Diffusion-Limit-Preserving Lumped DFEMs on AMR Meshes
Explore the source record for details and available documents.
Nuclear science and engineering, Mathematics and C↗
SEARCH · Search NASA
Results for “diffusion limitation”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
On Diffusion Limit Preserving Unlocked Step Method
Explore the source record for details and available documents.
Mathematics and Computing↗
Diffusion-Limit-Preserving Lumped DFEM's on AMR Meshes
Explore the source record for details and available documents.
Mathematics and Computing↗
Discretization Writeup for Grey Flux-Limited Radiation Diffusion
This report documents the time and space discretizations for grey flux-limited diffusion applied to the thermal radiative transfer (TRT) equations. We begin with a description of the physics being solved before moving into the diffusion approximation. Once we have the TRT system, we show a finite-volume-inspired discretization from Jim Morel (Texas A&M University, NUEN 627 class notes, lecture 8). As systems become hotter they emit more photons in the form of blackbody radiation. Because average photon energy of the blackbody source is proportional to the temperature of the system, we call these thermal photons or thermal radiation. As material temperatures increase, increasing fractions of the total energy in the system go into the radiation field. In addition, radiation can deposit energy and momentum non-locally, making it an important phenomenon for heating and impulse. In order to accurately study systems at high temperatures, we wish to add the physics of thermal radiation to our hydrodynamic system. In practice, coupling radiation and hydrodynamics is often done by operator-splitting each timestep into two consecutive, non-overlapping phases: (1) update the hydrodynamics for a fixed radiation state (2) update the radiation and internal energy for an otherwise fixed hydrodynamic state. Because of this clean separation of physics updates, in this report we show only the latter phase, which involves solely the TRT equations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Mathematical Framework Underlying the In Situ Electrochemical Diagnosis of Adsorbed Intermediates Formed during Redox Reactions at Electrode Surfaces
Previously, we have presented an electrochemical technique wherein an electroactive tracer species is employed to probe the rate-limiting factors governing redox reactions at an electrode surface. In this technique, the electrode is first held potentiostatically to facilitate a redox process (step 1), and then the potential is released to open circuit conditions (step 2) so as to monitor the time-dependent re-equilibration of the electrode potential in the presence of the tracer. The time-dependent potential response in step 2 has been shown to contain information about diffusion—limited or desorption—limited steps, enabling in situ probing of the electrochemistry at the electrode surface during step 1. In the present contribution, a theoretical model governing the transient response in step 2 is developed for two limiting cases: diffusion—limited and desorption—limited recovery of the electrode potential. Mathematical modeling shows that, during re-equilibration, the step 2 potential transient corresponding to a case where step 1 involves surface adsorbed species which undergo desorption in step 2 exhibits a much longer time constant than that when re-equilibration occurs under diffusion limitations. The mathematical framework presented herein provides a sound fundamental basis for applying the aforementioned technique to studying adsorption-desorption processes during electrochemistry. Also, technique limitations are presented in light of the modeling findings.
25 ENERGY STORAGE↗
Structural Tuning of Self‐Conductive Polymer as Gas Diffusion Layer for Electrocatalytic Reactions at High Current
Electrocatalytic conversions offer a promising route for sustainable chemical production using renewable energy. Gas diffusion layers (GDLs) enable selective product formation at high current densities but suffer from electrolyte flooding, and polytetrafluoroethylene (PTFE)-based GDLs typically require metal conductive layers, which constrain catalyst development. A recently developed GDL configuration, electropolymerized poly(3,4-ethylenedioxythiophene) (PEDOT)-coated PTFE, demonstrates notable flooding resistance, but suffers from gas diffusion limitations at elevated currents due to limited gas diffusion through the PEDOT layer. Here, different dopants in PEDOT are exploited to modify the physical properties and enhance gas transport. ClO 4 − -doped PEDOT exhibits superior performance due to optimized physical structure, leading to increased gas permeance and faradaic efficiency (FE) for CO production during electrocatalytic CO 2 reduction. Further optimization of coverage and thickness achieved by adjusting charge density led to an optimal configuration at 33 mC cm −2 . This GDL supports various metal electrocatalysts and demonstrates FE CO of > 90% for over 150 h at −200 mA cm −2 using a commercial silver electrocatalyst. This work highlights the importance of GDL engineering in enhancing performance and durability for long-term electrocatalytic processes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport
Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.
97 MATHEMATICS AND COMPUTING↗
Oxidation of NiCr and NiCrMo Alloys at Low Temperatures
Oxidation of Ni-Cr and Ni-Cr-Mo was studied in operando with near ambient pressure x-ray photoelectron spectroscopy in the Cabrera-Mott regime. The oxidation temperature was 200 °C - a severely diffusion limited regime. The near-surface alloy is Cr-enriched after reduction of natives oxide in vacuum, and especially so for Ni-15Cr-6Mo. Mo-cations are integrated in the oxide and Mo(VI) dominates at the surface. The surface chemistry driven promotion of chromia by Mo predicted by theory is negated by the limited surface diffusion of reactants. Furthermore, pre-oxidation processing is proposed to control the oxide properties for use of Ni-Cr superalloys at low temperatures.
36 MATERIALS SCIENCE↗
Diffusion of acceptor dopants in monoclinic 𝛽−Ga 2 O 3
𝛽−Ga 2 O 3 is a promising material for next-generation power electronics because of its ultrawide band gap and high critical breakdown voltage. However, realizing its full potential requires precise control over dopant incorporation and stability. In this work, we use first-principles calculations to systematically assess the diffusion behavior of eight potential deep-level substitutional acceptors (Au, Ca, Co, Cu, Fe, Mg, Mn, and Ni) in 𝛽−Ga 2 O 3 . We consider two key diffusion mechanisms: (i) interstitial diffusion under nonequilibrium conditions relevant to ion implantation, and (ii) trap-limited diffusion (TLD) under near-equilibrium thermal annealing conditions. Our results reveal a strong diffusion anisotropy along the 𝑏 and 𝑐 axes, with dopant behavior governed by competition between diffusion and incorporation (or dissociation) activation energies. Under interstitial diffusion, Ca$^{2+}_{i}$ and Mg$^{2+}_{i}$ show the most favorable combination of low migration and incorporation barriers, making them promising candidates for efficient doping along the 𝑏 and 𝑐 axes, respectively. In contrast, Au$^{+}_{i}$ diffuses readily, but exhibits an incorporation barrier that exceeds 5 eV, rendering it ineffective as a dopant. From a thermal stability perspective, Co$^{2+}_{i}$ shows poor activation but high diffusion barriers, which may suppress undesirable migration at elevated temperatures. Under trap-limited diffusion, the dissociation of dopant-host complexes controls mobility. Mg$^{2+}_{i}$ again emerges as a leading candidate, exhibiting the lowest dissociation barriers along both axes, whereas Co$^{2+}_{i}$ and Fe$^{2+}_{i}$ display the highest barriers, suggesting improved dopant retention under thermal stress. In conclusion, our findings guide dopant selection by balancing activation and thermal stability, essential for robust semi-insulating substrates.
Defects↗
Machine Learning Guided Synthesis of Flash Graphene
Advances in nanoscience have enabled the synthesis of nanomaterials, such as graphene, from low-value or waste materials through flash Joule heating. Though this capability is promising, the complex and entangled variables that govern nanocrystal formation in the Joule heating process remain poorly understood. In this work, machine learning (ML) models are constructed to explore the factors that drive the transformation of amorphous carbon into graphene nanocrystals during flash Joule heating. An XGBoost regression model of crystallinity achieves an r 2 score of 0.8051 ± 0.054. Feature importance assays and decision trees extracted from these models reveal key considerations in the selection of starting materials and the role of stochastic current fluctuations in flash Joule heating synthesis. Furthermore, partial dependence analyses demonstrate the importance of charge and current density as predictors of crystallinity, implying a progression from reaction-limited to diffusion-limited kinetics as flash Joule heating parameters change. Finally, a practical application of the ML models is shown by using Bayesian meta-learning algorithms to automatically improve bulk crystallinity over many Joule heating reactions. Furthermore, these results illustrate the power of ML as a tool to analyze complex nanomanufacturing processes and enable the synthesis of 2D crystals with desirable properties by flash Joule heating.
01 COAL, LIGNITE, AND PEAT↗
Comparison of microwave and conventional heating for CO 2 desorption from zeolite 13X
In this study, we investigate microwave irradiation as an alternative to conventional heating for temperature swing adsorption processes. The performance of microwave and conventional heating during sorbent regeneration was evaluated by measuring CO 2 desorption from zeolite 13X at different temperatures. Experimentally, a fixed bed of zeolite 13X was saturated by a 150 sccm flow of 15 % CO 2 at room temperature followed by sorbent regeneration under nitrogen at 55, 100, or 150 °C by applying either microwave irradiation or conventional heating. Microwaves reduced sorbent regeneration times by at least half compared to regeneration by conventional heating. Under conventional regeneration, desorption curves were resolved into two peaks representing physisorbed CO 2 (mass diffusion limited) at low temperature and bicoordinated CO 2 (thermally limited) with increasing temperature. Under microwave regeneration, only one desorption peak was observed suggesting that CO 2 desorption was limited by mass diffusion through the porous zeolite 13X structure, rather than by temperature. Depending on microwave power, apparent activation energy of the microwave-assisted regeneration was 15.8–18.1 kJ/mol, compared to 41.5 kJ/mol for conventional regeneration. The reduction in apparent activation energy is mainly attributed to selective microwave heating of CO 2 adsorption sites (Na + sites) resulting in greater steady state temperatures of Na + relative to framework atoms, suggesting greater heating efficiency due to microwaves compared to conventional heat transfer. Due to rapid cycling and efficient heat transfer to CO 2 sites on zeolite 13X, microwave regeneration is found to increase adsorption/desorption cycling productivity and potentially reduce the energy penalty of temperature swing capture.
54 ENVIRONMENTAL SCIENCES↗
Crystallization Mechanisms of Poly(vinylidene Fluoride- co -chlorotrifluoroethylene): Nucleation Transitions, Growth Kinetics, and Microstructure Evolution
The crystallization kinetics of FK-800, a commercial semicrystalline copolymer of chlorotrifluoroethylene and vinylidene fluoride (poly(CTFE-co-VDF)), dictate its microstructure and functional performance. Crystallization occurs between the glass transition (T g ≈ 31 °C) and melting point (T m ≈ 110 °C), with grain boundaries playing a key role in applications such as memristors, where they regulate filament growth. This study integrates in situ atomic force microscopy (AFM), grazing-incidence wide-angle X-ray scattering (GIWAXS), and differential scanning calorimetry (DSC) to characterize nucleation, growth, and morphology across the full crystallization window. Hot-stage AFM reveals a transition from homogeneous to heterogeneous nucleation near 45 °C and a shift from reaction-limited to diffusion-limited growth above 60 °C. Kinetics are analyzed using Lauritzen–Hoffman, Turnbull–Fisher, and Avrami models to extract surface free energies and activation barriers. A multiscale modeling framework is developed in which nucleation densities and growth rates measured by AFM are used to reconstruct Avrami kinetics, which are then validated against coverage data, and extrapolated to predict bulk crystallization behavior observed by DSC. GIWAXS confirms a primarily flat-on chain orientation at all temperatures, linking orientation to domain morphology. This integrative approach quantitatively connects nanoscale crystallization dynamics with macroscopic phase evolution, establishing a quantitative framework for modeling crystallization across time, temperature, and length scales.
Crystallization↗
Uncovering the predictive pathways of lithium and sodium interchange in layered oxides
Ion exchange is a powerful method to access metastable materials with advanced functionalities for energy storage applications. However, high concentrations and unfavourably large excesses of lithium are always used for synthesizing lithium cathodes from parent sodium material, and the reaction pathways remain elusive. Here, using layered oxides as model materials, we demonstrate that vacancy level and its corresponding lithium preference are critical in determining the accessible and inaccessible ion exchange pathways. Taking advantage of the strong lithium preference at the right vacancy level, we establish predictive compositional and structural evolution at extremely dilute and low excess lithium based on the phase equilibrium between Li 0.94 CoO 2 and Na 0.48 CoO 2 . Such phase separation behaviour is general in both surface reaction-limited and diffusion-limited exchange conditions and is accomplished with the charge redistribution on transition metals. Guided by this understanding, we demonstrate the synthesis of Na y CoO 2 from the parent Li x CoO 2 and the synthesis of Li 0.94 CoO 2 from Na y CoO 2 at 1-1,000 Li/Na (molar ratio) with an electrochemical assisted ion exchange method by mitigating the kinetic barriers. Our study opens new opportunities for ion exchange in predictive synthesis and separation applications. Ion exchange is a powerful method to access metastable materials for energy storage, but identifying lithium and sodium interchange in layered oxides remains challenging. Using such model materials, vacancy level and corresponding lithium preference are shown to be crucial for ion exchange pathway accessibility.
25 ENERGY STORAGE↗
An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model
A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.
97 MATHEMATICS AND COMPUTING↗
Inhibition of Chromium(III) Oxidation through Manganese(IV) Oxide Passivation and Iron(II) Abiotic Reduction
Manganese (Mn) oxides are strong oxidants that are ubiquitous in soils and can oxidize redox-active metals, including chromium (Cr). In soil environments, trivalent chromium (Cr(III)) is a benign, immobile micronutrient, whereas the hexavalent Cr(VI) form is present as a highly mobile, toxic chromate oxyanion. Although many studies have characterized the capacity of Mn(III/IV) oxides to oxidize Cr(III) to toxic Cr(VI), the oxidative capacity of Mn oxides in the presence of potentially passivating soil constituents, specifically reduced soluble iron (Fe(II) aq ), remains unresolved. We hypothesized that chemical processes at redox interfaces, such as diffusion-limited environments within soil aggregates, can lead to decreased Cr(VI) production from Mn oxide-driven oxidation due to passivation by Fe(II) aq . A multichamber diffusion-limited reactor was used to simulate transport at soil redox interfaces and investigate the capacity of poorly crystalline and crystalline Mn oxides to oxidize solid Cr(III) minerals to Cr(VI) in the presence of Fe(II) aq . As predicted, Cr(VI) was produced through the Mn oxide-catalyzed oxidation of Cr(III) at a rate controlled by the solubility of Cr(OH) 3 . However, in the presence of Fe(II) aq , the concentration of aqueous Cr(VI) decreased as a function of the Fe(II) aq concentration, where high concentrations of Fe(II) aq completely inhibited Cr(VI) production, likely through both the passivation of the Mn oxide and the direct reduction of Cr(VI) by Fe(II). At both low (14 μM) and high (100 μM) Fe(II) aq concentrations, the iron oxide minerals hematite (Fe 2 O 3 ) and goethite (α-FeOOH) were associated with the Mn oxides, which can cause surface passivation, a likely role that decreases Cr(III) oxidation. Additionally, the Cr(III) oxidation rate decreased with increasing crystallinity of the Mn oxides whether or not Fe(II) was present.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Constraining the Reaction Rate of Criegee Intermediates with Carboxylic Acids during the Multiphase Ozonolysis of Aerosolized Alkenes
Criegee intermediates (CIs) are central to the ozonolysis of unsaturated organic compounds, controlling the formation of small fragmentation reaction products and higher molecular weight oligomeric compounds through competing unimolecular and bimolecular pathways. In particular, the reaction of thermalized CI with carboxylic acids (RCOOH) to produce oligomeric α-acyloxyalkyl hydroperoxides (AAHPs) is of interest to the chemical transformation of organic compounds in the atmosphere. In the gas phase, the CI + RCOOH reaction proceeds at supercollisional rates, consistent with a barrierless reaction mechanism. However, the rate of this reaction in condensed phases remains uncertain. Here, we report the results of aerosol flow tube studies of the ozonolysis of submicron organic aerosol containing mixtures of an internal n-alkene (Z-9-tricosene, tri) and a saturated acid (2-hexyldecanoic acid, HDA). The decay of the reactants and formation of reaction products are monitored using atmospheric pressure chemical ionization mass spectrometry (APCI–MS). A 6-fold decrease in the reactive uptake of ozone is observed with increasing acid concentration, consistent with a previous study using alcohol additives. The decay of HDA with ozone exposure shows that HDA scavenges CIs at rates comparable to competing unimolecular pathways involving CIs. The decay kinetics of HDA are analyzed using a simple kinetic model in order to constrain the ratio of the CI + RCOOH and unimolecular CI rate constants. Empirical fitting to this model, combined with theoretical estimates of the unimolecular loss rate, yields a CI + RCOOH rate constant of 1.85 ± 0.27 × 10 –19 cm 3 molec –1 s –1 , which is six orders of magnitude slower than the expected diffusion limit in a liquid organic matrix. Stochastic kinetic simulations are conducted with different values of the CI + RCOOH rate constant to validate this result and show that the diffusion-limited rate is indeed much too rapid to reproduce the experimental results.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Designing Particle Morphologies for Materials with Solid Transport Limitations: A Case Study of Lithium and Manganese Rich Cathode Oxides
A lithium and manganese rich nickel-manganese-cobalt oxide (LMR-NMC) cathode is a promising candidate for next-generation batteries due to its high specific capacity, low cost, and low cobalt content. However, the material suffers from poor rate capability due to the diffusion limitations of lithium in the cathode particles. Understanding the material performance requires careful control of the morphology of the cathode particles, taking into account the primary and agglomerated diffusion pathways and the presence of pores, some of which could be closed from electrolyte infiltration. Here, in this study, we use a microstructure-based mathematical model combined with experimental data to understand the role of the complex cathode particle morphology in the rate performance of the material. Scanning electron microscopy images of cathodes made under different synthesis conditions, which results in different agglomerate morphologies, serve as the input into the mathematical model. The model is then compared to rate data to understand the controlling parameters. The presence of intra-agglomerate closed pores results in a large agglomerate diffusion length in comparison to the ideal condition, where the primary particles are agglomerated in an open and dispersed manner such that the entire interfacial area is available for electrochemical reaction. Smaller primary and agglomerate diffusion lengths result in better electrochemical performance. This points us toward designing the morphology of the cathode particles to compensate for the diffusion limitation of LMR-NMC while maximizing the density.
Tewari, Deepti↗
Evaluation of lithium as a tritium storage medium for betavoltaics
Lithium foils were demonstrated to absorb surrogate protium for tritium-powered betavoltaics. 20μm thick lithium foils were hole-punched from a ribbon of electrodeposited lithium on copper foil. The lithium foils were loaded with hydrogen in a custom Sievert apparatus where the pressure drop showed full hydriding at a hydrogen pressure of 2 bar and at all loading temperatures above the lithium melting point at 190, 200, 225, 250, and 300. Lithium hydride formation was confirmed with Raman spectroscopy after hydrogen loading. The kinetics of experimental hydride formation was compared to the diffusion-limited Mintz–Bloch model. While the Mintz–Bloch model showed good fit with the experimental loadings, the model overpredicted the loading kinetics starting at 250 °C and at higher temperatures. In conclusion, The overprediction was either caused by lithium hydride outgassing due to some reduction with some residual lithium hydroxide created from brief air exposure when sealing the lithium in the reactor or a transition from diffusion-limited hydride growth to surface or metal–hydride interface-limited hydride growth.
25 ENERGY STORAGE↗