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At least 1,279 records · Page 71
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. We focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Electron transfer in a crystalline cytochrome with four hemes

Diffusion of electrons over distances on the order of 100 μm has been observed in crystals of a small tetraheme cytochrome (STC) from Shewanella oneidensis [J. Huang et al . J. Am. Chem. Soc. 142, 10459–10467 (2020)]. Electron transfer between hemes in adjacent subunits of the crystal is slower and more strongly dependent on temperature than had been expected based on semiclassical electron-transfer theory. Here, in this work, we explore explanations for these findings by molecular-dynamics simulations of crystalline and monomeric STC. New procedures are developed for including time-dependent quantum mechanical energy differences in the gap between the energies of the reactant and product states and for evaluating fluctuations of the electronic-interaction matrix element that couples the two hemes. Rate constants for electron transfer are calculated from the time- and temperature-dependent energy gaps, coupling factors, and Franck–Condon-weighted densities of states using an expression with no freely adjustable parameters. Back reactions are considered, as are the effects of various protonation states of the carboxyl groups on the heme side chains. Interactions with water are found to dominate the fluctuations of the energy gap between the reactant and product states. The calculated rate constant for electron transfer from heme IV to heme Ib in a neighboring subunit at 300 K agrees well with the measured value. However, the calculated activation energy of the reaction in the crystal is considerably smaller than observed. We suggest two possible explanations for this discrepancy. The calculated rate constant for transfer from heme I to II within the same subunit of the crystal is about one-third that for monomeric STC in solution.

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

Two-body weak currents in heavy nuclei

In light and medium-mass nuclei, two-body weak currents from chiral effective field theory account for a significant portion of the phenomenological quenching of Gamow-Teller transition matrix elements. Here we examine the systematic effects of two-body axial currents on Gamow-Teller strength and β-decay rates in heavy nuclei within energy-density functional theory. Using a Skyrme functional and the charge-changing finite amplitude method, we add the contributions of two-body currents to the usual one-body linear response in the Gamow-Teller channel, both exactly and though a densitymatrix expansion. The two-body currents, as expected, usually quench both summed Gamow-Teller strength and decay rates, but by an amount that decreases as the neutron excess grows. They can enhance individual low-lying transitions, however, leading to decay rates that are quite different from those that an energy-independent quenching would produce, particularly in neutron-rich nuclei. We show that both these effects are related to changes in the total nucleon density as the number of neutrons increases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Polymer-fiber-reinforced polymers with enhanced interfacial bonding between polypropylene fiber and polyethylene matrix

Self-reinforced composites (SRCs) consist of reinforcing fibers and a base matrix made of the same thermoplastic polymer, offering lightweight, recyclability, and sustainability benefits. However, limited research exists on composites where the reinforcing thermoplastic polymer fibers differ from the base thermoplastic matrix. Here, this study focuses on investigating the mechanical behavior of such composites and exploring different surface modification methods to enhance the fiber/matrix interfacial bonding using polypropylene fibers and a polyethylene matrix as an example. It is shown that surface treatment with a commercial adhesion promoter containing n-butyl acetate significantly improves the interfacial shear strength between polypropylene fibers and the polyethylene matrix, increasing it by 145% compared to other methods investigated. Additionally, increasing the length of the embedded polymer fiber in the matrix leads to a notable increase in specific interfacial energy. Consequently, the thermoplastic polymer-fiber-reinforced polymers (PFRPs) using surface-treated woven polypropylene fabrics and a polyethylene matrix exhibit a 20% higher tensile strength and a 65% higher toughness compared to non-treated PFRPs. This study also shows that specific mechanical properties (normalized by the composite density) of the investigated woven PFRPs are similar to those of non-treated SRCs under uni-axial tension. Particularly, their ductility outperforms carbon-/glass-/aramid-fiber-reinforced polymers by at least 6 times at a same fiber volume fraction. The investigation of such composites and the exploration of surface modification methods present important progress in the field of thermoplastic PFRPs, which serve as a solution for addressing concerns related to recyclability and sustainability.

Fiber pull-out↗
DOE OSTI2025

Computational Design of Cost-Effective High-Entropy Thermal/Environmental Barrier Coatings

Developing cost-effective thermal/environmental barrier coatings (TEBC) requires balance among various properties including low thermal conductivity, matching coefficient of thermal expansion (CTE), high thermal stability, high fracture toughness, and high recession resistance while being affordable. Low oxygen diffusivity is desirable as it can slow down oxygen transport to reach the underlying bond coating and hence delay oxidation of the bond coating. This project aims to design low-cost high-performance TEBC based on high entropy rare earth disilicates to protect SiC-based ceramic matrix composites from chemical and thermal attack for better performance of components in the hot section of gas turbine engines. To accelerate the TEBC design, we utilize first-principles density functional theory to predict key properties including phase stability, CTE, lattice thermal conductivity, temperature-dependent elastic constants, and oxygen diffusivity. Alloying elements including Yb, Y, Er, Eu, Gd, Lu, La, and Ce are considered, and modeling prediction are compared with available experimental results.

coefficient of thermal expansion↗
DOE OSTI2024

Accelerated Design of Cost-Effective Thermal/Environmental Barrier Coatings based on High-Entropy Rare Earth Disilicates: A First-Principles Study

This project aims to design cost-effective thermal/environmental barrier coatings (TEBC) based on high entropy rare earth disilicates to protect SiC-based ceramic matrix composites from chemical and thermal attack for better performance of components in the hot section of gas turbine engines. To accelerate the alloy design, we utilize first-principles density functional theory (DFT) together with combinatorial chemistry methodology to predict key properties including phase stability, apparent bulk coefficient of thermal expansion (ABCTE), intrinsic lattice thermal conductivity, and temperature-dependent elastic constants. Specifically, this project focuses on β-RE2Si2O7 (RE=Yb, Y, Er, Lu, La, Ce,) with β-Yb2Si2O7 and β-Y2Si2O7 as the benchmark. Our DFT calculations predict that Er1/4Lu1/4Y3/4Yb3/4Si2O7 and Er1/2Lu1/2Y1/2Yb1/2Si2O7 have ultralow lattice thermal conductivity < 0.23 W/m/K at 1500 K and a good match of average ABCTE (5.1 - 5.2×10-6 K-1) with SiC. Owing to the low cost and abundant supply of Ce and La, the A- and G-La2Si2O7/Ce2Si2O7 disilicates are also studied. Our study shows that G-phase Ce2Si2O7 has an ultralow thermal conductivity (0.26 W/m/K at 1500 K) and the apparent bulk ABCTE (≈6.9×10-6 K-1) slightly higher than SiC, demonstrating great potential as low-cost high-performance T/EBC. However, La2Si2O7 and Ce2Si2O7 undergo an A-phase to G-phase polymorphic transition at around 1470 K.

environmental barrier coatings↗
NASA NTRS2010

Silica/Polymer and Silica/Polymer/Fiber Composite Aerogels

Aerogels that consist, variously, of neat silica/polymer alloys and silica/polymer alloy matrices reinforced with fibers have been developed as materials for flexible thermal-insulation blankets. In comparison with prior aerogel blankets, these aerogel blankets are more durable and less dusty. These blankets are also better able to resist and recover from compression . an important advantage in that maintenance of thickness is essential to maintenance of high thermal-insulation performance. These blankets are especially suitable as core materials for vacuum- insulated panels and vacuum-insulated boxes of advanced, nearly seamless design. (Inasmuch as heat leakage at seams is much greater than heat leakage elsewhere through such structures, advanced designs for high insulation performance should provide for minimization of the sizes and numbers of seams.) A silica/polymer aerogel of the present type could be characterized, somewhat more precisely, as consisting of multiply bonded, linear polymer reinforcements within a silica aerogel matrix. Thus far, several different polymethacrylates (PMAs) have been incorporated into aerogel networks to increase resistance to crushing and to improve other mechanical properties while minimally affecting thermal conductivity and density. The polymethacrylate phases are strongly linked into the silica aerogel networks in these materials. Unlike in other organic/inorganic blended aerogels, the inorganic and organic phases are chemically bonded to each other, by both covalent and hydrogen bonds. In the process for making a silica/polymer alloy aerogel, the covalent bonds are introduced by prepolymerization of the methacrylate monomer with trimethoxysilylpropylmethacrylate, which serves as a phase cross-linker in that it contains both organic and inorganic monomer functional groups and hence acts as a connector between the organic and inorganic phases. Hydrogen bonds are formed between the silanol groups of the inorganic phase and the carboxyl groups of the organic phase. The polymerization process has been adapted to create interpenetrating PMA and silica-gel networks from monomers and prevent any phase separations that could otherwise be caused by an overgrowth of either phase. Typically, the resulting PMA/silica aerogel, without or with fiber reinforcement, has a density and a thermal conductivity similar to those of pure silica aerogels. However, the PMA enhances mechanical properties. Specifically, flexural strength at rupture is increased to 102 psi (=0.7 MPa), about 50 times the flexural strength of typical pure silica aerogels. Resistance to compression is also increased: Applied pressure of 17.5 psi (=0.12 MPa) was found to reduce the thicknesses of several composite PMA/silica aerogels by only about 10 percent.

Ou, Danny↗
DOE OSTI2024

Interfacial Engineering Using Covalent Organic Frameworks in Polymer Composites for High‐Temperature Electrostatic Energy Storage

Abstract The use of inorganic nanofillers has been an effective method to improve high‐temperature capacitive performance of dielectric polymers, though there are unmet challenges such as undesirable organic–inorganic compatibility, and low efficiencies and energy densities. Herein, a surface functionalization strategy using covalent organic frameworks (COFs) is employed to address such challenges in realizing high‐performing polymer composites. Specifically, core–shell structured nanoparticles, where ZrO 2 nanoparticles act as the core and a COF material forms the shell, are constructed and composited with the polyetherimide (PEI) matrix. The design leverages the high electron affinity ( E A ) of the outer COF shell to create energy traps, thereby capturing free charges and limiting electrical conduction. Concurrently, the low E A and wide bandgap of the ZrO 2 core introduce energy barriers to impede charge injection and migration. This orchestrated “energy level cascade” results in a marked reduction of leakage current and energy loss. The resulting polymer composite showcases an impressive discharged energy density of 6.21 J cm −3 at an efficiency above 90%, with a maximum discharged energy density reaching 7.43 J cm −3 at 150 °C. These performance metrics position the PEI/ZrO 2 @COF polymer composite to surpass or be on par with state‐of‐the‐art high‐temperature PEI composites and other advanced polymer dielectrics.

Xie, Zongliang↗
NASA NTRS1981

Abradable dual-density ceramic turbine seal system

A plasma sprayed dual density ceramic abradable seal system for direct application to the HPT seal shroud of small gas turbine engines. The system concept is based on the thermal barrier coating and depends upon an additional layer of modified density ceramic material adjacent to the gas flow path to provide the desired abradability. This is achieved by codeposition of inert fillers with yttria stabilized zirconia (YSZ) to interrupt the continuity of the zirconia struture. The investigation of a variety of candidate fillers, with hardness values as low as 2 on Moh's scale, led to the conclusion that solid filler materials in combination with a YSZ matrix, regardless of their hardness values, have a propensity for compacting rather than shearing as originally expected. The observed compaction is accompanied by high energy dissipation in the rub interaction, usually resulting in the adhesive transfer of blade material to the stationary seal member. Two YSZ based coating systems which incorported hollow alumino silicate spheres as density reducing agents were surveyed over the entire range of compositions from 100 percent filler to 100 percent YSZ. Abradability and erosion characteristics were determined, hardness and permeability characterized, and engine experience acquired with several system configurations.

Clingman, D. L.↗
DOE OSTI2026

Effect of 316 stainless steel powder processing conditions on microstructure

One parameter that has both economic and performance effects in the manufacturing of steel parts is the powder feedstock used. 316 L steel powder can be produced through water atomization or gas atomization, where both the powder size and the atomization process determine the cost of powder feedstock. Gas atomized powder is spherical and has a lower oxygen content than water atomized powder, making it the preferred choice for performance, but comes at a higher financial cost. Here, in this study, various 316 L powder batches are characterized to understand physical properties and microstructural variations. Density and flowability were determined using gas pycnometry and Hall flow tests. Powder morphology and porosity were qualitatively analyzed via optical microscopy and scanning electron microscopy, Finally, transmission electron microscopy was used to determine changes in phases present. Spherical gas atomized powder of 30–100 μm contained Mn$-$Si rich oxides both on the surface and within the matrix. Meanwhile, irregular water atomized powder 30 μm in diameter contained silicon oxides without manganese. All powder particles contained a nickel rich cellular structure which was shown to support the formation of additional phases. While literature has observed general microstructural features across 316 L powder particles, transmission electron microscopy (TEM) in this study has identified variations in precipitation and cell structures. Information regarding morphology, flowability, density, and phase distributions can be applied to understand variations in part consolidation, which will in turn show which powder aspects are significant for production.

Chemical segregation↗
DOE OSTI2021

(U) A Linear Response Model Predicts Reactivity From a Density Profile

We tested the ability to predict the system reactivity, described by alpha, given a density profile using a simple linear system response. We generated a suite of 1-dimensional density profiles that consisted of nominal density, a discontinuity, and a decay. These profiles were prescribed a functional form and the mass was conserved in all cases. From these density profiles, we calculated the alpha value of the 3-dimensional system.We calculated a linear response function given a training set of the 1-dimensional density profiles, and the system reactivity described by alpha. We tested the robustness of the response function using the remaining test data. Our results showed very good agreement between the predicted and calculated test values, where the distribution of alpha differences was centered about zero and had a standard deviation of 0.005 gens/shake. The predicted and calculated alpha values did not significantly differ (t=-0.0009 p<0.99). We used Singular Value Decomposition (SVD) to reduce the matrix rank by retaining95% of the cumulative singular value contributions. This reduced the matrix rank by 91.7%. We generated the linear response matrix and calculated the difference between the predicted and calculated alpha values. Using the reduced order matrix, we showed good agreement between the predicted and calculated alpha values where the distribution of differences was centered near zero, the standard deviation was 0.006 gens/shake, and the statistical t-test showed good agreement (t=0.02, p<0.98). These results show a linear relationship between a series of 1-dimensional density profiles,where the mass was conserved, and the system reactivity. The next steps of this work will be to investigate the linear response using 2-dimensional density profiles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Molecular-Dynamics Analysis of the Mechanical Behavior of Plasma-Facing Tungsten

We report a systematic computational analysis of the mechanical behavior of plasma-facing component (PFC) tungsten focusing on the impact of void and helium (He) bubble defects on the mechanical response beyond the elastic regime. Specifically, we explore the effects of porosity and He atomic fraction on the mechanical properties and structural response of PFC tungsten, at varying temperature and bubble size. We find that the Young modulus of defective tungsten undergoes substantial softening that follows an exponential scaling relation as a function of matrix porosity and He atomic content. Beyond the elastic regime, our high strain rate simulations reveal that the presence of nanoscale spherical defects (empty voids and He bubbles) reduces the yield strength of tungsten in a monotonically decreasing fashion, obeying an exponential scaling relation as a function of tungsten matrix porosity and He concentration. Our detailed analysis of the structural response of PFC tungsten near the yield point reveals that yielding is initiated by emission of dislocation loops from bubble/matrix interfaces, mainly 1/2<111> shear loops, followed by gliding and growth of these loops and reactions to form <100> dislocations. Furthermore, dislocation gliding on the <111>{211} twin systems nucleates 1/6<111> twin regions in the tungsten matrix. These dynamical processes reduce the stress in the matrix substantially. Subsequent dislocation interactions and depletion of the twin phases via nucleation and propagation of detwinning partials lead the tungsten matrix to a next deformation stage characterized by stress increase during applied straining. Furthermore, our structural analysis reveals that the depletion of twin boundaries (areal defects) is strongly impacted by the density of He bubbles at higher porosities. After the initial stress relief upon yielding, increase in the dislocation density in conjunction with decrease in the areal defect density facilitates the initiation of dislocation-driven deformation mechanisms in the PFC crystal.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Structural Changes during the Conversion Reaction of Tungsten Oxide Electrodes with Tailored, Mesoscale Porosity

In-plane tungsten oxide nanostructures, including hexagonally patterned cylinders and holes in a matrix, were fabricated via sequential infiltration synthesis (SIS) on self-assembled block copolymer templates. Using the tailored morphology and porosity of these model electrodes with in situ grazing incidence small angle X-ray scattering, the intrinsic structural change of nanoscale active materials during the conversion reaction of WO 3 + 6Li ↔ W + 3 Li 2 O was investigated at controlled electrochemical conditions. Reversible electrode volume expansion and contraction was observed during lithiation and delithiation cycles, respectively. The potential where electrode’s thickness expansion started was ~1.6 V, which is close to thermodynamically expected one for conversion reaction of WO 3 with lithium (1.65 V). The temporal evolution of the electrode volume at constant electrode potentials revealed high overpotential for bulk lithiation and slow conversion reaction kinetics, despite the tailored porosity of the SIS electrodes. Oxide cylinders showed smaller overall electrode thickness change, likely due to unconstrained lateral volume change, as compared to a matrix with holes. On the other hand, better connectivity and guided volume change of the latter electrode morphology provided improved cycling stability. Additionally, heterogeneity in an electrode, from internal pores and density gradients, was found to aggravate the fragmentation of the electrode during conversion reaction. Insights into oxide conversion reaction kinetics and the relationship between electrode mesostructure and cycling behavior obtained from this study can help guide the more rational design of conversion electrode for high performing batteries.

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

Cyclic olefin copolymer-based reinforced anion exchange membranes for water electrolyzers

Anion exchange membranes (AEMs) have emerged as a promising technology for water electrolysis in hydrogen production since they offer significant cost reduction in choices of electrocatalysts and bipolar plates. However, AEMs satisfying multiple requirements of high ionic conductivity, good chemical stability, robust mechanical properties, scalable synthesis, and low manufacturing costs are rare. Herein, we introduce quaternary ammonium functionalized cyclic olefin copolymers (COCs) as a new class of chemically stable and low-cost AEM materials. To further enhance the mechanical robustness, we prepared reinforced composite AEMs by impregnating the ionically functionalized COC into a mechanically robust matrix. The resulting reinforced composite membrane exhibits a high hydroxide conductivity of 127 mS cm −1 and excellent mechanical strength. In water electrolyzers, the MEA demonstrated outstanding performance, achieving a current density of 2.24 A cm −2 at 1.8 V, attributable to high conductivity, enhanced mechanical properties, and good alkaline stability of the composite membrane. These results indicate that the COC-based AEMs demonstrate good potential for application in AEM electrolyzers.

08 HYDROGEN↗
DOE OSTI2026

Pressure-induced 𝐵⁢1 to 𝐵⁢2 phase transition in CeN studied by 𝑎⁢𝑏 𝑖⁢𝑛⁢𝑖⁢𝑡⁢𝑖⁢𝑜 correlation matrix renormalization theory calculations

We apply correlation matrix renormalization theory (CMRT) to cerium nitride (CeN) under pressure. For 𝐵⁢1 (NaCl-type) phase, CMRT gives an equation of state consistent with ambient pressure experiments. It produces electronic density-of-state (DOS) characterized by a sharp 4⁢𝑓 quasiparticle resonance peak pinned at the Fermi level and two subbands formed by strong hybridization between the localized Ce-4⁢𝑓 electrons and the itinerant Ce-5⁢𝑑 and N-2⁢𝑝 electrons below the Fermi level, consistent with x-ray photoemission spectroscopy experiments. Upon compression, CMRT predicts a first-order 𝐵⁢1 → 𝐵⁢2 (CsCl-type) transition with ∼11% volume collapse in agreement with experiments. Across the transition, the 4⁢𝑓 spectrum broadens, the 4⁢𝑓 orbital occupancy increases, and the hybridization with conduction states enhances, signaling a crossover from partially localized to more itinerant 4⁢𝑓 behavior. Furthermore, these features are in excellent agreement with experimental observations, demonstrating that CMRT provides a parameter-free description and prediction of correlation-driven structural and electronic transitions in rare-earth compounds.

Ab initio calculations↗
DOE OSTI2026

Chiral spin liquid and quantum phase transition in the triangular-lattice Hofstadter-Hubbard model

Recent advances in moiré engineering motivate the study of lattice models of strongly correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular-lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120° antiferromagnetic phases. Here, we use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.

Divic, Stefan [University of Pennsylvania, Philade↗
DOE OSTI2023

Shear Assisted Processing and Extrusion (ShAPE) of Plastics: Recycling and Remolding

Polyethylene (PE) and polypropylene (PP) are often disposed as mixed plastic wastes. The challenges in recycling and upcycling these mixed polyolefin wastes lie in the difficulty in separating individual constituents in a cost-effective and scalable manner. Direct recycling the mixed PE and PP wastes in conventional melt-phase extruders typically result in a product with poor properties and low added value, because of immiscibility, phase separation, and lack of crystallinity. Friction extrusion (FE), a solid phase processing technique that has successfully extruded metal matrix composites with desired end products, has never been utilized to address the issue of recycling mixed plastic wastes. In this study, FE was performed on single-stream low-density polyethylene (LDPE), single-stream PP and mixed-stream LDPE+PP. Consolidated filaments of 2.5 mm diameter were extruded from different precursors. The thermal, infrared, and microscopic properties of extruded filaments were measured to evaluate the effects of FE process on the structure of recycled polymers. Meanwhile, the energy efficiency of FE was estimated based on extrusion rates and compared with conventional melt extrusion processes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1990

Kinetics of gas-to-liquid and liquid-to-solid transfer of particles in metal-matrix composites

Analytical models for transfer of particles from gas to liquid and from liquid to solid are introduced. The model for calculation of the pushing/engulfment transition in directionally solidified particulate metal matrix composites, considers process thermodynamics, process kinetics, thermophysical properties and buoyant forces. Based on processing variables (solidification velocity and direction) and on material variables (interface energies, particle size, particle and liquid density, volume fraction of particles and particle/liquid thermal conductivity ratio) four types of behavior were predicted. Also, two numerical models for liquid-to-solid transfer are discussed, as well as the limitations of presently available models.

Stefanescu, D. M.↗