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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Particle Size and Density Measurement

This project has developed a miniature gravity settling classifier (flow cell) and flow system that separates slurry particles by settling rate into six different Cuts. The settling rates for particles in each Cut were determined from COMSOL computational fluid dynamics (CFD) modeling of the flow in the flow cell together with particle tracking for particles of differing settling rates. For particles collected in each Cut, the particle concentration and size distribution were measured. The effective particle densities from each Cut are calculated from their respective CFD modeled settling rates using a relationship between the unhindered settling rate, particle size distribution (PSD), and effective density. The particle size and density distribution (PSDD) of the slurry sample is then calculated by combining the size and density distributions determined for the particles collected in each of the settling rate Cuts.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Charged particle motion in spherically symmetric distributions of magnetic monopoles

The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single monopole, the solution was given long ago by Poincaré. In the case of a uniform distribution of monopoles, the solution can be expressed in terms of parabolic cylinder functions (essentially the eigenfunctions of an inverted harmonic oscillator). Further, this solution is relevant to recent studies of nonassociative star products, symplectic lifts of twisted Poisson structures, and fluids and plasmas of electric and magnetic charges.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗
DOE OSTI2021

In-medium modification of dijets in PbPb collisions at $ \sqrt{s_{\mathrm{NN}}} $ = 5.02 TeV

Modifications to the distribution of charged particles with respect to high transverse momentum (p$_{T}$) jets passing through a quark-gluon plasma are explored using the CMS detector. Back-to-back dijets are analyzed in lead-lead and proton-proton collisions at $ \sqrt{s_{\mathrm{NN}}} $ = 5.02 TeV via correlations of charged particles in bins of relative pseudorapidity and angular distance from the leading and subleading jet axes. In comparing the lead-lead and proton-proton collision results, modifications to the charged-particle relative distance distribution and to the momentum distributions around the jet axis are found to depend on the dijet momentum balance x$_{j}$ , which is the ratio between the subleading and leading jet p$_{T}$. For events with x$_{j}$ ≈ 1, these modifications are observed for both the leading and subleading jets. However, while subleading jets show significant modifications for events with a larger dijet momentum imbalance, much smaller modifications are found for the leading jets in these events.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Toward the core-edge coupling of delta-f and total-f gyrokinetic models

The coupling of core reduced delta-f and edge total-f gyrokinetic models could enable a significant speed-up of the whole device modeling simulations. It is thus interesting to compare these models in the core where they will be coupled. The main difference between these models is the presence of the zeroth order term on the right-hand side of the total-f gyrokinetic equation. This term is responsible for driving a radial electric field that is also associated with Geodesic acoustic mode-like oscillations. To investigate the coupling between these models, the subsequent large-scale gyrokinetic 3D turbulence simulations have been performed starting from an already saturated gyrokinetic axisymmetric equilibria (collisions are not included). This work has also been extended to couple different axisymmetric and turbulent models available in XGC. It is shown that the radial electric field and its drive have to be taken care of consistently while coupling different models together.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Multimodal Atomic Force Microscopy for the Characterization of Metallic Particulates

This study investigates the utility of multimodal, or functional, atomic force microscopy (AFM) for the characterization of individual particles and particle ensembles. In single-particle analyses, AFM imaging modes provided orthogonal insights into mechanical and magnetic properties that are not accessible through conventional electron microscopy. Although the experiments were inherently delicate and time-intensive, with an observed sample loss rate of approximately 30%, these techniques enabled the qualitative differentiation of grain structures and magnetic domains, underscoring the challenges of experimental robustness. For particle ensembles, AFM enabled the extraction of reliable 2D and 3D particle size distributions. However, efforts to chemically differentiate particles based on mechanical property contrasts were limited by scaling effects and the qualitative nature of the data. Overall, multimodal AFM offers valuable complementary information, but its application requires careful consideration of methodological limitations, particularly for sample integrity, calibration, and scalability of mechanical and magnetic measurements. This report is organized to first address the application of AFM to single-particle analysis using various imaging modalities, followed by its potential role in ensemble-level particle screening and differentiation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Characterization of Virgin, Re-used, and Oxygen-reduced Copper Powders processed by the Plasma Spheroidization Process

We report that fabrication of parts with high mechanical properties heavily depend on the quality of powder deployed in the fabrication process. Copper powder in three different powder types were spheroidized using radio-frequency inductively coupled plasma (ICP) spheroidization process (TekSphero-15 system). The characterized powders include virgin powder as purchased from the powder manufacturer, powder used in electron beam powder bed fusion (EB-PBF) process, and reconditioned powder, which was used powder that underwent an oxygen-reduction treatment. The goal of spheroidizing these powder types was to evaluate the change in powder morphology, the possibility of enhancing the powder properties back to their as-received conditions, and assess oxygen reduction of the powder lots given their initial oxygen contents. Also, to investigate the impact of re-spheroidization on powder properties, the second round of spheroidization was performed on the already used-spheroidized powder. The impact of powder type on powder sphericity and particle size distribution was evaluated using the image analysis of scanning electron microscope (SEM) micrographs and laser diffraction, respectively. The spheroidized powder showed higher sphericity and more uniform particle size distribution overall. Depending on the powder collection bin, second round of spheroidization affected the powder sphericity differently. The possibility of deploying the plasma spheroidization process as an alternative oxygen-reduction technique was also investigated through tracking the powders’ oxygen content using inert gas fusion method before and after the spheroidization. The plasma spheroidized powder showed less oxygen content than the hydrogen-treated powder. The second round of spheroidization caused no change in oxygen content. The correlation between oxygen-reduction and created cracks was discussed and compared between plasma spheroidization and hydrogen-treatment. The plasma spheroidization process created a powder with higher sphericity, uniform particle size, and less oxygen content.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Understanding Biases in Sample Preparation Techniques for Coupled Scanning Electron Microscopy and MAMA PuO 2 Morphological Analysis

In this project, the scanning electron microscopy (SEM) sampling method used during the statistical design study (SDS) was investigated to determine if any sampling biases were present in the analyzed data. Using standard particle size distribution powders from the National Institute of Standards and Technology (NIST 1984 standard reference material) with the origin wet dispersion method, it was determined that a bias to smaller particles was present. This was supported by theoretical calculations using Stokes’ law to determine the settling rate of spherical particles of roughly the same size and mass as those found in the SDS. Based on the theoretical calculations, it was determined that the settling rate for each of the 76 powder sets in the SDS could be unique based on specific particle shape and mass distributions, making a universal correction factor/formula not applicable. Therefore, priority shifted to developing an improved wet dispersion method that significantly reduced the particle settling rate for all particle size and shapes. This was achieved by replacing the original solvent (isopropyl alcohol) with a heavy liquid (lithium heteropolytungstates), which dramatically slowed the settling rate and allowed for the capture of a suitable homogeneous aliquot. SEM imaging and Morphological Analysis for Material Attribution (MAMA) software analysis were conducted on the NIST standard, and the SEM/MAMA data were compared to data captured by a dynamic image analysis particle size analyzer. The resulting data confirmed that the new wet dispersion method does indeed deliver an improved representative aliquot to the SEM stub. For instance, in the NIST certificate, the average particle size is ~17.1 µm ± 2.2 µm with a normal distribution. The initial wet dispersion method resulted in a drastically reduced average particle size of 6.1 µm in addition to a non-representative heavy bi-modal distribution whereas the improved LST wet dispersion method resulting in an average particle size that was much closer to the NIST certificate (12.7 µm) with a similar normal distribution. Although the improved method was still short of the NIST certificate average, atomic force microscopy analysis determined that the resulting ~20-25% reduction in size was due to particles sinking into the carbon sticky tape used for SEM imaging. It is believed that that this bias can be calibrated in a much more predicable manner than the original settling rate bias. In addition, the matching normal distribution curves between the NIST certificate and the heavy liquid method indicate a much-improved representative aliquot has been sampled and imaged. A surrogate CeO 2 powder was used to reflect PuO 2 more accurately and to aid in implementing radiological controls and shielding. The resulting data sets from the SEM/MAMA method and the particle size analyzer give almost identical average particle sizes and particle distribution statistics. Future work will re-analyze several select runs from the SDS to determine if morphological signatures can be found with the improved sampling method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

TGA Study of the Reaction Kinetics of a CuFeMnAlO 4+δ Oxygen Carrier for Methane Chemical Looping Combustion under High Pressure and Atmospheric Pressure Conditions

Reduction and oxidation kinetics of a CuFeMnAlO 4+δ oxygen carrier for methane were studied using an atmospheric thermogravimetric analyzer (TGA) and a pressurized TGA. Important parameters such as temperature (500–900 °C), particle size distribution (150–650 μm), and partial pressures of reactants (methane and oxygen) were evaluated. Results showed that the reduction of the oxygen carrier was not affected by particle size distribution studied in this work, and that above 750 °C, the effect of the temperature on oxygen carrier reduction started to diminish. The reaction time approaches an asymptotic limit as methane partial pressure increases. For oxygen carrier oxidation, it was found that the rate of oxidation increased with increasing oxygen concentration. The effect of the oxygen concentration was more noticeable when the oxygen concentration was below 7.5%. Because of the inherent feature of the oxygen carrier, its chemical looping with oxygen uncoupling property was also assessed. A phase boundary-controlled shrinking sphere model was used to model the test data from the TGAs. Modeling results showed that the oxygen carrier reduction had a reaction order of 1 with an activation energy of ∼46 kJ/mol. Oxygen carrier oxidation demonstrated a reaction order of 1.1 with an activation energy of ∼55 kJ/mol. Additionally, the differences of the experimental results between the atmospheric pressure TGA and the pressurized TGA were discussed in detail and the limitations of the pressurized TGA were highlighted.

Hydrocarbons↗
DOE OSTI2020

Cesium Removal and Hydraulic Performance Comparisons of CST Ion Exchange Media Batches in Support of the Tank Closure Cesium Removal Project - 20522

Three batches of Crystalline Silicotitanate (CST) ion exchange media have been evaluated for cesium removal efficiency from a Savannah River Site (SRS) High Level Waste (HLW) supernate simulant in support of the Tank Closure Cesium Removal (TCCR) Project, which involves at-tank column waste treatment. Results will be utilized to select the CST media batch to be added to the next TCCR unit columns. Two of the CST media samples were recent production batches and the third was an archived batch studied extensively at SRS nearly two decades ago. The archived CST batch had a significantly smaller average particle diameter than more recent batches. Small-scale (∼23 mL), side-by-side column tests were conducted at 35 deg. C with each of the CST batches using the same simulant at flow rates near 1.2 mL/min (3.0-3.4 CST bed volumes/hr). The cesium ion exchange column performance results were lower than expected for all three CST batches, but the data indicated that 30% more simulant volume and 40% more equivalent CST bed volumes of solution can be processed with the older CST batch prior to reaching the 50% cesium breakthrough point than can be processed with the newer CST batches. Hydraulic evaluations of the CST columns were also conducted in simulant at 24 deg. C to determine the impact of the different particle size distributions and associated bed porosities on frictional pressure drop under dynamic flow conditions. Higher differential pressure drops were observed with the archived CST batch relative to recent production batches, due to the smaller particle size distribution and the packing characteristics of the archived batch. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Explosive Soot Challenge (Final Report)

This project assembled a broad ensemble of modeling and experimentation tools to study the morphological and optical properties of detonation soots in explosive fireballs. A gram-scale hemispherical high explosive was studied in a low-pressure controlled environment using in-situ experimentation with diffusely illuminated visible absorption spectroscopy, particle sizing through light scattering techniques, and post-test collections with subsequent morphological analysis. Hydrocode modeling was performed to replicate the detonation flow observations, and subsequent aerosol kinetics models provided particle size distributions and extinction coefficients from the hydrocode results. Experimentally observed soot morphologies agreed with expectation from the literature - a bimodal distribution was found, brought upon by the particles growing to a size where their inertia and fluid wakes are non-negligible. The aerosol kinetics model did not replicate the observed bimodal size distribution for lack of a coagulation kernel to represent the behavior. To recover particulate optical properties, a spectrally resolved absorption spectroscopy method termed Spectral diffuse back-illuminated extinction imaging (SBI-EI) was developed and implemented on two explosive types. Inverting the absorption spectra using a Kramers-Kronig consistent method yielded the complex index of refraction for the soots produced by the explosives. This method resulted in an unrealistic index of refraction for one of the two explosives, and this is suspected to be due to the model neglecting scattering brought upon by the large particle sizes observed. In addition to the core work, three additional studies were performed in parallel. These investigated the impact of scattering on diffuse absorption spectroscopy, studied how soots oxidate and sublimate in a well-controlled shock tube, and laid the theoretical groundwork for a new collision kernel to replicate the bimodal size distribution from the observations. Summaries of these efforts are included at the end of this report.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

U Metal Oxidation with Steam (U)

The Savannah Rive National Laboratory 9SRNL) is evaluating a method to produce uranium oxide (UO 2 ) from uranium metal using steam. The typical methods for making UO 2 yield powders with particle-size ranges of 1 to 50 micron. The goal of the steam oxidation is to produce a depleted uranium (DU) product with a larger particle size that can be used as a surrogate for testing physical and mechanical process techniques to refine uranium and/or plutonium bearing residues. Several studies in the literature indicated that reactions between uranium metal and steam will yield UO 2 as fine powders in the 160 to 500 °C range, but granular materials form above 500°C. Above 880 °C, a hard compact scale forms on the U metal. Furthermore, sintering of UO 2 occurs at about 1300 °C, but it has been stated that the presence of steam enhances the sintering characteristics of UO 2 . Initial studies into the oxidation of DU metal in an atmosphere of argon and steam have been completed. Oxidation of depleted uranium metal in Ar/steam at 600, 710, 700, and 830 °C yielded at UO 2 product with little or no impurity at each temperature. Although not enough sample was available to perform sieve analysis for particle size distribution, SEM images reveal that a significant volume fraction of the products at 710, 770, and 830 °C exceeds 100 microns. The material produced at 600 °C was too fine for programmatic needs. Questions associated with the UO 2 include morphology of product, mechanical strength of the particles, and performance in milling operations. The size of the samples produced in these tests did not allow for quantitative assessment of particle size of mechanical strength. A qualitative assessment of the particles formed at 710, 770, and 830 °C was that the samples produced at 710 and 770 °C were friable, and the sample produced 830 °C had more mechanical strength. Sintering of the samples in Ar/steam at 970 °C appeared to increase the strength of the particles without changing their general particle size characteristics. Due to the small sample sizes, the increase in strength could not be quantified. If the sintering at 970 °C is inadequate, higher sintering temperatures in Ar/steam can be evaluated. Future work will increase scale of the steam oxidation conditions which yield the most-favorable particle-size distributions with sufficient mechanical strength for programming usage. Further consideration will be given to oxidation temperature, steam addition to the reaction vessel, U metal pretreatment, and sintering conditions after oxidation. The UO 2 production could involve a two-step process where particles are formed in steam at lower temperatures (700-850 °C) and then sintered in Ar/steam at elevated temperatures (950-1200 °C). Larger samples (50-100 g each) will provide sufficient UO 2 product for sieve analysis and assessment of mechanical strength relatives to subsequent milling operations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Portable Optical Particle Spectrometer aboard an Airborne Platform (POPS_AIR) Instrument Handbook

The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility portable optical particle spectrometer (POPS) is a lightweight particle spectrometer designed for aerosol particle size distribution measurement. Several POPS of different versions have been procured to serve as routine instruments for the ARM Aerial Facility (AAF) unmanned aerial systems (UAS) and tethered balloon system (TBS) deployment since 2018. POPS measures the aerosol particle size distribution approximately between 0.13 and 3 μm.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The influence of cooling rate on condensation of iron, aluminum, and uranium oxide nanoparticles

Fundamental observations of particle size distributions are needed to develop models that predict the fate and transport of radioactive materials in the atmosphere following a nuclear incident. The extent of material transport is influenced by the time scales of particle formation processes (e.g., condensation, coagulation). In this study, we investigated the influence of cooling time scales on size distributions of uranium, aluminum, and iron oxide particles that are synthesized separately under identical run conditions inside the controlled environment of an argon plasma flow reactor. Two distinct temperature distributions are imposed along the flow reactor by varying the argon flow rate downstream of the plasma torch. The vaporized reactants of uranium, aluminum, and iron are cooled from about 5000K to 1000K before they are collected on silicon wafers for ex situ scanning electron microscope analysis. The microscope images show that the sizes of the largest aluminum and iron oxide particles heavily depend on the cooling time scales, whereas significant size variation with cooling rate is not observed for uranium oxide particles. In addition, the size distribution of aluminum oxide particles exhibits the broadest range among all three metal oxides studied. We performed simulations of particle size distributions using a kinetic model that couples gas phase oxidation chemistry with particle formation processes, including nucleation, condensation, and coagulation. The model results demonstrate the strong sensitivity of particle size distribution to different cooling histories (i.e., temperature vs residence time) along the flow reactor. In conclusion, the kinetic model also helps identify directions for future research to improve the predictions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Jet wake from linearized hydrodynamics

We explore how to improve the hybrid model description of the particles originating from the wake that a jet produced in a heavy ion collision leaves in the droplet of quark-gluon plasma (QGP) through which it propagates, using linearized hydrodynamics on a background Bjorken flow. Jet energy and momentum loss described by the hybrid model become currents sourcing linearized hydrodynamics. By solving the linearized hydrodynamic equations numerically, we investigate the development of the wake in the dynamically evolving droplet of QGP, study the effect of viscosity, scrutinize energy-momentum conservation, and check the validity of the linear approximation. We find that linearized hydrodynamics works better in the viscous case because diffusive modes damp the energy-momentum perturbation produced by the jet. We calculate the distribution of particles produced from the jet wake by using the Cooper-Frye prescription and find that both the transverse momentum spectrum and the distribution of particles in azimuthal angle are similar in shape in linearized hydrodynamics and in the hybrid model. Their normalizations are different because the momentum-rapidity distribution in the linearized hydrodynamics analysis is more spread out, due to sound modes. Since the Bjorken flow has no transverse expansion, we explore the effect of transverse flow by using local boosts to add it into the Cooper-Frye formula. After including the effects of transverse flow in this way, the transverse momentum spectrum becomes harder: more particles with transverse momenta bigger than 2 GeV are produced than in the hybrid model. Although we defer implementing this analysis in a jet Monte Carlo, as would be needed to make quantitative comparisons to data, we gain a qualitative sense of how the jet wake may modify jet observables by computing proxies for two example observables: the lost energy recovered in a cone of varying open angle, and the fragmentation function. We find that linearized hydrodynamics with transverse flow effects added improves the description of the jet wake in the hybrid model in just the way that comparison to data indicates is needed. Our study illuminates a path to improving the description of the wake in the hybrid model, highlighting the need to take into account the effects of both transverse flow and the broadening of the energy-momentum perturbation in spacetime rapidity on particle production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A novel flow cell for optical particle analyzers—application to measurements of Malvern Insitec under high pressure and temperature

A flow cell is a necessary measurement interface for some important optical analyzers. In our application of the flow cell, we utilize a state-of-the-art optical analyzer (Malvern Insitec) to measure particle size distribution and concentration in-situ in a sampled flow from a novel pressurized oxygen-fuel combustion process. However, since this sampling flow is a flow of moist flue gas under high temperature and pressure, and the flow contains particles and corrosive acid gases, it is an extreme challenge to obtain a flow cell with a high optical quality that does not perturb the measurement. To address this challenge, we propose a new design for an optical flow cell. By using a unique flow field in the proposed flow cell, the measurement zone can be well defined by the sampling flow, minimizing the influence of purge flow. To demonstrate this flow cell, we have built a test system, and conduct measurements utilizing polydisperse-particle standards (10-100 µm and 1-10 µm). The results reveal that the optical windows are well protected by the purge flow field, without risk of deposition from the sampling flow, and the Malvern Insitec can measure the particle size distribution by using this flow cell, without generating sample bias.

Cheng, Mao↗
DOE OSTI2021

Polarimetric Radar Variables in Snowfall at Ka- and W-Band Frequency Bands: A Comparative Analysis

Dual-frequency millimeter-wavelength radar observations in snowfall are analyzed in order to evaluate differences in conventional polarimetric radar variables such as differential reflectivity (ZDR) specific differential phase shift (K DP ) and linear depolarization ratio (LDR) at traditional cloud radar frequencies at Ka and W bands (~35 and ~94 GHz, correspondingly). Low radar beam elevation (~5°) measurements were performed at Oliktok Point, Alaska, with a scanning fully polarimetric radar operating in the horizontal–vertical polarization basis. This radar has the same gate spacing and very close beam widths at both frequencies, which largely alleviates uncertainties associated with spatial and temporal data matching. It is shown that observed Ka- and W-band Z DR differences are, on average, less than about 0.5 dB and do not have a pronounced trend as a function of snowfall reflectivity. The observed Z DR differences agree well with modeling results obtained using integration over nonspherical ice particle size distributions. For higher signal-to-noise ratios, KDP data derived from differential phase measurements are approximately scaled as reciprocals of corresponding radar frequencies indicating that the influence of non-Rayleigh scattering effects on this variable is rather limited. This result is also in satisfactory agreement with data obtained by modeling using realistic particle size distributions. Observed Ka- and W-band LDR differences are strongly affected by the radar hardware system polarization “leak” and are generally less than 4 dB. Smaller differences are observed for higher depolarizations, where the polarization “leak” is less pronounced. Realistic assumptions about particle canting and the system polarization isolation lead to modeling results that satisfactorily agree with observational dual-frequency LDR data.

42 ENGINEERING↗
DOE OSTI2021

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗