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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 793 records · Page 44

Modeling Single-Crystal Battery Materials: From Fundamental Understanding to Performance Evaluation

The performance of rechargeable batteries is fundamentally influenced by the physicochemical properties and microstructural features of their key material components. Recent experimental advancements have highlighted the potential of single-crystal (SC) morphologies to address inherent limitations of polycrystalline (PC) electrodes and solid-state electrolytes, offering tunable charge transport kinetics and improved cell cycling performance. Here, this review examines how state-of-the-art computational modeling, from atomistic and mesoscale to continuum-level approaches, including machine learning methodologies, has been utilized to investigate the critical factors governing the electrochemical behavior of SC battery materials. We explore how predictive modeling can elucidate the processing–structure–property–performance relationships of SC cathodes, anodes, and solid-state electrolytes, with a focus on unique SC characteristics such as crystallographic anisotropy, size effects, and facet-dependent properties. Additionally, we identify limitations in commonly used modeling techniques and discuss strategies to address these challenges. By integrating high-fidelity simulations with experimental insights, this review aims to outline a clear path for the rational design and optimization of SC battery components, paving the way for accelerated advancements in energy storage technologies.

Materials science↗

Enabling “lithium-free” manufacturing of pure lithium metal solid-state batteries through in situ plating

Abstract The coupling of solid-state electrolytes with a Li-metal anode and state-of-the-art (SOA) cathode materials is a promising path to develop inherently safe batteries with high energy density (>1000 Wh L −1 ). However, integrating metallic Li with solid-electrolytes using scalable processes is not only challenging, but also adds extraneous volume since SOA cathodes are fully lithiated. Here we show the potential for “Li-free” battery manufacturing using the Li 7 La 3 Zr 2 O 12 (LLZO) electrolyte. We demonstrate that Li-metal anodes >20 μm can be electroplated onto a current collector in situ without LLZO degradation and we propose a model to relate electrochemical and nucleation behavior. A full cell consisting of in situ formed Li, LLZO, and NCA is demonstrated, which exhibits stable cycling over 50 cycles with high Coulombic efficiencies. These findings demonstrate the viability of “Li-free” configurations using LLZO which may guide the design and manufacturing of high energy density solid-state batteries.

25 ENERGY STORAGE↗

Ferroelectric capacitors and field-effect transistors as in-memory computing elements for machine learning workloads

Abstract This study discusses the feasibility of Ferroelectric Capacitors (FeCaps) and Ferroelectric Field-Effect Transistors (FeFETs) as In-Memory Computing (IMC) elements to accelerate machine learning (ML) workloads. We conducted an exploration of device fabrication and proposed system-algorithm co-design to boost performance. A novel FeCap device, incorporating an interfacial layer (IL) and$$\text {Hf}_{0.5}\text {Zr}_{0.5}\text {O}_2$$ Hf 0.5 Zr 0.5 O 2 (HZO), ensures a reduction in operating voltage and enhances HZO scaling while being compatible with CMOS circuits. The IL also enriches ferroelectricity and retention properties. When integrated into crossbar arrays, FeCaps and FeFETs demonstrate their effectiveness as IMC components, eliminating sneak paths and enabling selector-less operation, leading to notable improvements in energy efficiency and area utilization. However, it is worth noting that limited capacitance ratios in FeCaps introduced errors in multiply-and-accumulate (MAC) computations. The proposed co-design approach helps in mitigating these errors and achieves high accuracy in classifying the CIFAR-10 dataset, elevating it from a baseline of 10% to 81.7%. FeFETs in crossbars, with a higher on-off ratio, outperform FeCaps, and our proposed charge-based sensing scheme achieved at least an order of magnitude reduction in power consumption, compared to prevalent current-based methods.

Science & Technology - Other Topics↗

Simulating the sensitivity of evapotranspiration and streamflow to large-scale groundwater depletion

Groundwater pumping has caused marked aquifer storage declines over the past century. In addition to threatening the viability of groundwater-dependent economic activities, storage losses reshape the hydrologic landscape, shifting groundwater surface water exchanges and surface water availability. A more comprehensive understanding of modern groundwater-depleted systems is needed as we strive for improved simulations and more efficient water resources management. Here, we begin to address this gap by evaluating the impact of 100 years of groundwater declines across the continental United States on simulated watershed behavior. Subsurface storage losses reverberate throughout hydrologic systems, decreasing streamflow and evapotranspiration. Evapotranspiration declines are focused in water-limited periods and shallow groundwater regions. Streamflow losses are widespread and intensify along drainage networks, often occurring far from the point of groundwater abstraction. Our integrated approach illustrates the sensitivity of land surface simulations to groundwater storage levels and a path toward evaluating these connections in large-scale models.

54 ENVIRONMENTAL SCIENCES↗

Technology Implementation Plan: Accident Tolerant Fuel Mo and MoLa Alloy Cladding for Light Water Reactor Application

The technology implementation plan for Mo and MoLa fuel cladding materials involves elements required for the design, testing, characterization, and demonstration of the advanced technology. These elements are currently integrated in the cladding development plan. This document summarizes the technical objectives and describes the path, milestones, and task periods needed to achieve them. The document describes the development plan leading to cladding materials and technologies providing significant performance and safety advantages over current Light Water Reactors (LWR) fuel cladding. Other key objectives are meeting the fabrication, economic and licensability requirements, needed to deploy Accident Tolerant Fuels in operating commercial LWRs. The bulk of recent update work has been funded and performed by EPRI with some collaboration with Los Alamos National Laboratory (LANL). Future activities may involve a collaboration with AREVA under funding by the Department of Energy (DOE) Funding Opportunity Announcement (FOA).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Practical Application of Integrated Systems Engineering and Project Management on a Complex EPC Project - 17207

This paper introduces how an integrated set of Systems Engineering (SE) and Project Management (PM) processes were applied in a practical way, to address the challenges on a complex, highly technical, Engineering Procurement Construction project within the nuclear field. This approach was inspired by: - the principles contained in a Community of Practice on Lean in Program Management jointly established in May 2012 by MIT, PMI and INCOSE; - an opportunity to apply international standard ISO/IEC 15288:2008(E) Systems and software engineering - System life cycle processes on a real-life situation; - and the belief that there is great value in applying Systems Engineering and Project Management in an integrated manner on a project. The project offering this opportunity was the Detail Engineering, Procurement, Construction and Cold Commissioning (EPC) of the Silo Direct-encapsulation Plant (SDP). This project was undertaken by the Joint Venture (JV) formed by Areva, Mace and Atkins (a.m.a. Nuclear Ltd). Unfortunately, early termination of the project, at a stage when only a part of the processes and tools were being implemented, did not allow this integrated approach to be demonstrated in full. However, the benefits achieved in the early stages in aligning and forming an integrated project execution team, showed potential for great benefits. This paper covers an introductory analysis of the situation, the successes and benefits achieved from implementing an integrated SE - PM approach up to the stage when the project was terminated, and possible path forward had the project continued. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Chemical Vapor Deposition-Grown Hexagonal Boron Nitride and Graphene for Tandem Dielectric Capacitive Polymer Devices

To address the low energy density of polymeric capacitors, this work explores how tandem combinations of antagonistic properties can enhance energy storage. We introduce multilayer architecture integrating chemical vapor deposition (CVD)-grown ≈2 nm hexagonal boron nitride (hBN) and graphene with ferroelectric polyvinylidene fluoride (PVDF) and linear polyetherimide (PEI) layers to suppress leakage paths, reduce loss, and promote Maxwell–Wagner–Sillars polarization. Raman spectroscopy, X-ray diffraction (XRD), atomic force microscopy (AFM), scanning electron microscopy (SEM), and plasma focused ion beam (PFIB) analyses confirm robust material integration. In conclusion, for the tandem device, E BD ≈600 V/μm, while individual layers show lower values (PVDF|Graphene (Gr)|PVDF ≈ 50 V/μm and PEI|hBN|PEI ≈ 275 V/μm), yielding an overall ≈6000% enhancement and demonstrating the effectiveness of the 2D multilayer design.

Chemical vapor deposition (CVD)↗

Advanced manufacturing—A transformative enabling capability for fusion

Additive Manufacturing (AM) can create novel and complex engineered material structures. Features such as controlled porosity, micro-fibers and/or nano-particles, transitions in materials and integral robust coatings can be important in developing solutions for fusion subcomponents. A realistic understanding of this capability would be particularly valuable in identifying development paths. Major concerns for using AM processes with lasers or electron beams that melt powder to make refractory parts are the power required and residual stresses arising in fabrication. A related issue is the required combination of lasers or e-beams to continue heating of deposited material (to reduce stresses) and to deposit new material at a reasonable built rate while providing adequate surface finish and resolution for meso-scale features. Some Direct Write processes that can make suitable preforms and be cured to an acceptable density may offer another approach for PFCs.

Additive Manufacturing, fusion energy, Fusion Mate↗

An arc-length method for controlled cohesive crack propagation using high-order XFEM and Irwin’s crack closure integral

Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure. To address these challenges, here we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin’s crack closure integral, which allows for direct control of the applied loads necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin’s integral, since SIFs can be written in closed-form. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle. Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.

42 ENGINEERING↗

Near-Infrared Nanophotonics through Dynamic Control of Carrier Density in Conducting Ceramics

Major breakthroughs in silicon photonics often come from the integration of new materials into the platform, from bonding III-Vs for on-chip lasers to growth of Ge for high-speed photodiodes. This report describes the integration of transparent conducting oxides (TCOs) onto silicon waveguides to enable ultra-compact (<10 μm) electro-optical modulators. These modulators exploit the "epsilon-near-zero" effect in TCOs to create a strong light-matter interaction and allow for a significant reduction in footprint. Waveguide-integrated devices fabricated in the Sandia Microfab demonstrated gigahertz-speed operation of epsilon-near-zero based modulators for the first time. Numerical modeling of these devices matched well with theory and showed a path for significant improvements in device performance with high-carrier-mobility TCOs such as cadmium oxide. A cadmium oxide sputtering capability has been brought online at Sandia; integration of these high mobility films is the subject of future work to develop and mature this exciting class of Si photonics devices.

36 MATERIALS SCIENCE↗

Mega salt-stone Disposal Units at the Savannah River site - 15322

The Liquid Waste (LW) System at Savannah River Site (SRS) is a highly integrated operation involving safely storing radioactive liquid waste in underground storage tanks; vitrifying the higher activity waste; and storing the vitrified waste in stainless steel canisters until permanent disposition is provided; and removing, treating, and dispositioning the low-level waste (LLW) fraction in concrete with final disposition being the salt-stone Disposal Units (SDUs) at the SRS salt-stone Disposal Facility (SDF). Treatment and disposition of salt waste is the critical path to completion of the SRS Liquid Waste (LW) Disposition Program. Successful and timely salt waste removal and disposal is integral to efforts by SRS to proceed with all aspects of tank cleanup and removal from service. The construction and implementation of the first-of-a-kind Mega SDU (MSDU) is underway to provide the most environmentally safe and cost-effective solution for salt processing and long term storage of the LLW at SRS. The MSDU design is a duplicate of the Water Treatment Tanks located in Syracuse, New York. This commercial design, developed by an affiliate of Savannah River Remediation LLC (SRR), was slightly modified to meet the requirements of the nuclear industry. The MSDU is a critical link in salt disposition. In comparison to the current SDU design, approximately 46 meters (150 feet) in diameter and 7 meters (22 feet) tall with a capacity of approximately 11,000 m{sup 3} (3.0 million gallons), the MSDU is 114 meters (375 feet) in diameter and 13 meters (43 feet) tall which will provide a capacity of approximately 121,000 m{sup 3} (32.0 million gallons) to receive the LLW fraction embedded in a grout-like form. The MSDU will provide the taxpayers an estimated $300 M in life cycle savings at SRS by reducing the number of SDUs from the estimated 72 smaller vessels to 7 of the new larger vessels. Additionally, based on the reduced number of SDUs, the environmental footprint is significantly reduced as well. Due to the similarities between the existing SDU design and the MSDU design, efforts to integrate the MSDU into the LW system are minimal. Required infrastructure modifications will consist of tying into the existing grout and drain lines, as well as the installation of new electrical and instrumentation services for the MSDU. Grout flow testing has been successfully completed, with results showing the MSDU will be a safe and cost-effective replacement for the existing SDUs. The MSDU design is complete, Critical Decision (CD)-3 was approved on June 17, 2014, and the first MSDU, salt-stone Disposal Unit n.6 (SDU 6), is being constructed in the existing LW SDF operated by SRR as a Capital Line Item project. As an added benefit, once constructed, lessons learned will be available for future MSDUs at SRS and throughout the complex as necessary. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Pyomo.GDP: an ecosystem for logic based modeling and optimization development

We present three core principles for engineering-oriented integrated modeling and optimization tool sets—intuitive modeling contexts, systematic computer-aided reformulations, and flexible solution strategies—and describe how new developments in Pyomo.GDP for Generalized Disjunctive Programming (GDP) advance this vision. We describe a new logical expression system implementation for Pyomo.GDP allowing for a more intuitive description of logical propositions. The logical expression system supports automated reformulation of these logical constraints to linear constraints. We also describe two new logic-based global optimization solver implementations built on Pyomo.GDP that exploit logical structure to avoid “zero-flow” numerical difficulties that arise in nonlinear network design problems when nodes or streams disappear. These new solvers also demonstrate the capability to link to external libraries for expanded functionality within an integrated implementation. We present these new solvers in the context of a flexible array of solution paths available to GDP models. Finally, we present results on a new library of GDP models demonstrating the value of multiple solution approaches.

42 ENGINEERING↗

Simulated moving bed-inspired method for continuous adsorptive denitrogenation of model fuel

Efficient, continuous routes for removing nitrogen-containing compounds from hydrothermal liquefaction-derived synthetic aviation fuel are needed to enable direct blending with conventional jet fuels. Here, we report a simulated moving bed-inspired process for adsorptive denitrogenation of a model fuel. Unlike conventional simulated moving bed systems, which are designed for sharp separations between similar solutes, this approach was run deliberately outside the classical separation region so that both pyridine and indole were removed together from the hydrocarbon stream. Alcohol solvents were used to regenerate the silica adsorbent, maintaining performance over extended operation and avoiding the downtime and energy demand associated with calcination. Under these conditions, the system demonstrates removal of more than 98% of nitrogen while cutting solvent use by 28% compared to batch operation. Classical modeling tools predicted column concentration profiles even in this nontraditional regime, suggesting a straightforward path to scaling. Together, these results motivate solvent-efficient, continuous denitrogenation strategies that could be integrated with biorefinery processes.

Adsorption↗

Thermal hydraulic analysis of the AFIP-7 irradiation test in the Advanced test Reactor – Model correlation and performance evaluation

We report as a system level code, RELAP5 is widely used in the nuclear field for the reactor hydraulic analysis. In the component/experimental level, it is frequently employed as well. This paper demonstrates that the RELAP5 flow simulation of the AFIP-7 irradiation experiment which has a complicated 3D geometry/flow path deviates by ~28% from the flow evaluation through a computational fluid dynamics (CFD) simulation, which has been validated against a flow test performed at Oregon State University. Thermal safety compliance analysis of an experiment planned to be irradiated in the Advanced Test Reactor is usually performed using the finite element analysis code, Abaqus. This research reveals the disadvantages of the Abaqus simulation in the flow instability and departure from nucleate boiling evaluations via a conjugate heat transfer analysis of the AFIP-7 irradiation experiment. As a result, a detailed CFD simulation is suggested for irradiation experiments with complicated flow paths, rather than a simplified RELAP5 simulation or hand calculations. The validated simulation approach will be integrated with the Boehmite correlations to investigate the oxide growth prediction on the fuel cladding in Part II of this research.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

PathTracer Comprehensively Identifies Hypoxia-Induced Dormancy Adaptations in Mycobacterium tuberculosis

Mining large-scale data to discover biologically relevant information remains a challenge despite the rapid development of bioinformatics tools. Here, we have developed a new tool, PathTracer, to identify biologically relevant information flows by mining genome-wide protein–protein interaction networks following integration of gene expression data. PathTracer successfully mines interactions between genes and traces the most perturbed paths of perceived activities under the conditions of the study. Here, we further demonstrated the utility of this tool by identifying adaptation mechanisms of hypoxia-induced dormancy in Mycobacterium tuberculosis (Mtb).

59 BASIC BIOLOGICAL SCIENCES↗

Integrating a Water Tracer Model Into WRF‐Hydro for Characterizing the Effect of Lateral Flow in Hydrologic Simulations

Abstract Most current land models approximate terrestrial hydrological processes as one‐dimensional vertical flow, neglecting lateral water movement from ridges to valleys. Such lateral flow is fundamental at catchment scales and becomes crucial for finer‐scale land models. To test the effect of incorporating lateral flow toward three‐dimensional representations of hydrological processes in the next generation land models, we integrate a water tracer model into the WRF‐Hydro framework to track water movement from precipitation to discharge and evapotranspiration. This hydrologic‐tracer integrated system allows us to identify the key mechanisms by which lateral flow affects the flow paths and transit times in WRF‐Hydro. By comparing modeling experiments with and without lateral routing in two contrasting catchments, we determine the impacts of lateral flow on the transit times of precipitation event‐water. Results show that with limited hydrologic connectivity, lateral flow extends the transit times by reducing (increasing) event‐water drainage loss (accumulation) in ridges (valleys) and allowing reinfiltration of infiltration‐excess flow, which is missing in most land models. On the contrary with high hydrologic connectivity, lateral flow can effectively accelerate the water release to streams and reduce the transit time. However, the transit times are substantially underestimated by the model compared with isotope‐derived estimates, indicating model limitations in representing flow paths and transit times. This study provides some insights on the fundamental differences in terrestrial hydrology simulated by land models with and without lateral flow representation.

54 ENVIRONMENTAL SCIENCES↗

Development of NDE/NDT Tools for High-Volume & High-Speed Inspection of CFRP Structures in Automotive Manufacturing

Main advantages of the air-coupled ultrasound testing (ACUT) and electromagnetic testing (EMT) techniques for NDE of CFRP composites were non-contact sensing, scalability for high-speed inspection, cost-effectiveness, and non-hazardous operation. Despite these advantages, no systems that would satisfy the project requirements were commercially available. Hence, one of the major efforts of the Michigan State University (MSU) team at the initial stage of the project was to close this technological gap by developing, optimizing, and validating array sensors that would provide sufficient sensitivity, spatial coverage, and resolution for robust defect detection. Optimization of the ACUT and EMT sensor designs was performed using experimentally validated finite element models. Initial experiments using array probes were conducted on relatively flat CFRP samples. In parallel, the MSU team designed and assembled a portable platform with two robotic arms. The robots were equipped with newly designed sensors that enabled high-speed NDE of curved CFRP parts. Presently, the developed robotic platform can be used as a demo/template NDE system, which is easily adaptable to manufacturing environments and in-line NDE. The ACUT NDE system developed by the MSU team used a high-power 4-channel pulser receiver for parallel data acquisition. The array probes were designed by stacking commercially available ACUT transducers, which operated in the frequency range between 100 kHz and 500 kHz. MSU optimized the excitation procedure and developed wave focusing cones so as to reduce the crosstalk between the transducers and to provide higher pulse repletion frequency (PRF). The through-transmission (TT) and single-side access (SSA) inspection modes were successfully implemented. In the TT-ACUT, structural defects in CFRP were detected by passing ultrasonic waves through the test part. Hence, the ACUT transmitters and receivers needed to be placed on the opposite sides of the test part. In the SSA-ACUT, guided waves (GW) were excited in the test part using the transmitters and were sensed by the receivers from the same side. Multi-channel TT-ACUT and SSA-ACUT provided high-speed NDE, and were successfully validated on CFRP test samples with interlaminar delaminations and other embedded defects The EM techniques developed by the MSU team included: 1) eddy current testing (ECT), 2) capacitive imaging (CI) and hybrid dual-mode imaging. In ECT, structural damage was detected in CFRP using coils sensor arrays. In ECT, the excitation magnetic field is generated by passing an alternating current through a coil, which is placed above the test sample. The excitation field penetrates the conductive sample and induces the eddy currents in its transect. In turn, the eddy currents generate the reaction field, which affects the total field sensed by a coil. Hence, the presence of structural flaws will alter the eddy current flow and the picked-up signal. ECT is mostly sensitive to local changes of the electric conductivity of the test sample, and CFRPs are mostly conductive in the direction of carbon fibers. Hence, ECT was well suited for the detection of fiber damage/fiber irregularities. The MSU team developed printed circuit boards (PCB) with coil sensor arrays optimized for NDE of CFRP. Unlike most commercial probes designed for ECT of metallic structures, the MSU array probes were designed for operation in [1-10] MHz frequency range, which was optimal for low-conductive CFRP. Multiple sensing topologies (coil groups excitation/sensing arrangements) were implemented and successfully validated. Capacitive Imaging (CI) technique developed by MSU was complementary to ECT. In contrast to ECT, which was sensitive to local changes of the electrical conductivity, the CI was sensitive to local changes of the dielectric constant. Therefore, CI could provide information about matrix damage/matrix irregularities in CFRP. The MSU CI sensor arrays were made of multiple circular or rectangular open-plate capacitors printed on PCB. Sensors of this type are not commercially available. In addition to ECT and CI, the MSU team developed a hybrid (dual-mode) inductive/capacitive measurement technique that synergistically combined the benefits of inductive and capacitive sensing for rapid NDE of fiber reinforced polymer (FRP) composite structures. Fiber damage and fiber irregularities in FRPs were detected by configuring hybrid sensors as coil sensors. Similarly, matrix damage, matrix irregularities and interlaminar delaminations were detected by configuring hybrid sensors as capacitive sensors. ECT and CI were performed sequentially by means of electronic switching. Hence, eliminating the need for mounting two separate sensor arrays on the probe. Portable robotic platform was developed by MSU for multi-technique high-speed NDE of CFRP test parts. The platform had two 6-axis robots, which enabled inspection of curved parts in approximately a 6×6×6 ft 3 active scan area. On the software side, the MSU team integrated scripts for NDE hardware control with scripts for robot motion control. MSU also implemented automated path planning for the robots, reconstruction of part’s surfaces via stereovision, 3D rendering of inspection data, and image processing algorithms for enhanced defect detection. Automotive composite parts manufactured by Plasan Composites from Phase I were used to validate the ACUT and EMT techniques on representative testbeds. Among those parts were three X-braces for a Dodge Viper, one composite calibration plaque with known defects at known locations, and four other test sections, including sections from a front splitter, a corner section from a composite hood, and a high-pressure RTM panel made using non crimp fabric. Other test samples included CFRP and GFRP calibration plates with fiber/matrix defects fabricated at MSU/CVRC.

36 MATERIALS SCIENCE↗

Derivation of a Multi-Species Mix Model

Multi-species flow takes place when two or more gases, plasmas or fluids are flowing and interacting with one another through particle collisions, chemical reactions, turbulence, and thermonuclear processes; this list is not exhaustive. It has a wide range of applications in geological, biological and engineering systems. In what follows species refers to different species of atoms or molecules that may or may not be partially or fully ionized. The interactions between these species takes place at an atomic or molecular level. The species are electrically neutral. These are very important points, because the coupling between species that are interacting on a mesoscale level or are immiscible would be very different than what is being considered in this work. In addition, in section 4, we present a heuristic argument to enhance the collisional mean free path to incorporate the effects of turbulent eddies by use of Prandtl’s assumption that the integral scale length of a turbulent boundary layer is proportional to the width of the turbulent layer. This leads to coupling terms that are non-Newtonian, because they are a function of the dynamics of the flow. It is also assumed that the turbulent stress terms are much smaller than the species partial pressures. This may be a good assumption if the species are hot, dense plasmas that exist in ICF targets.

74 ATOMIC AND MOLECULAR PHYSICS↗