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At least 217 records · Page 12

A multiple-scale turbulence model for incompressible flow

A multiple-scale eddy viscosity model is described in this paper. This model splits the energy spectrum into a high wave number regime and a low wave number regime. Dividing the energy spectrum into multiple regimes simplistically emulates the cascade of energy through the turbulence spectrum. The constraints on the model coefficients are determined by examining decaying turbulence and homogeneous turbulence. A direct link between the partitioned energies and the energy transfer process is established through the coefficients. This new model has been calibrated and tested for boundary-free turbulent shear flows. Calculations of mean and turbulent properties show good agreement with experimental data for two mixing layers, a plane jet and a round jet.

Duncan, B. S.↗

A multiple-scale turbulence model for incompressible flow

A multiple-scale eddy viscosity model is described. This model splits the energy spectrum into a high wave number regime and a low wave number regime. Dividing the energy spectrum into multiple regimes simplistically emulates the cascade of energy through the turbulence spectrum. The constraints on the model coefficients are determined by examining decaying turbulence and homogeneous turbulence. A direct link between the partitioned energies and the energy transfer process is established through the coefficients. This new model was calibrated and tested for boundary-free turbulent shear flows. Calculations of mean and turbulent properties show good agreement with experimental data for two mixing layers, a plane jet and a round jet.

Duncan, B. S.↗

Apatite-Melt Partitioning of Volatiles in Basaltic Systems: Implications for Determining Volatile Abundances in Planetary Bodies from Apatite

Apatite [Ca5(PO4)3(F,Cl,OH)] is present in a wide range of planetary materials, and due to the presence of volatiles within its crystal structure (X-site), many recent studies have attempted to use apatite to constrain the volatile contents of planetary magmas and mantle sources [i.e., 1]. Experimental studies have investigated the apatite-melt partitioning behavior of F, Cl, and OH in basaltic systems [e.g., 2- 3], reporting that apatite-melt partitioning of volatiles is best described as exchange equilibria similar to Fe-Mg partitioning between olivine and silicate melt. However, exchange coefficients may vary as a function of temperature, pressure, melt composition, and/or oxygen fugacity. Furthermore, exchange coefficients may vary in portions of apatite compositional space where F, Cl, and OH do not mix ideally in apatite [3]. In these regions of ternary space, we anticipate that crystal chemistry could influence partitioning behavior. Consequently, we conducted experiments to investigate the effect of apatite crystal chemistry on apatite-melt partitioning of F, Cl, and OH.

McCubbin, F. M.↗

Radial diffusion and ion partitioning in the Io torus

A model is presented for radial diffusion and charge state partitioning of sulfur and oxygen ions in the Io torus, including effects of electron impact and charge exchange. When applied to Voyager 1 radial profiles of total ion flux tube content, the model shows that the ion residence time in the torus, tau(D), as defined in spectroscopic studies of ion partitioning, is related to the radial diffusion coefficient, D(LL), at L = 7 by tau(D) approximately 8/D(LL)(7). This result appears to bring spectroscopic estimates of the ion residence time (tau/D/ greater than about 60 to 100 days) into reasonable agreement with estimates of D(LL) from magnetospheric diffusion studies, D(LL) equals approximately 10 to the -6th/s.

Cheng, A. F.↗

Enhanced reactivity at the oil–water interface accelerates the synthesis of zymonic acid in microemulsions

Chemical reactions in microscale compartments, such as aerosols and emulsions, can exhibit significantly faster reaction rates relative to macroscale containers. This enhancement in chemistry is often due to the elevated importance of surfaces as reaction vessels are reduced to picoliter volumes. While most studies have focused on the air-water interface of droplets, there are comparably fewer studies of reactions in micron-scale aqueous solutions encapsulated by oil. Here we investigate the condensation reaction of pyruvic acid (PA) to form zymonic acid (ZA) and water. Using microfluidics and optical trapping, chemical kinetics are measured in monodisperse micron-sized emulsion droplets in situ via Raman spectroscopy. Relative to a macroscopic bulk solution, which exhibits little to no reaction over many days, we find efficient production of ZA over the same time period. A kinetic model is developed to elucidate the role of the interface in accelerating the microdroplet reaction kinetics. After quantifying the surface partitioning of PA from interfacial tension measurements, the rate coefficient for the condensation reaction at the oil-water interface is determined to be 1.8 × 10-2 M-1 s-1. This rate coefficient is estimated to be 105 larger than the reaction rate in bulk aqueous solutions. Compared to previous studies of accelerated ZA formation at the air-water interface on nanodroplets, we find that the reaction at the oil-water interface is 20 times more efficient. Despite this difference, the overall ZA formation rate in emulsions is significantly slower than in the same-sized aerosols, which arises from the weaker partitioning of PA to the oil-aqueous relative to air-water interface. These results highlight the interplay between interfacial partitioning and reactivity in accelerating chemistry in microcompartments and provides new insights into how interfacial composition influences condensation reactions.

Wallace, Brandon J↗

Partitioning of flight data for aerodynamic modeling of aircraft at high angles of attack

It is sometimes necessary to determine aerodynamic model structure and estimate associated stability and control derivatives for airplanes from flight data that cover a large range of angle of attack or sideslip. One method of dealing with that problem is through data partitioning. The main purpose of this paper is to provide an explanation of a data partitioning procedure and its application and to discuss both the power and limitations of that procedure for the analysis of large maneuvers of aircraft. The partitioning methodology is shown to provide estimates for coefficients of those regressors that are well excited in the aircraft motion. In particular, primary lateral stability and damping derivatives are identified throughout the maneuver ranges.

Batterson, James G.↗

Effect of Silicon on the Activity Coefficient of Rhenium in Fe-Si Liquids: Implications for HSE and Os Isotopes in Planetary Mantles

Metallic cores contain light alloying elements that can be a combination of S, C, Si, and O, all of which have important chemical and physical influences. For Earth, Si may be the most abundant light element in the core. Si dissolved into Fe liquids can have a large effect on the magnitude of the activity coefficient of siderophile elements (SE), and thus the partitioning behavior of those elements between core and mantle. The effect of Si on the highly siderophile elements is only beginning to be studied and the effects on Au, Pd and Pt are significant. Here we report new experiments designed to quantify the effect of Si on the partitioning of Re between metal and silicate melt. A solid understanding of Re partitioning is required for a complete understanding of the Re-Os isotopic systems. The results will be applied to understanding the HSEs and Os isotopic data for planetary mantles, and especially Earth.

Righter, K.↗

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗

Metal-silicate Partitioning of Re, Ru, Pt, Os, Ti, Nb, and Ta in Reduced Differentiated Planetary Bodies

Siderophile (iron-loving) elements are strongly fractionated during differentiation of planetary bodies into core and mantle [1]. Because the fractionation is controlled by the pressure, temperature, redox conditions, and composition, this group of elements can provide important constraints on the conditions of accretion and core formation in early solar system bodies (planetesimals) and planets (Earth, Mercury, Venus)[2]. At the reducing conditions thought to prevail in the early solar system, Si is known to alloy with FeNi metallic liquids (e.g., [3]) affecting the activity coefficients of siderophile elements in FeNi liquids and thus ultimately their detailed partitioning between metal and silicate melt. The effect of Si can be significant for some siderophile elements, as demonstrated previously by (e.g., [4]: Ni, Co; [5,6]: Ge, As, Sb, Pd, Pt, Au). The effect of Si has not yet been determined for several key groups of siderophile elements including the highly siderophile Re, Ru and Os, and the weakly siderophile Ta, Nb, and Ti. Here, we report new experiments designed to quantify the effect of Si on the partitioning of Re, Pt, Os, Ru, Ti, Ta and Nb between metal and silicate melts. The results will be used to evaluate metal/silicate equilibrium for Nb, Ta, Ti and Nb/Ta ratios in planetary mantles, mantle concentrations of Ru, Re, Pt, Os during accretion, the evolution of Re/Os, Pt/Os ratios in magma oceans, and the role of late veneer in establishing Re and Ru abundances in the terrestrial mantle.

core formation↗

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Liu, Yen↗

Partitioning of Ni/2+/ between basaltic and synthetic melts and olivines An experimental study

Olivine/liquid distribution coefficients for Ni in basaltic and simple synthetic melts are found in the 1400-1070 C temperature range. The results suggest that: (1) the Ni distribution coefficients and NiO activity coefficients are strongly temperature dependent, (2) the Ni distribution coefficients are functions of melt composition and structure at a constant temperature although the dependence is small for most basaltic magmas, (3) differences in melt composition do not significantly influence generally 'basaltic' melts, (4) the Ni distribution coefficients may be used as geothermometers to predict the olivine crystallization temperatures of basaltic magmas to within plus or minus 50 C, (5) the Ni distribution coefficients are greater than one at all natural magmatic temperatures, and (6) the Ni distribution coefficients do not significantly vary as functions of the Ni content of the melt to at least one mole percent.

Leeman, W. P.↗

Kinetic effects on trace element partitioning

A potential difficulty regarding the application of trace element abundance data to problems in igneous petrogenesis is related to the possibility that partitioning of trace elements among minerals and melt may not be an equilibrium process. It may rather be controlled by kinetic processes, specifically the interplay between crystal growth and diffusion of the trace elements in crystals and melt. The present investigation has the objective to quantify kinetic effects on trace element partitioning. Crystals of olivine, pyroxene, and plagioclase were grown rapidly from synthetic melts resembling naturally-occurring mafic melts and doped with La, Sm, and Lu to quantify the magnitude of the effect of crystal growth rate on concentration of excluded trace elements. Olivine melt partitioning failed to show any appreciable kinetic effects, while diopside/melt distribution coefficients increased by 70 percent when the crystals grew very rapidly.

Lindstrom, D. J.↗

Effect of Silicon on Activity Coefficients of Siderophile Elements (P, Au, Pd, As, Ge, Sb, and In) in Liquid Fe, with Application to Core Formation

Earth's core contains approximately 10 percent light elements that are likely a combination of S, C, Si, and O, with Si possibly being the most abundant. Si dissolved into Fe liquids can have a large effect on the magnitude of the activity coefficient of siderophile elements (SE) in Fe liquids, and thus the partitioning behavior of those elements between core and mantle. The effect of Si can be small such as for Ni and Co, or large such as for Mo, Ge, Sb, As. The effect of Si on many siderophile elements is unknown yet could be an important, and as yet unquantified, influence on the core-mantle partitioning of SE. Here we report new experiments designed to quantify the effect of Si on the partitioning of P, Au, Pd, and many other SE between metal and silicate melt. The results will be applied to Earth, for which we have excellent constraints on the mantle siderophile element concentrations.

Righter, K.↗

Effect of Silicon on Activity Coefficients of Platinum in Liquid Fe-Si, With Application to Core Formation

Earth's core contains approximately 10% of a light element that is likely a combination of S, C, Si, and O, with Si possibly being the most abundant light element. Si dissolved into Fe liquids can have a large effect on the magnitude of the activity coefficient of siderophile elements (SE) in Fe liquids, and thus the partitioning behavior of those elements between core and mantle. The effect of Si can be small such as for Ni and Co, or large such as for Mo, Ge, Sb, As. The effect of Si on many siderophile elements is unknown yet could be an important, and as yet unquantified, influence on the core-mantle partitioning of SE. Here we report new experiments designed to quantify the effect of Si on the partitioning of Pt (with Re and Ru in progress or planned) between metal and silicate melt. The results will be applied to Earth, for which we have excellent constraints on the mantle Pt concentrations.

Righter, K.↗

Reflection and transmission of acoustic waves from a moving layer

The refraction of acoustic waves by a moving medium layer is theoretically treated and the expressions for reflection and transmission coefficients are determined. The moving medium layer velocity is assumed to have a space dependence in one direction. A partitioning of the moving medium layer into constant-velocity sublayers is introduced and the number of sublayers is allowed to increase until the reflection and transmission coefficients converage to their respective values. Numerical results for several sublayer approximations of Poiseuille's flow are presented as functions of the moving layer velocity for several angles of incidence of the acoustic wave. The degenerate case of single constant-velocity layer is also treated, both theoretically and by a numerical analysis.

Steinmetz, G. G.↗

Crystal/liquid partitioning of REE in basaltic systems Extreme fractionation of REE in olivine

The calculation of partial coefficients for Nd, Sm, Gd, and Yb between olivine and synthetic basaltic melts using the percent level doping technique and microprobe analytical techniques is examined. The experimental and analytical procedures are described. The relationship between rare earth elements (REEs) concentrations and crystal margins caused by Rees X-rays from surrounding glass is discussed. Average olivine/liquid distribution coefficients for Nd, Sm, Gd, and Yb for mare and highlands basaltic melts are presented. The data reveal that the distribution coefficients for light REEs are lower than those obtained in previous studies, and the slope of the olivine/liquid distribution coefficient pattern is steeper; potential sources of error in the previous and present studies which could explain the differences in distribution coefficients and slope are investigated.

Mckay, G. A.↗

Apatite-Melt Partitioning at 1 Bar: An Assessment of Apatite-Melt Exchange Equilibria Resulting from Non-Ideal Mixing of F and Cl in Apatite

The mineral apatite [Ca5(PO4)3(F,Cl,OH)] is present in a wide range of planetary materials. Due to the presence of volatiles within its crystal structure (X-site), many recent studies have attempted to use apatite to constrain the volatile contents of planetary magmas and mantle sources. In order to use the volatile contents of apatite to precisely determine the abundances of volatiles in coexisting silicate melt or fluids, thermodynamic models for the apatite solid solution and for the apatite components in multi-component silicate melts and fluids are required. Although some thermodynamic models for apatite have been developed, they are incomplete. Furthermore, no mixing model is available for all of the apatite components in silicate melts or fluids, especially for F and Cl components. Several experimental studies have investigated the apatite-melt and apatite-fluid partitioning behavior of F, Cl, and OH in terrestrial and planetary systems, which have determined that apatite-melt partitioning of volatiles are best described as exchange equilibria similar to Fe-Mg partitioning between olivine and silicate melt. However, McCubbin et al. recently reported that the exchange coefficients may vary in portions of apatite compositional space where F, Cl, and OH do not mix ideally in apatite. In particular, solution calorimetry data of apatite compositions along the F-Cl join exhibit substantial excess enthalpies of mixing. In the present study, we conducted apatite-melt partitioning experiments in evacuated, sealed silica-glass tubes at approximately 1 bar and 950-1050 degrees Centigrade on a synthetic Martian basalt composition equivalent to the basaltic shergottite Queen Alexandria Range (QUE) 94201. These experiments were conducted dry, at low pressure, to assess the effects of temperature and apatite composition on the partitioning behavior of F and Cl between apatite and basaltic melt along the F-Cl apatite binary join, where there is non-ideal mixing of F and Cl in apatite.

McCubbin, F. M.↗

Direct Measurements of Dimethyl Sulfide Oxidation Chemistry: Uncovering the Primary Pathways from Gas Phase to Sulfate Aerosols

We report experimental measurements of dimethyl sulfide oxidation, focusing on a major chemical intermediate, hydroperoxymethyl thioformate (HPMTF). The (photo)chemistry and transport properties of HPMTF, which are critical to accurate modeling of tropospheric sulfur, are not known, partly because current analytical methods are not optimized for elusive chemical intermediates. We investigated dimethyl sulfide oxidation using a custom time-resolved photoionization mass spectrometer, interfaced with pulsed laser photolysis, continuous photolysis, and liquid droplet reactors. We detected and characterized HPMTF (along with other reaction intermediates), quantified its yield, and measured its formation rate coefficient. We also developed a clean, intense, online HPMTF source, suitable for further experimental investigations. Lastly, we measured the mass accommodation coefficient of HPMTF on water droplets – a critical quantity for modeling its atmospheric partitioning between the gas and condensed phases. The experimental platform we developed here enables the exploration of other critical elusive reaction intermediates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗