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NASA NTRS1994

Remote sensing of potential lunar resources. 2: High spatial resolution mapping of spectral reflectance ratios and implications for nearside mare TiO2 content`

High spatial resolution maps illustrating variations in spectral reflectance 400/560 nm ratio values have been generated for the following mare regions: (1) the border between southern Mare Serenitatis and northern Mare Tranquillitatis (including the MS-2 standard area and Apollo 17 landing site), (2) central Mare Tranquillitatis, (3) Oceanus Procellarum near Seleucus, and (4) southern Oceanus Procellarum and Flamsteed. We have also obtained 320-1000 nm reflectance spectra of several sites relative to MS-2 to facilitate scaling of the images and provide additional information on surface composition. Inferred TiO2 abundances for these mare regions have been determined using an empirical calibration which relates the weight percent TiO2 in mature mare regolith to the observed 400/560 nm ratio. Mare areas with high TiO2 abundances are probably rich in ilmenite (FeTiO3) a potential lunar resource. The highest potential TiO2 concentrations we have identified in the nearside maria occur in central Mare Tranquillitatis. Inferred TiO2 contents for these areas are greater than 9 wt% and are spatially consistent with the highest-TiO2 regions mapped previously at lower spatial resolution. We note that the morphology of surface units with high 400/560 nm ratio values increases in complexity at higher spatial resolutions. Comparisons have been made with previously published geologic maps, Lunar Orbiter IV, and ground-based images, and some possible morphologic correlatins have been found between our mapped 400/560 nm ratio values and volcanic landforms such as lava flows, mare domes, and collapse pits.

Melendrez, David E.↗

DOE OSTI2025

CFD modeling of non-catalytic, partial-oxidation engine reformer for flare mitigation

Flaring associated natural gas is commonly employed in the oil and gas industry to reduce methane (CH 4 ) emissions but generates carbon dioxide (CO 2 ) and harmful pollutants, significantly contributing to air pollution and posing risks to public health. To mitigate this impact, M2X Energy Inc. has developed a small-scale, modular gas-to-methanol system. This system features an engine reformer that performs fuel-rich partial oxidation of wellhead gas to produce syngas—a mixture of carbon monoxide (CO) and hydrogen (H 2 )—followed by a downstream reactor for methanol synthesis. This study focused on computational fluid dynamics (CFD) modeling of the engine reformer to simulate partial oxidation chemistry, predict the rich-burn operating limit, and assess syngas quality, ultimately aiding in design and operational optimization. The CFD model, developed within a Reynolds-Averaged Navier-Stokes (RANS) turbulence framework, incorporated sub-models for turbulent combustion, a chemical mechanism with polycyclic aromatic hydrocarbon (PAH) pathways, and soot emissions to accurately capture the fuel-rich, turbulent jet ignition and combustion processes. Model validation against experimental data showed good agreement across pre- and main-chamber pressures, apparent heat release rates, and exhaust gas concentrations of key species (H 2 , CO, CO 2 , CH 4 ) for varying intake equivalence ratios. Here, the model identified a rich-burn operating limit near a fuel-air equivalence ratio of 2.35, consistent with experimental observations. Furthermore, syngas quality analysis revealed that extending the rich-burn limit through engine reformer optimization could enhance syngas production, contributing to higher methanol synthesis efficiency.

Computational Fluid Dynamics↗

DOE OSTI2024

Effects of particle size and AQDS on the flow of electron equivalents between magnetite and aqueous Fe2+

Magnetite can occur naturally in nano- to micro-size regimes and widely coexists with aqueous Fe2+ (Fe2+ (aq)) in natural environments. However, the effects of magnetite particle size on its interaction with Fe2+ (aq) in anoxic subsurface environments, particularly with redox-active organics, remain unclear. In this study, the interactions of Fe2+ (aq) with magnetite particles of 12 nm versus 109 nm (Mag-12 vs. Mag-109), with/without anthraquinone- 2,6-disulfonate (AQDS), were studied based on equilibrium Fe2+ (aq) concentrations, kinetics of AQDS reduction, and structural versus surface-localized Fe(II)/Fe(III) ratios (xstru and xsurf) of magnetite. In the absence of AQDS, Mag-12 tends to release Fe2+ (aq) at pH 7 but sorb Fe2+ (aq) at pH 8, while Fe2+ (aq) uptake by Mag-109 is observed at both pH 7 and 8. The amounts of Fe2+ (aq) adsorbed per unit area of Mag-109 is higher than that of Mag-12, due to the higher electron-accepting capacity of Mag-109 that facilitates interfacial electron transfer (IET) from surfaceassociated Fe(II) to structural Fe(III). The increases of xstru and xsurf in Mag-109 after reaction with Fe2+ (aq) at pH 7 and 8 suggest Fe2+ (aq) incorporation or electron injection into the structure of Mag-109. The presence of AQDS promotes Fe2+ (aq) uptake by both Mag-12 and Mag-109. However, AQDS reduction by Fe2+-amended Mag-12 results in the decrease of xstru and inhibits Fe2+ (aq) incorporation or electron injection into the structure. On the contrary, the increase of xstru observed in Fe2+-amended Mag-109 after reaction with AQDS suggests that Fe2+ (aq) incorporation or electron injection into the surface structure and then consequently into the interiors is more favorable for magnetite with larger particle sizes. The different flow directions of electron equivalents across the solid-solution interfaces can be attributed to the relatively higher electron-accepting capacity, i.e. redox potential, of Mag-109 than Mag-12; larger particle sizes facilitate IET from surface-associated Fe(II) to structural Fe(III) and promotes further Fe2+ (aq) uptake, culminating in the pronounced changes of redox potentials in magnetitebearing solutions. The results demonstrate that particle size and redox-active organics are important factors to affect reductive activity of Fe2+-magnetite system in redox-oscillating environments.

Peng, Huan↗

DOE OSTI2020

Modeling the processes of soil moisture in regulating microbial and carbon-nitrogen cycling

Soil carbon (C) and nitrogen (N) cycles and their complex responses to hydro-climatic forcing have gained increasing attention. While the temperature effects have been intensively studied, soil moisture response functions (SMRFs) are not well documented for various microbial and enzymatic processes due to the difficulties in directly measuring and differentiating the moisture effects on various processes. In this work we extended our C-only Microbial-ENzyme Decomposition (MEND) model to the C-N coupled MEND model with flexible element stoichiometry. Our model calibration showed good agreement between simulated and observed C:N ratios in soil organic matter and microbial biomass, as well as the ammonium and nitrate concentrations. We show that the selection of SMRFs for specific biogeochemical processes could result in significant differences in model simulated microbial and C-N processes. In particular, it is essential to account for the soil moisture effects on microbial dormancy and resuscitation, as the changes in microbial physiology under favorable or stressful conditions will exert strong controls on soil C and N dynamics. We also advocate the utilization of dynamic (time-variant) data (e.g., litter input, N deposition, soil temperature and moisture), instead of time-invariant data, to drive model simulations and analyses. Dynamic forcing data (particularly dynamic soil moisture) better represent the real-world climate and environmental conditions, which could facilitate more realistic modeling and understanding of soil C and nutrient cycling in a changing world.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Unveiling the influence of selective-area-regrowth interfaces on local electronic properties of GaN p-n junctions for efficient power devices

Here, we report correlated nanoscale mapping of the structure, composition, and properties of regrown GaN p-n junctions to identify how etching and non-planar regrowth processes limit diode performance via the introduction of unintentional dopants and defect states. p-GaN was selectively regrown in n-GaN trenches with SiO 2 masks of variable mask-to-trench-width ratio. Dilute Al layers were periodically introduced during regrowth as markers of the growth interface. Correlated nanoscale mapping of doping, conductivity, and dopant complexes was achieved with atom probe tomography (APT), scanning spreading resistance microscopy (SSRM), and cathodoluminescence (CL) spectroscopy, respectively. The Al marker layers, detected by APT, enabled reconstruction of the faceted growth interface and correlation of the dopant concentration with position and time. The p-GaN growth rate is proportional to the mask-to-trench width ratio while the dopant incorporation rate is invariant. At trench edges, magnesium incorporation is suppressed, and oxygen incorporation enhanced, due to preferential incorporation on the semi-polar growth surface, leading to compensation and less abrupt p-n junctions; the SiO 2 mask is a source of oxygen. Residual etch damage below the regrowth interface induces n-type and p-type conductivity, creating leakage pathways. The non-uniform Mg incorporation is driven by crystal anisotropy and is thus inherent to non-planar regrowth, but can be mitigated by engineering the regrowth interface and process parameters. The unprecedented integration of spatially resolved mapping of dopants, impurities, conductivity, and carrier type is a powerful approach to discriminating distinct factors that limit the performance of regrown diodes, enabling the rational optimization of process and device design.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Measurements of Intermediate Species in Fuel-Rich Oxidation of Ethylene, Toluene, and n -Decane

Polycyclic aromatic hydrocarbons (PAHs) are important precursors to the formation of soot and are also pollutant emissions from combustion devices, including internal combustion engines. To understand the formation of PAHs, the low-molecular-weight hydrocarbon chemistry leading to their formation needs to be understood. Toward this goal, fuel-rich oxidation of three different hydrocarbons, i.e., ethylene, toluene, and n-decane, has been investigated in an atmospheric pressure flow reactor at varying temperatures (1000–1350 K), equivalence ratios (φ = 3.0–12.0), and residence times of 0.25–1.5 s. The major C 1 to C 7 intermediates, such as methane, acetylene, ethylene, allene, propyne, propylene, vinylacetylene, 1,3-butadiene, cyclopentadiene, benzene, and toluene, were quantified using a gas chromatograph equipped with a flame ionization detector. The experimental tendency of intermediate species formation, e.g., the dependence of temperature, equivalence ratio, and residence time, was similar in ethylene oxidation and n-decane oxidation. The concentrations of intermediate species up to C 4 were higher in ethylene/n-decane oxidation than toluene oxidation, while a nearly equal or larger amount of C5–C7 species was produced in toluene oxidation. The experimental data were compared with modeling results using a detailed chemical kinetic mechanism. The calculated data using the kinetic model were in agreement with the experimental results. Additionally, a comprehensive kinetic analysis on the reaction pathways of each species was conducted to assess the differences in the oxidation chemistry with the change in the structure of hydrocarbons. In particular, in-depth analysis of benzene formation was performed, elucidating that two benzene formation pathways were important in ethylene and n-decane oxidation: (1) H elimination of the 2,4-cyclohexadienyl radical produced from the isomerization of the 2,4-cyclopentadienylmethyl radical, and (2) dehydrogenation of cyclohexadiene produced from reactions of vinyl radical with 1,3-butadiene. In toluene oxidation, it was found that benzene was primarily produced from toluene through the replacement of the methyl group with hydrogen.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2021

Transformation of an Embedded Five-Membered Ring in Polycyclic Aromatic Hydrocarbons via the Hydrogen-Abstraction–Acetylene-Addition Mechanism: A Theoretical Study

Five-membered rings are constituents of many polycyclic aromatic hydrocarbons (PAHs) and their presence on the edges of large PAHs has been repeatedly observed experimentally. However, modern kinetic combustion models often do not consider the growth of PAHs through the transformation of the five-membered rings. Here, in connection with the above, we carried out a theoretical study of the mechanism of Hydrogen-Abstraction-aCetylene-Addition (HACA) transformation of an embedded five-membered ring on the armchair PAH edge to a six-membered ring, considering cyclopenta[d,e,f]phenanthrene (4,5-methylenephenanthrene) as a prototype system for this process. The potential energy surface for the reactions of cyclopenta[d,e,f]phenanthrenyl radicals produced by direct H abstractions from cyclopenta[d,e,f]phenanthrene with acetylene has been compiled at the G3(MP2,CC)//B3LYP/6-311G(d,p) level of theory including zero-point vibrational energy corrections. The computed energies and molecular parameters were then used to solve the Rice-Ramsperger-Kassel-Marcus Master Equation (RRKM-ME) in order to calculate reaction rate at various pressures and temperatures, which were fitted to modified Arrhenius equation for further kinetic modeling. The results show that the HACA transformation of the embedded five-membered ring to a six-membered ring is possible, albeit slow. The most viable reaction mechanism involves the R2 + C 2 H 2 reaction, where the acetylene molecules adds to a σ-radical in the six-membered ring adjacent to the five-membered ring via a low entrance barrier. The predominant product of R2 + C 2 H 2 is predicted to be 3 ethynyl 4H cyclopenta[def]phenanthrene Pr5 via immediate H elimination from the initial addition complex. Next, Pr5 undergoes H-assisted isomerization to 4aH-pentaleno[4,3,2,1-cdef]phenanthrene Pr4, and the latter adds an H atom eventually forming the 1-pyrenylmethyl radical Pr3: R2 + C 2 H 2 ⇌ 3 ethynyl 4H cyclopenta[def]phenanthrene (Pr5) + H ⇌ 4aH-pentaleno[4,3,2,1-cdef]phenanthrene (Pr4) + H Pr5 + H ⇌ Pr4 + H Pr4 + H → 1-pyrenylmethyl (Pr3) This HACA sequence may be competitive with the methyl radical addition to the R1 radical formed by H abstraction from the CH 2 group in the five-membered ring of cyclopenta[d,e,f]phenanthrene, which provides a pathway to pyrene following two H atom losses. Relative contributions of the two mechanisms of the five- to six-membered ring transformation would strongly depend on the branching ratios of the R1 and R2 radicals produced by the H abstractions and the available concentration of C 2 H 2 vs. CH 3 and hence differ in different flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Evaluating the Physisorption and Chemisorption of Iodine on Bismuth-Functionalized Carbon Foams

Bismuth-containing carbon materials have been shown to be highly promising sorbents for the capture of radioiodine. However, there is still a need to understand the effects of carbon and bismuth on the iodine sorption mechanism. In this study, we show the relationship between the physical and chemical sorption of iodine under different bismuth loading conditions. Here, highly porous and non-friable conductive carbon foams were prepared and bismuth was electrodeposited to provide strong iodine binding sites. For pure carbon foams, equal ratios of physisorbed and chemisorbed iodine-carbon phases were detected before desorption. As the concentration of bismuth increased, the chemisorption between bismuth and iodine dominated the total capture mechanism and physisorption was almost completely eliminated. Additionally, chemisorption of iodine depended upon the size and specific surface area of the bismuth particles present within the framework of the foam.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Seasonal variations in fire conditions are important drivers in the trend of aerosol optical properties over the south-eastern Atlantic

Abstract. From June to October, southern Africa produces one-third of the global biomass burning (BB) emissions by widespread fires. BB aerosols are transported westward over the south-eastern Atlantic with the mid-tropospheric winds, resulting in significant radiative effects. Ascension Island (ASI) is located midway between Africa and South America. From June 2016 to October 2017, a 17-month in situ observation campaign on ASI found a low single-scattering albedo (SSA) as well as a high mass absorption cross-section of black carbon (MACBC), demonstrating the strong absorbing marine boundary layer in the south-eastern Atlantic. Here we investigate the monthly variations of critical optical properties of BB aerosols, i.e. SSA and MACBC, during the BB seasons and the driving factors behind these variations. Both SSA and MACBC increase from June to August and decrease in September and October. The average SSA during the BB seasons is 0.81 at 529 nm wavelength, with the highest mean ∼ 0.85 in October and the lowest ∼ 0.78 in August. The absorption enhancement (Eabs) derived from the MACBC shows similar trends with SSA, with the average during the whole of the BB seasons at ∼ 1.96 and ∼ 2.07 in 2016 and 2017, respectively. As the Eabs is higher than the ∼ 1.5 commonly adopted value by climate models, this result suggests the marine boundary layer in the south-eastern Atlantic is more absorbing than model simulations. We find the enhanced ratio of BC to CO (ΔBC/ΔCO, equal to BC/ΔCO as the BC background concentration is considered to be 0) is well correlated with SSA and MACBC, providing a simple way to estimate the aerosol optical characteristics in the south-eastern Atlantic. The exponential function we proposed can approximate SSA and MACBC with BC/ΔCO, and when BC/ΔCO is small it can capture the rapid growth of SSA as BC/ΔCO decreases. BC/ΔCO is influenced by combustion conditions and aerosol scavenging. From the analysis of the location of BB, the primary source fuel, the water content in the fuel, combined with the mean cloud cover and precipitation in the transport areas of the BB plume, we conclude that the increase in BC/ΔCO from June to August is likely to be caused by burning becoming more flaming. The reduction in the water content of fuels may be responsible for the change in the burning conditions from June to August. The decrease in BC/ΔCO in September and October may be caused by two factors, one being a lower proportion of flaming conditions, possibly associated with a decrease in mean surface wind speed in the burning area, and the other being an increase in precipitation in the BB transport pathway, leading to enhanced aerosol scavenging, which ultimately results in an increase in SSA and MACBC.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

The annual cycle and sources of relevant aerosol precursor vapors in the central Arctic during the MOSAiC expedition

Abstract. In this study, we present and analyze the first continuous time series of relevant aerosol precursor vapors from the central Arctic (north of 80° N) during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition. These precursor vapors include sulfuric acid (SA), methanesulfonic acid (MSA), and iodic acid (IA). We use FLEXPART simulations, inverse modeling, sulfur dioxide (SO2) mixing ratios, and chlorophyll a (chl a) observations to interpret the seasonal variability in the vapor concentrations and identify dominant sources. Our results show that both natural and anthropogenic sources are relevant for the concentrations of SA in the Arctic, but anthropogenic sources associated with Arctic haze are the most prevalent. MSA concentrations are an order of magnitude higher during polar day than during polar night due to seasonal changes in biological activity. Peak MSA concentrations were observed in May, which corresponds with the timing of the annual peak in chl a concentrations north of 75° N. IA concentrations exhibit two distinct peaks during the year, namely a dominant peak in spring and a secondary peak in autumn, suggesting that seasonal IA concentrations depend on both solar radiation and sea ice conditions. In general, the seasonal cycles of SA, MSA, and IA in the central Arctic Ocean are related to sea ice conditions, and we expect that changes in the Arctic environment will affect the concentrations of these vapors in the future. The magnitude of these changes and the subsequent influence on aerosol processes remains uncertain, highlighting the need for continued observations of these precursor vapors in the Arctic.

Boyer, Matthew↗

NASA NTRS1984

Salts in the dry valleys of Antartica

The Dry Valleys of Antarctica are examples of polar deserts which are rare geological features on the Earth. Such deserts typically have high salinities associated with their closed-basin waters and on many surficial materials throughout them. In order to examine the possible sources for the salts observed in association with the soils in the Dry Valleys. The chloride and bromide concentrations of the water leachates from 58 soils and core samples were measured. The Cl/Br ratio for seawater is 289 and ratios measured for most of the 58 soils studied (greater than 85% of the soils studied) was larger than the seawater ratio (ratios typically were greater than 1000 and ranged up to 50,000). The enrichment in Cl relative to Br is strong evidence that the alts present within the soils were derived from seawater during ordinary evaporation processes, and not from the deposition of Cl and Br from aerosols or from rock weathering as has often been suggested.

Gibson, E. K., Jr.↗

NASA NTRS1987

Atmospheric measurements of pyruvic and formic acid

Pyruvic acid, a product of the atmospheric oxidation of cresols and probably of isoprene, has been determined together with formic acid in atmospheric aerosols and rain as well as in the vapor phase. Both acids are present predominantly as vapor; only about 10-20 percent of the total atmospheric pyruvate and 1-2 percent of the total formate are in the particulate phase. The concentrations of pyruvic and formic acid are highly correlated, with typical formic-to-pyruvic ratios of 10-30 in the gas phase, 20-30 in rain, and 2-10 in aerosols. The gas-phase and rain ratios are comparable to those predicted to result from isoprene oxidation. Pyruvic acid levels were similar in the eastern United States (during summer) and the Amazon Basin, suggesting that natural processes, particularly the photochemical oxidation of isoprene, could account for most of the pyruvic acid present in the atmosphere.

Andreae, Meinrat O.↗

NASA NTRS1987

Infrared spectroscopic measurements of halogenated sink and reservoir gases in the stratosphere with the ATMOS instrument

The Atmospheric Trace Molecule Spectroscopy (ATMOS) instrument recorded 19 sets of interferograms during solar occultations in both the Northern and Southern Hemispheres over the course of the Spacelab 3 mission. The resulting IR spectra furnish concentration profiles for over 25 atmospheric species. Attention is presently given to the volume mixing ratio profiles for HCl and HF in the 15-60-km altitude region, retrieved from northern sunsets and southern sunrises. The HF/HCl ratios deduced are in good agreement with model predictions. The total atmospheric chlorine at 50 km is nearly all in the form of HCl.

Raper, O. F.↗

NASA NTRS1989

High performance alloy electroforming

Electroformed copper and nickel are used in structural applications for advanced propellant combustion chambers. An improved process has been developed by Bell Aerospace Textron, Inc. wherein electroformed nickel-manganese alloy has demonstrated superior mechanical and thermal stability when compared to previously reported deposits from known nickel plating processes. Solution chemistry and parametric operating procedures are now established and material property data is established for deposition of thick, large complex shapes such as the Space Shuttle Main Engine. The critical operating variables are those governing the ratio of codeposited nickel and manganese. The deposition uniformity which in turn affects the manganese concentration distribution is affected by solution resistance and geometric effects as well as solution agitation. The manganese concentration in the deposit must be between 2000 and 3000 ppm for optimum physical properties to be realized. The study also includes data regarding deposition procedures for achieving excellent bond strength at an interface with copper, nickel-manganese or INCONEL 718. Applications for this electroformed material include fabrication of complex or re-entry shapes which would be difficult or impossible to form from high strength alloys such as INCONEL 718.

Malone, G. A.↗

NASA NTRS1989

Steady-state thermal-solutal diffusion in a float zone

A model for a float zone in a thin vertical sheet is used to study the formation of the zone configuration for both pure and binary systems of Si and GeGa. Equations describing the steady two-dimensional diffusion of solute in the melt and diffusion of heat in the feed material and the product crystal are presented. The material properties, asymptotic solutions for the temperature and concentration profiles, and melting, solidifying, and melt/gas interfacial shapes are determined in the small aspect ratio limit.

Young, G. W.↗

NASA NTRS1989

Polarographic study of cadmium 5-hydroxy 2-(hydroxymethyl) 4H-pyran-4-one complex

A polarographic study was performed on the products formed in the interaction of cadmium (II) with a 5-hydroxy 2-(hydroxymethyl) 4H-Pyran-4-one, using varying conditions of pH, supporting electrolytes, and concentrations. Measurements using the differential pulse method show that cadmium (II) exhibits a molar combining ratio of complexing agents to cation ranging from 1 to 1 to 3 to 1 depending on the pH and the supporting electrolyte employed.

Wilson, Ray F.↗

NASA NTRS1991

Experimental investigation of helicopter vibration reduction using rotor blade aeroelastic tailoring

A wind tunnel investigation has been conducted to parametrically investigate the effect of blade nonstructural mass on helicopter fixed- and rotating-system vibratory loads. The data were obtained using Mach- and aeroelastically-scaled model rotor blades which allowed for the addition of concentrated nonstructural masses at multiple points along the blade radius. Testing was conducted for advance ratios ranging from 0.10 to 0.35 for ten blade mass configurations. Three thrust levels were obtained at representative full-scale shaft angles for each configuration. Results indicate that proper placement of blade nonstructural mass can provide reductions in fixed-system vibratory loads, but that correct mass placement and the loads reduction realized are dependent upon flight condition. The data base obtained with this investigation provides a comprehensive set of fixed-system shears and moments, blade moment, and blade flap and lag response. The data set is well suited for use in the correlation and development of advanced rotorcraft analyses.

Wilbur, Matthew L.↗

NASA NTRS1954

Effect of water on carbon monoxide-oxygen flame velocity

The flame velocities were measured of 20 percent oxygen and 80 percent carbon monoxide mixtures containing either light water or heavy water. The flame velocity increased from 34.5 centimeters per second with no added water to about 104 centimeters per second for a 1.8 percent addition of light water and to 84 centimeters per second for an equal addition of heavy water. The addition of heavy water caused greater increases in flame velocity with equilibrium hydrogen-atom concentration than would be predicted by the Tanford and Pease square-root relation. The ratio of the flame velocity of a mixture containing light water to that of a mixture containing heavy water was found to be 1.4. This value is the same as the ratio of the reaction rate of hydrogen to that of deuterium and oxygen. A ratio of reaction rates of 1.4 would also be required for the square-root law to give the observed ratio of flame-velocity changes.

Mcdonald, Glen E↗