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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 OSTI2022

Effects of non-thermal termolecular reactions on detonation development in hydrogen (H 2 )/methane (CH 4 ) - air mixtures

The binary fuel blend of H 2 /CH 4 is one of the most promising hydrogen-enriched hydrocarbon fuels in spark-ignition (SI) engines. Yet, the undesirable phenomenon of super-knock, which can severely and in-stantaneously damage an SI engine, limits its widespread adoption. Moreover, there is still a lack of con-sensus on the precise mechanism by which this phenomenon occurs i.e. via flame acceleration or spon-taneous ignition, despite numerous previous investigations. At the same time, recent studies [M. P. Burke, S. J. Klippenstein, Nat. Chem. 9 (2017) 1078 -1082, Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515-522] have demonstrated a high probability of occurrence of non-thermal reactions in premixed flames of such H 2 /CH 4 fuel blends with air due to the presence of non-trivial amounts of highly reactive radicals including H, O and OH apart from O 2 . The present study focuses on the evolution of an initial deflagration front to a detonation wave in H 2 /CH 4 - air mixtures under SI engine relevant conditions through fully resolved, constant volume 1D simulations with and without non-thermal reactivity. Non-thermal reactions were included in the macroscopic kinetics model as chemically termolecular reactions facilitated by the H + CH 3 and H + OH radical-radical recombination and the H + O 2 radical-molecule association reactions. Further, the nonthermal reactions result in a corresponding decrease in the reaction fluxes of the incipient recombination/association reactions. Therefore, an additional set of simulations were performed by applying corrections to the respective incipient recombination/association rate constants using the methodology demonstrated by Tao et al. [Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515-522]. Compared to the baseline case, the onset of spontaneous ignition in the end-gas region was observed to be delayed in the presence of non-thermal termolecular reactions. Concurrently, the developing detonation was observed to be significantly stronger. In contrast, applying corrections to the recombi-nation/association rate constants resulted in a completely different behavior. Specifically, detonation was observed to occur due to self acceleration of the primary flame in the absence of spontaneous ignition in the end-gas region. Sensitivity analysis was performed to quantify the effects of non-thermal reactions on the duration of heat release rate and thereby the mechanism of detonation formation. In addition, chemical explosive mode analysis (CEMA) was performed to identify the dominant species/reactions re-sponsible for the observed results.

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

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote—and, in some cases, may be necessary for—the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Mechanochemical Synthesis of High-Purity Anhydrous Binary Alkali and Alkaline Earth Chloride Mixtures

A direct synthesis route for high-purity, anhydrous binary salt mixtures has been developed. This atom efficient, solvent-free process is easily scalable, with the potential to produce salt mixtures that meet the purity standards required for industrial heat transfer and nuclear applications. The essence of the methodology lies in mechanochemical synthesis of carnallite precursors that can mitigate the hydrolysis of MgCl 2 ·6H 2 O under direct heating. Each dehydrated salt carnallite was then analyzed for purity and oxide content through subsequent powder X-ray diffraction, and strong acid titration. In conclusion, this process presents a more effective alternative route compared to previous methods for obtaining low-oxide, high-purity chloride salt mixtures.

Alkali↗
DOE OSTI2021

Comprehensive Assessment of the Accuracy of the Ideal Adsorbed Solution Theory for Predicting Binary Adsorption of Gas Mixtures in Porous Materials

Quantifying the adsorption of chemical mixtures in porous adsorbents is critical to developing these materials for useful separation applications. The ideal adsorbed solution theory (IAST) is the most widely applied mixing theory for predicting mixture adsorption using single-component adsorption data, but a perceived lack of experimental data has limited previous efforts to explore the accuracy of IAST in a systematic way. In this paper, we take advantage of a large collection of binary experimental data for gas adsorption that became available recently to tackle this issue. Specifically, we identify more than 400 examples in which binary adsorption data and single-component data are available in the same publication and apply IAST to all these examples. This analysis includes experimental data from 63 gas mixtures of 37 different molecular species and 174 different adsorbents. In addition to being the most systematic evaluation to date of the accuracy of IAST for gas adsorption, these data will be valuable for future efforts to test or develop mixing theories that improve upon IAST.

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

Thermodynamic modeling of adsorption at the liquid-solid interface

Adsorptive separation techniques are significantly energy efficient in comparison to conventional thermal separation techniques such as distillation. Despite extensive research and development activities undertaken for mixed-gas adsorption, the use of adsorption techniques for the separation of multicomponent liquid mixtures is still limited. A major barrier is the lack of accurate adsorption thermodynamic models, which form the scientific foundation of process simulation of such systems, making the translation to industrial scale challenging. In this work, we have rigorously computed the surface excess of adsorption for six binary liquid mixtures on silica gel at 303 K using the frameworks of the generalized Langmuir isotherm (gL) and the adsorbed solution theory (AST). The six binary liquid mixtures were formed by the pair-wise combinations of four components: benzene, 1,2-dichloroethane, cyclohexane, and n-heptane. We have based our calculations by considering simultaneous equilibria of three phases: saturated vapor phase, bulk liquid phase, and adsorbed phase. Further, the composition of the corresponding saturated vapor phase was estimated by the Nonrandom Two-Liquid activity coefficient model and experimental vapor-liquid equilibria data. The activity coefficients of the adsorbed phase, the central issue of multicomponent adsorption thermodynamics, were calculated using the adsorption Nonrandom Two-Liquid activity coefficient model. Devoid of simplifying assumptions, gL and AST provide rigorous thermodynamic frameworks for adsorption equilibria of multicomponent liquid mixtures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Solvent Processing and Ionic Liquid-Enabled Long-Range Vertical Ordering in Block Copolymer Films with Enhanced Film Stability

Rapid and reliable processing methods for forming ordered block copolymer (BCP) materials with low defect density in a thin film geometry are required for many nanotechnology applications. Vertically aligned BCP structures, in particular, have applications ranging from nanolithography for electronics and photonics to nanoporous membranes for water remediation and novel batteries for flexible electronics. However, the attainment of nearly complete vertical orientational order of the BCP ordered phase remains challenging. Solvent-based techniques, such as direct immersion annealing (DIA) and solvent vapor annealing (SVA), have immense potential for these applications of BCP films, as it allows for tuning of their thermodynamic, structural, and chain mobility driven kinetic properties. We first demonstrate that DIA, using a judicious choice of binary solvent mixtures along with a relatively hydrophobic ionic liquid (IL), induces the rapid vertical ordering in polystyrene-b-polymethylmethacrylate (PS-PMMA) block copolymer in lamellar films. The IL establishes synergy to the binary solvent mixture of toluene and heptane to 1 create a near-neutral solvent environment for attaining the vertical microstructure of the BCP. Next, we show that IL can suppress the de-wetting of the PS-PMMA films to achieve long-range order using SVA in cylindrical films for long annealing times. Both vertical and horizontal morphology is attained in these films by selecting different solvent environments. Furthermore, attaining enhanced vertical and horizontal BCP structure with long-range defect-free order by tuning solvent quality and using additives like IL can render them useful for many nanotech applications.

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

Performance enhancement of aqueous ionic liquids with lower critical solution temperature (LCST) behavior through ternary mixtures

Thermally responsive ionic liquids (ILs) exhibit liquid–liquid phase separation when mixed with water and heated above a lower critical solution temperature (LCST), resulting in a water-rich (WR) and an IL-rich (ILR) phase. These binary IL–water mixtures can be employed in a variety of thermodynamic processes such as forward osmosis (FO) desalination, for which two solution properties are desirable: low phase separation temperature and high osmotic strength (osmolality). However, these two properties are interlinked, with ILs that exhibit higher osmotic strengths typically requiring higher phase separation temperatures. This behavior tends to arise from the hydrophilicity of the IL cations, which enhances osmotic strength while also elevating the phase separation temperature. In this work, we highlight a pathway to overcome this tradeoff by developing ternary IL mixtures (two ILs with varying cation hydrophilicity mixed with water), which lowers the phase separation temperature while maintaining and even enhancing the osmotic strength of the solution. We characterize the mixing behavior (osmolality, phase separation temperature, WR phase purity, and WR to ILR phase mass ratio) of four ILs as a function of their concentration in solution. We find that an enhancement of up to 81.6% in the osmolality with a concomitant reduction of up to 15.4% in the phase separation temperature can be achieved using this approach. The ternary mixture is also shown to improve the phase separation kinetics by nearly 95% compared to the binary mixture. Overall, this work highlights a new pathway to improve the performance of LCST ILs for water and energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Benchmark Solutions for Radiation Transport in Stochastic Media with Inhomogeneous Material Statistics

Accurately solving implicit Monte Carlo (IMC) thermal photon transport problems with mixed material cells is important in realistic applications. The production IMC package at LLNL treats mixed material cells arising from ALE remap and hydrodynamics using the same approximate model. The new Imp IMC thermal photon transport package currently under development has both a material interface reconstruction (MIR) algorithm and a Levermore-Pomraning (LP) stochastic medium algorithm for treating mixed material cells. Existing stochastic medium algorithms for treating mixed material cells in IMC lack a complete theoretical basis. The IMC LP algorithm implementation has been demonstrated to reproduce published deterministic LP solutions for the particular case of spatially homogeneous material statistics. Realistic simulations will include spatially inhomogeneous material statistics (material mean chord lengths). In a previous investigation, the LP-model for transport in binary stochastic media in rod geometry was generalized to accommodate spatially varying material chord lengths, i.e., the mixing statistics were allowed to be nonhomogeneous. Analytical solutions were obtained and used to produce a verifi cation suite for the Imp IMC Levermore-Pomraning implementation for different spatial variations of the chord lengths. However, the accuracy of the LP model when the mixing statistics are nonhomogeneous has not been assessed and leaves open the question of whether local accuracy is improved or further degraded when chord lengths are not uniform. This shortcoming is rectifi ed here by developing benchmark analytic solutions for transport in binary Markovian stochastic mixtures in rod geometry with nonhomogeneous mixing statistics, using spatially varying chord lengths considered in the previous investigation based on the LP model. Methods for sampling a nonhomogeneous Poisson process (NHPP) are first described and used to construct individual realizations of the binary mixtures in rod geometry. Analytic solutions are then obtained for the forward and backward directed fluxes on a given realization, now viewed as a deterministic medium with alternating layers of the two materials with known interface locations. Finally, material averaged scalar fluxes are obtained using these sampling schemes with spatially linear and quadratic chord lengths and used to assess the accuracy of the previously obtained LP-model results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Machine Learning-Based Upscaling of Finite-Size Molecular Dynamics Diffusion Simulations for Binary Fluids

Molecular diffusion coefficients calculated using molecular dynamics (MD) simulations suffer from finite-size (i.e., finite box size and finite particle number) effects. Results from finite-sized MD simulations can be upscaled to infinite simulation size by applying a correction factor. For self-diffusion of single-component fluids, this correction has been well-studied by many researchers including Yeh and Hummer (YH); for binary fluid mixtures, a modified YH correction was recently proposed for correcting MD-predicted Maxwell–Stephan (MS) diffusion rates. In this study we use both empirical and machine learning methods to identify improvements to the finite-size correction factors for both self-diffusion and MS diffusion of binary Lennard-Jones (LJ) fluid mixtures. Using artificial neural networks (ANNs), the error in the corrected LJ fluid diffusion is reduced by an order of magnitude versus existing YH corrections, and the ANN models perform well for mixtures with large dissimilarities in size and interaction energies where the YH correction proves insufficient.

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

Adsorption Equilibrium, Kinetics, and Column Breakthrough Data for Aqueous Solutions of Binary-Acid and Ternary-Acid Mixtures of Acetic Acid, Butyric Acid, and Lactic Acid on IRN-78 Ion-Exchange Resin at Initial pH Levels of ∼3–7 and at 25–55 °C

This work is part of an effort to develop thermophysical property data and models supporting adsorptive process development for organic acid separation from a dilute aqueous solution of fermentation broth. It presents systematic experimental measurements for aqueous-phase adsorption equilibrium, kinetics, and column breakthrough for three binary-acid aqueous mixtures (acetic acid + lactic acid, butyric acid + lactic acid, and acetic acid + butyric acid) and one ternary-acid aqueous mixture (acetic acid + butyric acid + lactic acid) on Amberlite IRN-78 ion-exchange resin. The equilibrium measurements covered broad ranges of the initial acid concentration (100–400 mmol/L), initial pH (∼3–7), and temperature (25–55 °C). The equilibrium data for the binary-acid and ternary-acid aqueous mixtures indicate selective adsorption of lactic acid at initial pH levels of ∼3 and 4, while acetic acid and butyric acid are selectively adsorbed at initial pH levels of 5, 6, and 7. The subsequent kinetics and column breakthrough experiments were performed at 200 mmol/L with equimolar ratios, an initial pH of 6, and 25 °C. In conclusion, the measurements provide essential data sets for rigorous thermodynamic modeling and process simulation of adsorptive separation processes for organic acid separation from fermentation broth.

Adsorption↗
DOE OSTI2022

Error quantification of the Arrhenius blending rule for viscosity of hydrocarbon mixtures

Six hundred and seventy-five measurements of dynamic viscosity and density have been used to assess the prediction error of the Arrhenius blending rule for kinematic viscosity of hydrocarbon mixtures. Major trends within the data show that mixture complexity–binary to hundreds of components—and temperature are more important determinants of prediction error than differences in molecular size or hydrogen saturation between the components of the mixtures. Over the range evaluated, no correlation between prediction error and mole fractions was observed, suggesting the log of viscosity truly is linear in mole fraction, as indicated by the Arrhenius blending rule. Mixture complexity and temperature also impact molar volume and its prediction. However, a linear regression between the two model errors explains less than 20% of the observed variation, indicating that mixture viscosity and/or molar volume are not linear with respect to temperature and/or mixture complexity. Extensive discussion of the intermolecular forces and the geometric arrangement of molecules and vacancies in liquids, which ultimately determines its viscosity, is brought into context with the implicit approximations behind the Arrhenius blending rule. The complexity of this physics is not compatible with a simple algebraic correction to the model. However, sufficient data is now available to determine confidence intervals around the prediction of fuel viscosity based on its component mole fractions and viscosities. At -40°C, when all identified components are pure molecules the modeling error is 13.2% of the predicted (nominal) viscosity times the root mean square of the component mole fractions.

10 SYNTHETIC FUELS↗
DOE OSTI2026

Scalable slot-die coating of phyllosilicate membranes for selective ion separations

Abstract Two-dimensional (2D) materials have recently drawn attention as candidate materials for molecular-scale membrane separations due to their tunable nanoscale interlayer properties. Phyllosilicates, a broad class of naturally abundant 2D clay minerals, offer significant advantages over synthetic 2D materials, including low cost, stability, and environmental compatibility. While these properties make phyllosilicates attractive for industrial-scale nanofiltration applications, phyllosilicate-based membranes have, to date, only been fabricated at the lab scale via vacuum filtration. Scalable fabrication methods are essential to advance the technical maturity of phyllosilicate membranes and bring these promising materials closer to large-scale adoption. Herein, we have successfully scaled up phyllosilicate (vermiculite) membrane fabrication via slot-die coating and roll-to-roll coating of an ethylenediamine–vermiculite (EDAVM) mixture onto nylon. The coated membranes are 1–2 μm $ \unicode{x03BC} \mathrm{m} $ mu m in thickness and exhibit similar structure and performance to vacuum-filtered EDAVM membranes. The membranes also show selectivity for monovalent ions over multivalent ions in binary salt mixtures. This work represents a major step toward scaling up phyllosilicate membranes for industrial ion separation applications such as resource recovery from water.

Booth, Austin [Princeton University]↗
DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗
DOE OSTI2023

Vapor and Liquid ( p –ρ– T–x ) Measurements of Binary Refrigerant Blends Containing R-32, R-152a, R-227ea, R-1234yf, and R-1234ze(E)

In this article, The pressure–density–temperature–composition (p–ρ–T–x) data of binary refrigerant mixtures containing R-32 (difluoromethane), R-152a (1,1,-difluoroethane), R-227ea (1,1,1,2,3,3,3-heptafluoropropane), R-1234yf (2,3,3,3-tetrafluoropropene), and R-1234ze(E) (trans-1,3,3,3-tetrafluoropropene) were measured in both the vapor and liquid phases using a two-sinker, magnetic suspension densimeter. The specific samples in this study comprised two compositions of approximately (0.3/0.7) and (0.7/0.3) mole fraction for each of the following four binary refrigerant blends: R-32 + R-1234yf, R-32 + R-1234ze(E), R-1234yf + R-152a, and R-1234ze(E) + R-227ea. Single-phase vapor densities were measured over a temperature range of approximately 253 to 293 K and pressures from 0.05 to 0.98 MPa. Single-phase liquid and supercritical densities were measured over a temperature range of approximately 230 to 400 K and pressures up to 22 MPa; for refrigerant blends containing R-1234yf, the maximum pressure was limited to 14 MPa. Overall relative combined, expanded (k = 2) uncertainties in density ranged from 0.025 to 0.191%, with an average uncertainty of approximately 0.05%. Here, we present measurement results, along with comparisons to available literature data and to default equations of state and mixture models included in REFPROP.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

High-Pressure Apparatus for Monitoring Solid–Liquid Phase Transitions

This work presents a new technique for observing the solid–liquid phase transformations in complex diesel fuel blends and diesel surrogates under high-pressure conditions intended to simulate those occurring in vehicle fuel injectors. A high-pressure apparatus based on a visual identification of freezing and thawing has been designed and built to monitor phase behavior and determine the crystallization temperature of complex fuels to predict wax precipitation. The proposed methodology was validated using pure substances—n-hexadecane (C16H34), cyclohexane (C6H12), and a binary cyclohexane/n-hexadecane mixture—all of which have been well-characterized previously. The crystallization temperatures of these compounds were measured from atmospheric pressure to 400 MPa for temperatures varying from 290 to 363 K and compared to those reported in the literature. The standard error of the estimated temperatures, based on a given pressure, between the experimental data obtained in this work was compared to data in the literature from Domanska et al. This methodology is being extended to investigate the properties of more complex fuel mixtures.

High-Pressure, phase change, diesel, solidificatio↗
DOE OSTI2024

Insights into water extraction and aggregation mechanisms of malonamide-alkane mixtures

Structure at the nanoscale in the organic phase of liquid–liquid extraction systems is often tied to separation performance. However, the weak interactions that drive extractant assembly lead to poorly defined structures that are challenging to identify. Here, in this work, we investigate the mechanism of water extraction for a malonamide extractant commonly applied to f-element separations. We measure extractant concentration fluctuations in the organic phase with small angle X-ray scattering (SAXS) before and after contact with water at fine increments of extractant concentration, finding no qualitative changes upon water uptake that might suggest significant nanoscopic reorganization of the solution. The critical composition for maximum fluctuation intensity is consistent with small water–extractant adducts. The extractant concentration dependence of water extraction is consistent with a power law close to unity in the low concentration regime, suggesting the formation of 1 : 1 water–extractant adducts as the primary extraction mechanism at low concentration. At higher extractant concentrations, the power law slope increases slightly, which we find is consistent with activity effects modeled using Flory–Huggins theory without introduction of additional extractant–water species. Molecular dynamics simulations are consistent with these findings. The decrease in interfacial tension with increasing extractant concentration shows a narrow plateau region, but it is not correlated with any change in fluctuation or water extraction trends, further suggesting no supramolecular organization such as reverse micellization. This study suggests that water extraction in this system is particularly simple: it relies on a single mechanism at all extractant concentrations, and only slightly enhances the concentration fluctuations characteristic of the dry binary extractant/diluent mixture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Pore size effect on selective gas transport in shale nanopores

In shale gas production, gas composition may vary over time. To understand this phenomenon, we use molecular dynamics simulations to study the permeation of CH 4 , C 2 H 6 and their mixture from a source container through a pyrophyllite nanopore driven by a pressure gradient. For a pure gas, the flow rate of CH 4 is always higher than that of C 2 H 6 , regardless of pore size. For a 1:1 C 2 H 6 : CH 4 mixture, however, C 2 H 6 :CH 4 flow rate ratio is higher than the compositional ratio in the container (i.e., 1:1) when the pore size is smaller than ~1.8 nm. The selective transport is caused by the competitive adsorption of C 2 H 6 over CH 4 in the nanopore. The selectivity is also determined by the interplay between the surface diffusion of the adsorbed molecules and the viscous flow in the center of the pore, and it diminishes as the viscous flow becomes to dominate the surface diffusion when the pore size becomes larger than 1.8 nm. Our work shows that compositional differentiation of shale gas in production is a consequence of nanopore confinement and therefore a key characteristic of an unconventional reservoir. Finally, the related compositional information can potentially be used for monitoring the status of a production well such as its recovery rate.

03 NATURAL GAS↗
DOE OSTI2021

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗