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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Chemo-Mechanics of α-V 2 O 5 During Lithiation and Implications for Rechargeable Battery Cathodes

Chemo-mechanical degradation of layered oxide electrodes is strongly influenced by crystallographic anisotropy, local stress evolution, and ion insertion, yet the intrinsic mechanical response of layered materials remains incompletely understood. Indeed, most prior studies have focused on polycrystalline materials but single crystals enable direct observation of coupling between anisotropic ion diffusion and mechanical response. This study aims to determine how crystallographic anisotropy and lithiation affect deformation, fracture, and mechanical properties in single-crystal V 2 O 5 , and compares this behavior with polycrystalline counterparts. Polycrystalline V 2 O 5 thin films and single-crystal α-V 2 O 5 were studied using nanoindentation, scanning electron microscopy, focused ion beam cross-sectioning, and Raman spectroscopy. Single crystals were tested in pristine and chemically lithiated states, including experiments in which crystals were first plastically deformed via nanoindentation and subsequently lithiated. Polycrystalline films exhibited significantly higher hardness and elastic modulus than single crystals. Single crystals indented normal to the exposed (001) basal plane exhibited pronounced anisotropic deformation, including directional slip, crystallographically-guided cracking, anisotropic crack propagation, interlayer separation, and shear localization. Lithiation caused substantial softening, reduced hardness and modulus, and suppressed displacement bursts during nanoindentation, while previously indented regions showed crack formation and growth upon lithiation. Mechanical behavior of α-V 2 O 5 is strongly governed by crystallographic anisotropy and further altered by lithiation, with pre-existing deformation serving as a strong driver of fracture during ion insertion. These findings illuminate the coupling among ion insertion, deformation, and fracture in layered oxides and provide a basis for understanding and mitigating mechanical failure in electrochemical energy-storage materials.

Anisotropy↗
DOE OSTI2022

An efficient high-order numerical solver for diffusion equations with strong anisotropy

In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. Additionally, we demonstrate the accuracy produced by the high-order scheme and develop an efficient preconditioning technique to solve the corresponding linear system, which is robust to the mesh size and anisotropy of the problem. Several numerical tests are provided to validate the accuracy and efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Coherent 3D nanostructure of γ-Al{sub 2}O{sub 3}: Simulation of whole X-ray powder diffraction pattern

The structure and nanostructure features of nanocrystalline γ-Al{sub 2}O{sub 3} obtained by dehydration of boehmite with anisotropic platelet-shaped particles were investigated. The original models of 3D coherent nanostructure of γ-Al{sub 2}O{sub 3} were constructed. The models of nanostructured γ-Al{sub 2}O{sub 3} particles were first confirmed by a direct simulation of powder X–Ray diffraction (XRD) patterns using the Debye Scattering Equation (DSE) with assistance of high-resolution transmission electron microscopy (HRTEM) study. The average crystal structure of γ-Al{sub 2}O{sub 3} was shown to be tetragonally distorted. The experimental results revealed that thin γ-Al{sub 2}O{sub 3} platelets were heterogeneous on a nanometer scale and nanometer-sized building blocks were separated by partially coherent interfaces. The XRD simulation results showed that a specific packing of the primary crystalline blocks in the nanostructured γ-Al{sub 2}O{sub 3} particles with formation of planar defects on (001), (100), and (101) planes nicely accounted for pronounced diffuse scattering, anisotropic peak broadening and peak shifts in the experimental XRD pattern. The identified planar defects in cation sublattice seem to be described as filling cation non-spinel sites in existing crystallographic models of γ-Al{sub 2}O{sub 3} structure. The overall findings provided an insight into the complex nanostructure, which is intrinsic to the metastable γ-Al{sub 2}O{sub 3} oxide. - Highlights: • Thin plate-like crystallites of γ-Al{sub 2}O{sub 3} were obtained. • Models of 3D coherent nanostructure of γ-Al{sub 2}O{sub 3} were constructed. • Models were verified by simulating XRD patterns using the Debye Scattering Equation. • Specific broadening of XRD peaks was explained in terms of planar defects. • Primary crystalline blocks in γ-Al{sub 2}O{sub 3} are separated by partially coherent interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Modeling Chemo-Mechanics with Electrolyte Infiltration to Quantify Degradation of Cathode Particles

One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. To that end, this talk investigates the formation of stress-induced fracture within polycrystalline cathode particles and the impact on capacity loss. Physically based cathode aging dynamics is simulated in a 3D, continuum-level chemo-mechanical model. The model captures anisotropic Li diffusion within a single polycrystalline particle comprised of hundreds to thousands of randomly oriented grains. A recent addition to this model includes electrolyte infiltration, which occurs when the electrolyte seeps into surface cracks within the particle. The model predicts that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains are misaligned, they expand a different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicts that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical "damage saturation" effect indicates that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. The principle contribution of this research is the use of an anisotropic chemo-mechanical model to test how particle geometry affect capacity fade, which predicts that particle size has a stronger effect on capacity fade than grain size and ultimately that small particles with large grains have the least capacity fade.

cathode↗
DOE OSTI2023

Electrochemical-mechanical coupling failure mechanism of composite cathode in all-solid-state batteries

Composite cathode composed of active particles and solid electrolytes (SEs) can considerably enlarge the particle-SE contact areas and achieve high areal loadings in all-solid-state batteries (ASSBs). However, the challenging interfacial instability and particle damage problems remain unsolved. Herein, we establish a 3D electrochemical-mechanical coupled model to investigate the underlying failure mechanism by considering the governing electrochemical and physics processes. Micro-scale heterogeneous primary particles with random crystallographic orientation and size inside the LiNi 1/3 Co 1/3 Mn 1/3 O 2 (NCM111) secondary particle of the model result in the anisotropic Li diffusion and volume variation within the secondary particle, leading to significant nonuniformity of the Li concentration, and GPa-level stress distributions at primary particle boundaries, and finally causing the particle internal cracks. The particle volume shrinkage under the constraint of stiff Li 7 La 3 Zr 2 O 12 (LLZO) SE triggers the interface debonding (gap>50 nm) with increased interfacial impedance to degrade cell capacity. Higher C-rates result in larger residual stress (~100 MPa)/strain/debonding gap at dis-charging end, more likely to deteriorate the cell performance. Increasing the interfacial strength between the particle and SE can suppress the interface debonding but induces high stress (up to 10 GPa). In conclusion, results reveal the underlying mechanism of the electrochemical-mechanical coupling failure mechanism for composite cathode and provide promising guidance on the further improvement of a more robust composite cathode for ASSBs.

25 ENERGY STORAGE↗
DOE OSTI2019

Growth Mechanism of Five-Fold Twinned Ag Nanowires from Multiscale Theory and Simulations

Five-fold twinned metal nanowires can be synthesized with high aspect ratios via solution-phase methods. The origins of their anisotropic growth, however, are poorly understood. Here, we combine atomic-scale, mesoscale, and continuum theoretical methods to predict growth morphologies of Ag nanowires from seeds and to demonstrate that high aspect ratio nanowires can originate from anisotropic surface diffusion induced by the strained nanowire structure. Nanowire seeds are similar to Marks decahedra, with {111} “notches” that accelerate diffusion along the nanowire axis to facilitate one-dimensional growth. The strain distribution on the {111} facets induces heterogeneous atom aggregation and leads to atom trapping at the nanowire ends. We predict that decahedral Ag seeds can grow to become nanowires with aspect ratios in the experimental range. Our studies show that there is a complex interplay between atom deposition, diffusion, seed architecture, and nanowire aspect ratio that could be manipulated experimentally to achieve controlled nanowire syntheses.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2015

A validation of the fibre orientation and fibre length attrition prediction for long fibre-reinforced thermoplastics

To improve the mechanical performance of polymeric parts, fibre reinforcement has established in industrial applications during the last decades. Next to the widely used Short Fibre-reinforced Thermoplastics (SFT) the use of Long Fibre-reinforced Thermoplastics (LFT) is increasingly growing. Especially for non-polar polymeric matrices like polypropylene (PP), longer fibres can significantly improve the mechanical performance. As with every kind of discontinuous fibre reinforcement the fibre orientations (FO) show a high impact on the mechanical properties. On the contrary to SFT where the local fibre length distribution (FLD) can be often neglected, for LFT the FLD show a high impact on the material’s properties and has to be taken into account in equal measure to the FOD. Recently numerical models are available in commercial filling simulation software and allow predicting both the local FOD and FLD in LFT parts. The aim of this paper is to compare i.) the FOD results and ii) the FLD results from available orientation- and fibre length attrition-models to those obtained from experimental data. The investigations are conducted by the use of different injection moulded specimens made from long glass fibre reinforced PP. In order to determine the FOD, selected part sections are examined by means of Computed Tomographic (CT) analyses. The fully three dimensional measurement of the FOD is then performed by digital image processing using grey scale correlation. The FLD results are also obtained by using digital image processing after a thermal pyrolytic separation of the polymeric matrix from the fibres. Further the FOD and the FLD are predicted by using a reduced strain closure (RSC) as well as an anisotropic rotary diffusion - reduced strain closure model (ARD-RSC) and Phelps-Tucker fibre length attrition model implemented in the commercial filling software Moldflow, Autodesk Inc., San Rafael, CA, USA.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Electron kinetics in a positive column of AC discharges in a dynamic regime

Abstract We have performed hybrid kinetic-fluid simulations of a positive column in alternating current (AC) argon discharges over a range of driving frequencies f and gas pressure p for the conditions when the spatial nonlocality of the electron energy distribution function (EEDF) is substantial. Our simulations confirmed that the most efficient conditions of plasma maintenance are observed in the dynamic regime when time modulations of mean electron energy (temperature) are substantial. The minimal values of the root mean square electric field and the electron temperature have been observed at f/p values of about 3 kHz Torr −1 in a tube of radius R = 1 cm. The ionization rate and plasma density reached maximal values under these conditions. The numerical solution of a kinetic equation allowed accounting for the kinetic effects associated with spatial and temporal nonlocality of the EEDF. Using the kinetic energy of electrons as an independent variable, we solved an anisotropic tensor diffusion equation in phase space. We clarified the role of different flux components during electron diffusion in phase space over surfaces of constant total energy. We have shown that the kinetic theory uncovers a more exciting and rich physics than the classical ambipolar diffusion (Schottky) model. Non-monotonic radial distributions of excitation rates, metastable densities, and plasma density have been observed in our simulations at pR > 6 Torr cm. The predicted off-axis plasma density peak in the dynamic regime has never been observed in experiments so far. We hope our results stimulate further experimental studies of the AC positive column. The kinetic analysis could help uncover new physics even for such a well-known plasma object as a positive column in noble gases.

Physics↗
DOE OSTI2025

Anisotropic Thermal Transport in Quasi-2D Ruddlesden-Popper Hybrid Perovskite Superlattices

Two-dimensional hybrid metal-halide perovskites (2D-MHPs) have emerged as important solution-processed semiconductors with favorable optical and electronic properties for diverse applications in photovoltaics, optoelectronics, and spintronics. The quasi-2D layered structures, featuring large acoustic impedance mismatches between the organic and inorganic sublattices, are expected to result in distinct and anisotropic thermal transport properties along the cross-plane and in-plane directions. Here, we introduce transducer-free vibrational-pump-visible-probe (VPVP) approaches that enable accurate quantification of anisotropic thermal transport properties in various archetypical single-crystalline 2D-MHPs. Specifically, using VPVP spectroscopy and VPVP microscopy, we measure the anisotropic thermal diffusivities of 2D-MHPs with systematically varied Pb-I octahedral layer thicknesses, as well as organic spacer types and lengths, revealing how these structural parameters alter the cross-plane and in-plane thermal transport properties in distinct ways. While diffuse interface scattering plays an important role in dictating cross-plane thermal transport, in-plane thermal transport is primarily determined by phonon transport within interconnected inorganic layers. Density functional theory incorporating four-phonon scatterings provides further insight into the low thermal conductivity and modest thermal conduction anisotropy in 2D-MHPs. Our work demonstrates a new all-optical and noncontact method, which requires minimal sample preparation and allows direct visualization of cross-plane and in-plane thermal transport, potentially compatible with sample environments. The demonstrated VPVP approaches can advance understanding of thermal transport in 2D-MHPs as well as wide-ranging hybrid and polymeric semiconductors beyond 2D-MHPs.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Resolution-induced anisotropy in large-eddy simulations

Large-eddy simulation (LES) of turbulence in complex geometries and domains is often conducted with high-aspect-ratio resolution cells of varying shapes and orientations. The effects of such anisotropic resolution are often simplified or neglected in subgrid model formulations. In this study, we examine resolution-induced anisotropy and demonstrate that even for isotropic turbulence, anisotropic resolution induces mild resolved Reynolds stress anisotropy and significant anisotropy in second-order resolved velocity gradient statistics. In large-eddy simulations of homogeneous isotropic turbulence with anisotropic resolution, it is shown that commonly used subgrid models, including those that consider resolution anisotropy in their formulation, perform poorly. The one exception is the anisotropic minimum dissipation model proposed by Rozema et al. [Phys. Fluids 27, 085107 (2015)]. A simple model is presented here that is an anisotropic eddy diffusivity extension of the “Kolmogorov expression” eddy viscosity of Carati et al. [A family of dynamic models for large-eddy simulation, in Annual Research Briefs, Center for Turbulence Research (Stanford University and NASA AMES, 1995), pp. 35–40] that depends explicitly on the anisotropy of the resolution. It also performs well and is remarkable because, unlike other LES subgrid models, the eddy diffusivity only depends on statistical characteristics of the turbulence (in this case, the dissipation rate), not on fluctuating quantities. In other subgrid modeling formulations, such as the dynamic procedure, limiting flow dependence to statistical quantities in this way could have advantages.

42 ENGINEERING↗
DOE OSTI2016

Predictive Engineering Tools for Injection-Molded Long-Carbon-Fiber Thermoplastic Composites - FY 2016 First Quarterly Report

During the first quarter of FY 2016, the following technical progress has been made toward project milestones: 1) Virginia Tech completed fiber orientation (FO) measurements for the samples taken at Locations A, B, C and D (Figure 1) from the 30wt% LCF/PP and 30wt% LCF/PA66 ribbed and non-ribbed complex parts using Virginia Tech’s established procedure. Virginia Tech delivered to PNNL all the measured fiber orientation data for validating ASMI fiber orientation predictions. 2)Virginia Tech performed fiber length distribution (FLD) measurements for the samples taken at Locations A, B, C and D from these complex parts using Virginia Tech’s established procedure. Virginia also re-assessed previous data and measured fiber length distributions in the corresponding nozzle purging materials and delivered to PNNL all the measured length data for validating ASMI fiber length predictions. 3)Based on measured fiber orientation data, Autodesk identified the parameters of the anisotropic rotary diffusion reduced strain closure (ARD-RSC) model [1] and provided PNNL with the values of these parameters that were used in ASMI analyses of the complex parts. 4) Magna provided Virginia Tech with additional samples cut out from the 30wt% LCF/PP and 30wt% LCF/PA66 ribbed parts (Figure 1) for fiber length and orientation measurements. 5) In discussion with Autodesk, PNNL performed 3D ASMI analyses of the 30wt% LCF/PP and 30wt% LCF/PA66 ribbed and non-ribbed complex parts to predict fiber orientations and length distributions in these parts. The issues observed through the analyses regarding fiber orientation distributions profiles and abnormal length distributions were reported to Autodesk. Autodesk is working to resolve these issues. 6) PNNL completed 3D ASMI analyses of the complex parts and compared predicted fiber orientation results at Locations A, B, and C on the non-ribbed parts, and at Locations A, B, C and D on the ribbed parts with the corresponding measured data. PNNL also evaluated the within-15%-agreement criterion using the principal tensile and flexural moduli computed based on predicted vs. measured fiber orientation results. 7) PNNL developed and discussed with Toyota, Magna and PlastiComp a method to perform weight and cost reduction for making the 30wt% LCF/PA66 ribbed part through comparative three-point bending simulations of this part and of similar parts in steel.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Predictive Engineering Tools for Injection-Molded Long-Carbon-Fiber Thermoplastic Composites - FY 2014 Fourth Quarterly Report

During the last quarter of FY 2014, the following technical progress has been made toward project milestones: 1) Autodesk, Inc. (Autodesk) has implemented a new fiber length distribution (FLD) model based on an unbreakable length assumption with Reduced Order Modeling (ROM) by the Proper Orthogonal Decomposition (POD) approach in the mid-plane, dual-domain and 3D solvers. 2) Autodesk improved the ASMI 3D solver for fiber orientation prediction using the anisotropic rotary diffusion (ARD) – reduced strain closure (RSC) model. 3) Autodesk received consultant services from Prof. C.L. Tucker at the University of Illinois on numerical simulation of fiber orientation and fiber length. 4) PlastiComp, Inc. (PlastiComp) suggested to Purdue University a procedure for fiber separation using an inert-gas atmosphere in the burn-off furnace. 5) Purdue University (Purdue) hosted a face-to-face project review meeting at Purdue University on August 6-7, 2014. 6) Purdue conducted fiber orientation measurements for 3 PlastiComp plaques: fast-fill 30wt% LCF/PP edged-gated, slow-fill 50wt% LCF/PP edge-gated, and slow-fill 50wt% LCF/PP center-gated plaques, and delivered the orientation data for these plaques at the selected locations (named A, B, and C) to PNNL. 7) PNNL conducted ASMI mid-plane analyses for the above PlastiComp plaques and compared the predicted fiber orientations with the measured data provided by Purdue at Locations A, B, and C on these plaques. 8) PNNL planned the project review meeting (August 6-7, 2014) with Purdue. 9) PNNL performed ASMI analyses for the Toyota complex parts with and without ribs, having different wall thicknesses, and using the PlastiComp 50wt% LCF/PP, 50wt% LCF/PA66, 30wt% LCF/PP, and 30wt% LCF/PA66 materials to provide guidance for tool design and modifications needed for molding these parts. 10) Magna Exteriors and Interiors Corp. (Magna) molded plaques from the 50% LCF/PP and 50% LCF/PA66 materials received from Plasticomp in order to extract machine purgings (purge materials) from Magna’s 200-Ton Injection Molding machine targeted to mold the complex part. 11) Toyota and Magna discussed with PNNL tool modification for molding the complex part.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Crystallization of ApoA1 and ApoE4 Nanolipoprotein Particles and Initial XFEL-Based Structural Studies

Nanolipoprotein particles (NLPs), also called “nanodiscs”, are discoidal particles with a patch of lipid bilayer corralled by apolipoproteins. NLPs have long been of interest due to both their utility as membrane-model systems into which membrane proteins can be inserted and solubilized and their physiological role in lipid and cholesterol transport via high-density lipoprotein (HDL) and low-density lipoprotein (LDL) maturation, which are important for human health. Serial femtosecond crystallography (SFX) at X-ray free electron lasers (XFELs) is a powerful approach for structural biology of membrane proteins, which are traditionally difficult to crystallize as large single crystals capable of producing high-quality diffraction suitable for structure determination. To facilitate understanding of the specific role of two apolipoprotein/lipid complexes, ApoA1 and ApoE4, in lipid binding and HDL/LDL particle maturation dynamics, and to develop new SFX methods involving NLP membrane protein encapsulation, we have prepared and crystallized homogeneous populations of ApoA1 and ApoE4 NLPs. Crystallization of empty NLPs yields semi-ordered objects that appear crystalline and give highly anisotropic and diffuse X-ray diffraction, similar to fiber diffraction. Several unit cell parameters were approximately determined for both NLPs from these measurements. Thus, low-background, sample conservative methods of delivery are critical. Here we implemented a fixed target sample delivery scheme utilizing the Roadrunner fast-scanning system and ultra-thin polymer/graphene support films, providing a low-volume, low-background approach to membrane protein SFX. This study represents initial steps in obtaining structural information for ApoA1 and ApoE4 NLPs and developing this system as a supporting scaffold for future structural studies of membrane proteins crystalized in a native lipid environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1981

Mesoscale convection in the clouds of Venus

A theory explaining the high aspect ratios for cloud level convection in the Venusian atmosphere is presented. The apparent flatness of large-scale convection cells in the Venusian clouds is accounted for by anisotropic eddy diffusion and radiative transfer effects. Horizontal eddy diffusivities must be at least ten-fold greater than vertical diffusivities. Anisotropy ratios greater than or approximately equal to 1,000 are sufficient to explain the flattening in cases where the vertical eddy diffusivity is greater than or approximately equal to 100,000 sq cm/s and the effects of radiative transfer are negligible. For vertical diffusivity greater than or approximately equal to 100,000 sq cm/s, radiative transfer contributes to the flattening. Radiative transfer alone can not account for the apparent aspect ratios, as this would require vertical heat diffusivities large enough to give a nonphysically high value of convective heat transport.

Covey, C. C.↗
NASA NTRS1986

A three dimensional model of the Venusian thermosphere with superrotation

An improved three dimensional spectral model of the thermosphere of Venus is described. The model solves the Navier-Stokes equations and includes nonlinear effects for an arbitrary number of atmospheric species. A two dimensional axisymmetric model of the superrotation of the thermosphere is also presented. This model addresses the Pioneer-Venus mission finding, which suggested the thermospheric rotation rate to be much higher than that of the planet as seen from the asymmetric distribution of hydrogen and helium. Both models include the effects of an anisotropic eddy diffusion that is consistent with atmospheric mixing length theory.

Stevens-Rayburn, D. R.↗
NASA NTRS1987

Modeling scalar flux and the energy and dissipation equations

Closure models derived from the Two-Scale Direct-Interaction Approximation were compared with data from direct simulations of turbulence. Attention was restricted to anisotropic scalar diffusion models, models for the energy dissipation equation, and models for energy diffusion.

Yoshizawa, A.↗
NASA NTRS1989

Interpretation and modeling of the averaged equations for a fluid-solid flow

A self-consistent derivation of the conservation laws is given for flows of a fluid-solid mixture. A unified analytical framework for obtaining constitutive relations is provided. This analysis uses a control volume/control surface approach that is widely used in fluid mechanics. All terms in the governing equations and the constitutive relations are written in terms of the mass-weighted averages except solid concentration. It is believed that the mass-weighted average is the natural bridge between micromechanics and constitutive relations. The derived momentum equations contain terms that differ from all existing models except that of Prosperetti and Jones (1984). However, their assumptions are not needed here. Special attention is given to the solid phase pressure. The physical basis of the previously assumed form for this pressure (Givler 1987) becomes clear. A number of related phenomena are also discussed. These include the anti-diffusion and anisotropic normal stresses. The energy equations are also different from existing models.

Shen, Hayley H.↗