimized surface resistance (higher Q0) previously expected only from 800° C. diffusive alloying with nitrogen.

Palczewski, Ari D.↗
DOE OSTI2020

On the Parameterization of Convective Downdrafts for Marine Stratocumulus Clouds

The role of nonlocal transport on the development and maintenance of marine stratocumulus (Sc) clouds in coarse-resolution models is investigated, with a special emphasis on the downdraft contribution. A new parameterization of cloud-top-triggered downdrafts is proposed and validated against large-eddy simulation (LES) for two Sc cases. The applied nonlocal mass-flux scheme is part of the stochastic multiplume eddy-diffusivity/mass-flux (EDMF) framework decomposing the turbulent transport into local and nonlocal contributions. The complementary local turbulent transport is represented with the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme. This EDMF version has been implemented in the Weather Research and Forecasting (WRF) single-column model (SCM) and tested for three model versions: without mass flux, with updrafts only, and with both updrafts and downdrafts. In the LES, the downdraft and updraft contributions to the total heat and moisture transport are comparable and significant. The WRF SCM results show a good agreement between the parameterized downdraft turbulent transport and LES. While including updrafts greatly improves the modeling of Sc clouds over the simulation without mass flux, the addition of downdrafts is less significant, although it helps improve the moisture profile in the planetary boundary layer.

Wu, Elynn↗
DOE OSTI2023

Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transport

Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition. Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Applying a Phase-Separation Parameterization in Modeling Secondary Organic Aerosol Formation from Acid-Driven Reactive Uptake of Isoprene Epoxydiols under Humid Conditions

Secondary organic aerosol (SOA) from acid-driven reactive uptake of isoprene epoxydiols (IEPOX) contributes up to 40% of organic aerosol (OA) mass in fine particulate matter. Our previous work showed substantial conversions of particulate inorganic sulfates to surface-active organosulfates (OSs) by IEPOX decreases aerosol acidity and creates a viscous organic-rich shell that poses as a diffusion barrier, inhibiting additional reactive uptake of IEPOX. In this study, to account for this “self-limiting” effect, a phase-separation box model was developed to evaluate parameterizations of IEPOX reactive uptake against time-resolved chamber measurements of IEPOX-SOA tracers, including 2-methyltetrols (2-MT) and methyltetrol sulfates (MTS), at ~ 50% relative humidity. The phase-separation model was most sensitive to mass accommodation coefficient, IEPOX diffusivity in the organic shell, and ratio of the third-order reaction rate constants forming 2-MT and MTS (k MT /k MTS ). In particular, k MT /k MTS had to be lower than 0.1 to bring model predictions of 2-MT and MTS in closer agreement with chamber measurements, while prior studies reported values larger than 0.71. The model-derived rate constants favor more particulate MTS formation due to 2-MT likely off-gassing at ambient-relevant OA loadings. Incorporating this parametrization into chemical transport models is expected to predict lower IEPOX-SOA mass and volatility due to the predominance of OSs.

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

Reduced Sediment Settling in Turbulent Flows Due To Basset History and Virtual Mass Effects

The behavior of suspended particles in turbulent flows is a recalcitrant problem spanning wide-ranging fields including geomorphology, hydrology, and dispersion of particulate matter in the atmosphere. One key mechanism underlying particle suspension is the difference between particle settling velocity (w s ) in turbulence and its still water counterpart (w so ). This difference is explored here for a range of particle-to-fluid densities (1 – 10) and particle diameter to Kolmogorov micro-eddy sizes (0.1 – 10). Conventional models of particle fluxes that equate w s to w so result in eddy diffusivities and turbulent Schmidt numbers contradictory to laboratory experiments. Incorporating virtual mass and Basset history forces resolves these inconsistencies, providing clarity as to why w s /w so is sub-unity for the aforementioned conditions. The proposed formulation can be imminently used to model particle settling in turbulence, especially when sediment distribution outcomes over extended time scales far surpassing turbulence time scales are sought.

Geology↗
DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

RF surface resistance tuning of superconducting niobium via thermal diffusion of native oxide

Recently, Nb superconducting radio frequency cavities vacuum heat treated between 300 and 400°C for a few hours have exhibited very high quality factors (~5 × 10 10 at 2.0 K). Secondary ion mass spectrometry measurements of O, N, and C show that this enhancement in RF surface conductivity is primarily associated with interstitial O alloying via dissolution and diffusion of the native oxide. We use a theory of oxide decomposition and O diffusion to quantify previously unknown parameters crucial in modeling this process. RF measurements of a vacuum heat-treated Nb superconducting radio frequency cavity confirm the minimized surface resistance (higher Q 0 ) previously expected only from 800 °C diffusive alloying with N.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Controlling Mass Transport in Direct Carbon Dioxide Zero-Gap Electrolyzers via Cell Compression

The development of high-performance CO 2 electrolyzers is crucial for accelerating the sustainable production of fuels and chemicals integrated with renewable energy sources. Here, we introduce a methodology to actively control mass transport inside a realistic zero-gap membrane electrode assembly of a CO 2 electrolyzer by varying the gasket thickness, which consequently changes the cell compression. This allows control over the thickness and porosity of the gas diffusion electrodes, influencing the overall electrolyzer performance, as demonstrated using Ag-deposited electrodes. At low operating voltages (<2.9 V), both high- and low-compression electrolyzers exhibit similar faradaic efficiencies and partial current densities for CO formation. However, at high voltages, the low-compression electrolyzer with high electrode porosity demonstrates superior CO selectivity and activity with suppressed H 2 formation. These experimental results are validated by the computational membrane electrode assembly (MEA) model developed by using the measured in situ electrode thicknesses and electrode porosities. Additionally, liquid electrolyte saturation at the catalyst layer is found to play a dominant role in determining the mass transport, resulting in a decreased electrolyzer performance with low electrode porosity. Finally, the systematic investigation in this study improves the understanding of the transport dynamics in MEA-based devices and provides insights into optimizing device design parameters for industry-relevant CO 2 electrolysis.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2025

Corrosion Response of Ni-19Cr-5Fe in Molten NaCl-MgCl 2 Salt

Ni-based alloys are strong candidates for use in high-temperature molten salt reactors due to their superior corrosion resistance and mechanical stability compared to stainless steels. In this study, the static corrosion behavior of a Ni-19Cr-5Fe model alloy was systematically evaluated in a purified molten NaCl-MgCl 2 salt at 700°C for 30, 240, and 500 h. Post-exposure analyses were conducted to assess microstructural evolution, corrosion depth, and elemental depletion profiles. Corrosion rates, quantified by chromium depletion depth, followed an inverse power-law trend with increasing exposure time, indicating diffusion-limited kinetics. This trend is attributed to limitations in mass transport in the static salt and to the progressive local depletion of reactive chromium species. Coupled electron backscatter diffraction and energy dispersive X-ray spectroscopy analysis further revealed that the grain boundary character significantly influences corrosion susceptibility: high-angle grain boundaries exhibited pronounced Cr depletion and pitting, while low-angle and Σ3 boundaries remained comparatively resistant. These results offer valuable insight into the role of microstructure in corrosion processes and reinforce the importance of time-dependent material evaluation in molten salt environments relevant to advanced reactor designs.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Unraveling the core of fuel cell performance: engineering the ionomer/catalyst interface

The biggest obstacle to the widespread implementation of polymer electrolyte membrane fuel cells (PEMFCs) is their cost, primarily due to the use of platinum catalysts. The high intrinsic catalyst activity exhibited on a rotating disk electrode (RDE) is rarely realized in a membrane electrode assembly (MEA), which is a long-standing challenge for PEMFCs and a cause of low catalyst utilization. To translate the high RDE performance of a catalyst into a MEA, the design of an ideal ionomer/catalyst interface is proposed: a thin, conformal ionomer film covers the maximum surface of a Pt nanoparticle and thus simultaneously maximizes catalyst utilization, (i.e., high mass activity and electrochemically active surface area) and O 2 diffusion rate (i.e., high current density performance) without compromising proton conduction. Building such an interface is a long-standing challenge due to the lack of interaction between the ionomer and catalyst particles, resulting in large ionomer agglomerates and inhomogeneous ionomer coverage over the catalyst nanoparticle, with consequent poor fuel cell performance. In this work, this ionomer/catalyst interface has been engineered, utilizing the electrostatic attraction between positively charged catalyst and negatively charged ionomer particles in a catalyst ink and preserved in a solid catalyst layer. As a result, this interface leads to previously unachieved proton exchange membrane fuel cell performance in terms of both catalyst utilization (75% vs. 45%) and peak/rated power density (i.e., 1.430/0.930 W cm -2 , H 2 /air, cathode Pt loading: 0.1 mgPt cm -2 ) for pure Pt catalysts, even better than those of Pt alloy catalysts. This work demonstrates the formation of an interface in the liquid phase (using ultra-small-angle X-ray scattering in combination with cryo-TEM, isothermal–titration–calorimetry) and the preservation of the interface in the solid catalyst layer (using TEM) and estimates the effective coverage and thickness of the ionomer film (using limiting current density, RDE and fuel cell performance).

25 ENERGY STORAGE↗
DOE OSTI2020

Modeling Interfaces to Support Low-Level Waste Disposal System Performance Assessments - 20366

In low-level waste (LLW) disposal sites, interfaces between cementitious materials, used as waste forms and/or engineered barriers, and the surrounding soil or backfill material are often encountered. Reactions across these interfaces may lead to chemical and structural alteration of the cementitious and backfill materials that may ultimately affect long-term performance. For example, the ingress of carbon dioxide from soil gas into a waste tank concrete shell at the Hanford Site or Savannah River Site (SRS) or a low-level waste disposal vault at SRS leads to carbonation of cement hydration products (e.g. portlandite, calcium-silicate hydrate or C-S-H, and ettringite). The result of carbonation is a decrease in pH in the cement paste portion of the tank wall or vault concrete structure that could ultimately lead to de-passivation of the embedded structural steel and, eventually, to cracking. Cracking can lead to increased ingress of water into the structure, corresponding increased release of constituents of concern, and to subsequent increased transport of these constituents to the surrounding environment. The mobility of trace constituents (e.g., radionuclides of concern) in waste forms may increase in response to changes in pH, pore structure, and mineralogical gradients. Depletion of portlandite results in subsequent decalcification of C-S-H that leads to changes in the cement strength and may lead to structural failure. At the boundary between waste forms and concrete vaults, the migration of sulfate ions from the salt waste form (e.g., the saltstone waste form used for LLW disposal at the Savannah River Site in Saltstone Disposal Units, or SDUs) into the barrier or vault concrete has been predicted to result in expansive mineral phase formation (or 'sulfate attack'). Expansive mineral formation could result in cracking and potential loss of structural integrity in the vault concrete. In the performance assessment (PA) for the SRS SDUs, prediction of both the carbonation and sulfate attack fronts are critical to assessing the long-term performance of these LLW disposal vaults. A general purpose geochemical reactive transport model has been developed in LeachXS/ORCHESTRA to evaluate typical interfaces for LLW disposal environments, including SDUs at SRS. The model may be used to predict the long-term performance of interfaces between cementitious materials and saltstone or backfill materials with respect to primary phases by considering mass transport, cement chemistry, geochemical speciation, and multi-ionic diffusion over interfaces between different materials. The present study compares the performance and interactions between vault concrete and saltstone waste form for a representative SDU scenario. The materials were characterized using pH-dependence leaching test (EPA 1313) and semi-dynamic transport tests (EPA 1315) with test results used to parameterize the interface model. The development of a credible inter model provides an important basis for supporting future PAs where carbonation and sulfate attack are important aging and degradation mechanisms. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Preserving Tracer Correlations in Moment-Based Atmospheric Transport Models

A linear non-diffusive algorithm for advective transport is developed that greatly improves the detail at which aerosols and clouds can be represented in atmospheric models. Linear advection schemes preserve tracer correlations but the most basic linear scheme is rarely used by atmospheric modelers on account of its excessive numerical diffusion. Higher-order schemes are in widespread use, but these present new problems as nonlinear adjustments are required to avoid occurrences of negative concentrations, spurious oscillations, and other non-physical effects. Generally successful at reducing numerical diffusion during the advection of individual tracers, for example, particle number or mass, the higher-order schemes fail to preserve even the simplest of correlations between interrelated tracers. As a result, important attributes of aerosol and cloud populations including radial moments of particle size distributions, molecular precursors related through chemical equilibria, aerosol mixing state, and distribution of cloud phase are poorly represented. We introduce a new transport scheme, minVAR, that is both non-diffusive and preservative of tracer correlations, thereby combining the best features of the basic and higher-order schemes while enabling new features such as the tracking of sub-grid information at arbitrarily fine scales with high computational efficiency.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Divergence of Velocity Fields in Electrochemical Systems

The passage of current through electrochemical systems results in the development of concentration gradients in the electrolytic phase that can be modeled using concentrated solution theory. Application of this theory requires knowledge of three concentration-dependent transport coefficients, which are often taken to be conductivity, diffusion coefficient, and the cation transference number with respect to the solvent velocity. The governing diffusion equation for molar concentration contains two additional terms - the thermodynamic factor which is related to activity of the electrolytic species and the solvent velocity. The main advance in this paper is the derivation of an expression for the divergence of the solvent velocity. Solving this equation requires knowledge of the partial molar volume of the electrolyte. Analogous expressions are derived for the mass average and molar average velocities. These velocities occur naturally in the diffusion equation if concentration is expressed as weight fraction and mole fraction of the electrolytic species, respectively.

diffusion↗