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A gas model of diffusion in liquid metals is presented. In this model, ions of liquid metals are assumed to behave like the molecules in a dense gas. Diffusion coefficient of solute is discussed with reference to its mass, ionic size, and pair potential. The model is applied to the case of solute diffusion in liquid silver. An attempt was made to predict diffusion coefficients of solutes with reasonable accuracy.
The reaction between Al2O3 and alpha2-Ti3Al was studied with a series of Al2O3/alpha2-Ti3Al multiphase diffusion couples annealed at 900, 1000 and 1100 C. The diffusion-paths were found to strongly depend on alpha2- Ti3Al(O) composition. For alloys with low oxygen concentrations the reaction involved the reduction of Al2O3, the formation of a gamma-TiAl reaction-layer and diffusion of Al and O into the alpha2-Ti3Al substrate. Measured concentration profiles across the interaction-zone showed "up-hill" diffusion of O in alpha2-Ti3Al(O) indicating a significant thermodynamic interaction between O and Al, Ti or both. Diffusion coefficients for the interstitial O in alpha2-Ti3Al(O) were determined independently from the interdiffusion of Ti and Al on the substitutional lattice. Diffusion coefficients are reported for alpha2-Ti3Al(O) as well as gamma-TiAl. Interpretation of the results were aided with the subsequent measurement of the activities of Al, Ti and O in alpha 2-Ti3Al(O) by Knudsen effusion-cell mass spectrometry.
The results of the spatial distribution of cosmic ray density, gradients, and anisotropy obtained on the basis of the numerical solution of the anisotropic diffusion equation with an account of solar wind velocity change depending on the latitudinal angle theta of the form U=u sub oe sup alpha theta and the diffusion coefficient depending on the spatial coordinates and the particle rigidity are presented. It is shown that the increase of the solar wind velocity and the diffusion coefficient with heliolatitude leads to gradient distributions that are in accord with experimental data observed in space. The results of the energetic spectrum of 11 and 22-year cosmic ray variations obtained with an account of direction of the general magnetic field of the Sun are presented are given.
Probability of a brittle crack formation in an elastic solid with fluctuating strength is considered. A set Omega of all possible crack trajectories reflecting the fluctuation of the strength field is introduced. The probability P(X) that crack penetration depth exceeds X is expressed as a functional integral over Omega of a conditional probability of the same event taking place along a particular path. Various techniques are considered to evaluate the integral. Under rather nonrestrictive assumptions, the integral is reduced to solving a diffusion-type equation. A new characteristic of fracture process, 'crack diffusion coefficient', is introduced. An illustrative example is then considered where the integration is reduced to solving an ordinary differential equation. The effect of the crack diffusion coefficient and of the magnitude of strength fluctuations on probability density of crack penetration depth is presented. Practical implications of the proposed model are discussed.
We consider the effect of oblique EMIC waves on relativistic electron scattering in the outer radiation belt using simultaneous observations of plasma and wave parameters from CRRES. The main findings can be s ummarized as follows: 1. In 1comparison with field-aligned waves, int ermediate and highly oblique distributions decrease the range of pitc h-angles subject to diffusion, and reduce the local scattering rate b y an order of magnitude at pitch-angles where the principle absolute value of n = 1 resonances operate. Oblique waves allow the absolute va lue of n > 1 resonances to operate, extending the range of local pitc h-angle diffusion down to the loss cone, and increasing the diffusion at lower pitch angles by orders of magnitude; 2. The local diffusion coefficients derived from CRRES data are qualitatively similar to the local results obtained for prescribed plasma/wave parameters. Conseq uently, it is likely that the bounce-averaged diffusion coefficients, if estimated from concurrent data, will exhibit the dependencies similar to those we found for model calculations; 3. In comparison with f ield-aligned waves, intermediate and highly oblique waves decrease th e bounce-averaged scattering rate near the edge of the equatorial lo ss cone by orders of magnitude if the electron energy does not excee d a threshold (approximately equal to 2 - 5 MeV) depending on specified plasma and/or wave parameters; 4. For greater electron energies_ ob lique waves operating the absolute value of n > 1 resonances are more effective and provide the same bounce_averaged diffusion rate near the loss cone as fiel_aligned waves do.
Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.
The radial diffusion equation with synchrotron losses is solved by the Laplace-transform method for near equatorially mirroring relativistic electrons. The evolution of a power-law distribution function is found, and the characteristics of synchrotron burnoff are stated in terms of explicit parameters for an arbitrary diffusion coefficient of a specific form. The peaking of the 10.4-cm volume emissivity from Jupiter at an L shell of about 1.8 provides an estimate of the diffusion coefficient in the radiation belts; one value is suggested as the appropriate modification, for an equatorial field strength of 4.2 G, of the Birmingham et al. (1974) result. Nonsynchrotron losses are included phenomenologically; from the phase-space densities reported by McIlwain and Fillius (1975), the particle lifetime is estimated. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.
Because of the presence of multiple ion species in the Io plasma torus, whistler mode noise can be converted to ion cyclotron waves via a polarization reversal process at the local crossover frequency. Using whistler mode intensity measurements in the Jovian magnetosphere from Voyager 1, the pitch-angle diffusion rates that would occur if the noise is converted to ion cyclotron waves is estimated. Typical pitch-angle diffusion coefficients range from 0.000001/sec for protons resonating near the equator to 0.0001/sec for 10-keV O(+) ions resonating at high latitudes. Although complete bounce averaged diffusion coefficients have not yet been computed, preliminary estimates indicate that the energetic ion precipitation caused by these waves may be able to account for the EUV auroral emissions at the foot of the torus field lines.
Oxygen self diffusion coefficients were determined in single crystal alpha-Al2O3 using the gas exchange technique. The samples were semi-infinite slabs cut from five different boules with varying background impurities. The diffusion direction was parallel to the c-axis. The tracer profiles were determined by two techniques, single spectrum proton activation and secondary ion mass spectrometry. The SIMS proved to be a more useful tool. The determined diffusion coefficients, which were insensitive to impurity levels and oxygen partial pressure, could be described by D = .00151 exp (-572kJ/RT) sq m/s. The insensitivities are discussed in terms of point defect clustering. Two independent models are consistent with the findings, the first considers the clusters as immobile point defect traps which buffer changes in the defect chemistry. The second considers clusters to be mobile and oxygen diffusion to be intrinsic behavior, the mechanism for oxygen transport involving neutral clusters of Schottky quintuplets.
Jovian electron intensity in the energy range 2-7 MeV was measured along the trajectory of Pioneer 11 up to 16 deg heliographic latitude. These electrons have crossed the average direction of the interplanetary magnetic field, propagating normal to the solar equatorial plane, and their intensity continues to be modulated by corotating interaction regions over this latitude range. From these data, the electron diffusion coefficient perpendicular to the equatorial plane (K2 = 2 x 10 to the 20th sq cm/s) was derived to within a factor 2 using a three-dimensional diffusion-convection model and the values of the parallel and perpendicular diffusion coefficients in the solar equatorial plane (Ky = 5 x 10 to the 22nd sq cm/s, K2 = 10 to the 21st sq cm/s, respectively), which had previously successfully described Jovian electron propagation near the equatorial plane from 1 to about 10 AU. These results indicate that the Jovian electron intensity may be very low at high solar latitudes.
Two triglycine sulphate crystals were grown from an aqueous solution in Spacelab 3 aboard a Space Shuttle. Using a diffusion coefficient of 0.00002 sq cm/s, a computerized simulation gave reasonable agreement between experimental and theoretical crystal sizes and interferometric lines in the solution near the growing crystal. This diffusion coefficient is larger than most measured values, possibly due to fluctuating accelerations on the order of .001 g (Earth's gravity). The average acceleration was estimated to be less than .000001 g. At this level, buoyancy driven convection is predicted to add approx. 20 percent to the steady state growth rate. Only very slight distortion of the interferometric lines was observed at the end of a 33 hr run. It is suggested that the time to reach steady state convective transport may be inversely proportional to g at low g, so that the full effect of convection was not realized in these experiments.
Two triglycine sulphate crystals were grown from an aqueous solution on the Spacelab 3 mission. Using a diffusion coefficient of 0.00002 sq cm/sec, a computer simulation gave reasonable agreement between experimental and theoretical crystal sizes and interferometric lines in the solution near the growing crystal. This diffusion coefficient is larger than most measured values, possibly due to fluctuating accelerations on the order of 0.001 g. The average acceleration was estimated to be less than 10 to the -6th g. At this level buoyancy-driven convection is predicted to add approximately 20 percent to the steady-state growth rate.
This report contains experimental results for the interdiffusion coefficient of the system, succinonitrile plus water, at a number of compositions and temperatures in the single phase region of the phase diagram. The concentration and temperature dependence of the measured diffusion coefficient has been analyzed in terms of Landau - Ginzburg theory, which assumes that the Gibb free energy is an analytic function of its variables, and can be expanded in a Taylor series about any point in the phase diagram. At most points in the single phase region this is adequate. Near the consolute point (critical point of solution), however, the free energy is non-analytic, and the Landau - Ginzburg theory fails. The solution to this problem dictates that the Landau - Ginzburg form of the free energy be replaced by Widom scaling functions with irrational values for the scaling exponents. As our measurements of the diffusion coefficient near the critical point reflect this non-analytic character, we are preparing for publication in a refereed journal a separate analysis of some of the data contained herein as well as some additional measurements we have just completed. When published, reprints of this article will be furnished to NASA.
The shallow water equations are used to investigate the interaction of planetary wave-breaking with a 'diabatic' forcing. The numerical integrations demonstrate the formation of a sharp gradient in potential vorticity at the edge of the polar vortex, despite 'diabatic relaxation' toward a smooth gradient. Successive cycles of Rossby wave-breaking accentuate the distinction between the vortex and the surf-zone. Persistent easterly acceleration in the tropics eventually produces a flow regime of little relevance to the atmosphere. For the period when the flow has some qualitative resemblance to the middle stratosphere diffusion coefficients are calculated from the meridional fluxes of potential vorticity and of passive tracers. It is found that the unique dynamical nature of potential vorticity among tracers is not reflected in its diffusion coefficient.
Recent measurements of the cosmic ray (CR) antiproton flux have been shown to challenge existing CR propagation models. It was shown that the reacceleration models designed to match secondary to primary nuclei ratio (e.g., Boron/Carbon) produce too few antiprotons, while the traditional non-reacceleration models can reproduce the antiproton flux but fall short of explaining the low-energy decrease in the secondary to primary nuclei ratio. Matching both the secondary to primary nuclei ratio and antiproton flux requires artificial breaks in the diffusion coefficient and the primary injection spectrum suggesting the need for other approaches. In the present paper we discuss one possibility to overcome these difficulties. Using the measured antiproton flux to fix the diffusion coefficient, we show that the spectra of primary nuclei as measured in the heliosphere may contain a fresh local unprocessed component at low energies, thus decreasing the measured secondary to primary nuclei ratio. A model reproducing antiprotons, B/C ratio, and abundances up to Ni is presented.
A fire in a spacecraft poses detrimental consequences and risks mission success in addition to crew safety. This is compounded during long-duration missions when the crew has limited options to recover from a fire. A common spacecraft fire concern is the smoldering of wire insulation, typically made from Polyvinyl chloride (PVC) or Polytetrafluoroethylene (PTFE). This creates acid gases such as Hydrogen Chloride (HCl), Hydrogen Fluoride (HF) and Hydrogen Cyanide (HCN). These poisonous gases are hazardous to the crew. They also interact with common surfaces within the spacecraft more than dominant combustion products such as CO2 and H2O. This makes them more difficult to track for potential fire detection techniques, or for postfire clean-up. It is imperative to be able to understand and predict the fate of these poisonous species in a microgravity environment in order to design a safe vehicle. HCl interacts with a number of materials inside a spacecraft. Primary among these materials is aluminum, which is abundantly used due to its strong and light weight nature. Aluminum has a natural oxide layer that protects it from corrosion but is typically treated to enhance this oxide layer. Among these treatments is a chromate conversion coating (CCC), which provides a thin enough protective oxide layer to still conduct electricity, and a traditional anodized material that has a thicker oxide layer that does not conduct electricity. Nomex is another common material found inside a spacecraft. It is a flame-resistant woven polymer that is related to nylon. This commercially available material is used for cargo storage bags and as a fire barrier. Physics-based models were developed to predict the uptake of HCl by these materials. The ultimate objective of these models is to predict the fate of HCl within the spacecraft so that sensors can be placed in meaningful locations in future missions based on the model predictions. To support these modeling efforts, experiments were performed in a cast acrylic test cell that measured the difference between the inlet and outlet concentration of HCl after inserting a sample rod of the test material. Different uptake capacities were realized for each type of sample tested. A computational fluid dynamics model (CFD) model of the reactor was then constructed that used a one-step global reaction rate with calibratable reaction (or kinetic) constants. These constants were calibrated to match the HCl uptake on the CCC aluminum samples, and the same kinetic constants were then tested for the stock and anodized aluminum samples. Model predictions matched the experimental data for the stock aluminum, and to a much lesser extent, the anodized aluminum. The model was additionally validated at different flow rates, sample surface areas, and inlet concentrations, and showed good agreement for all stock and CCC samples. The model did not accurately predict the HCl uptake in the anodized samples compared to the other two types of aluminum. Adjusting the kinetic constants and transport properties did little to improve the prediction. X-Ray Photoelectron Spectroscopy (XPS) was used to determine that the oxide layer thickness of anodized aluminum is approximately 5,000 nm, compared to 250 nm for CCC and 50 nm for stock. XPS also revealed presence of chlorine further down in the aluminum oxide layer in anodized samples than CCC and stock samples after the samples were saturated with HCl, indicating that accounting for diffusion of HCl into the oxide layer is important for accurate prediction of HCl uptake onto anodized aluminum. Consequently, a multi-scale model was developed and tested. First, a single pore inside the anodized aluminum oxide layer was modeled and is referred to as the pore-scale model. In this model, HCl diffused through the pore and reacted with the aluminum oxide pore wall to create aluminum chloride. The sample was then saturated when the mass transfer resistance through the growing aluminum chloride layer became too large for the HCl to reach the aluminum oxide wall and continue the reaction. This pore-scale model was coupled to the reactor-scale model using a concentration-dependent diffusion coefficient, resulting in much more accurate predictions (approximately half the sum square error of the aforementioned reactor-scale model that produced good agreement for stock and CCC) for a variety of operating conditions. The amount of water vapor or relative humidity (RH) in the flow during a reactor experiment was determined to influence HCl uptake. Experiments were performed to understand the interaction of gaseous HCl with aluminum surfaces in the presence of water vapor. The results show that increasing levels of RH increased the capacity of aluminum to adsorb HCl but decreased the capacity of Nomex to uptake HCl. A series of tests were performed on individual aluminum samples after they had been saturated with a fixed concentration of HCl in dry air conditions with the goal of determining how their HCl uptake capacity changes after various treatments with water relative to the original saturation tests. HCl-saturated aluminum samples subjected to a second dry air flow at the same HCl concentration as the original test had an uptake of 23.5% of the original sample with no treatment in between. Saturated aluminum samples subjected to an air flow with a RH of 90% in between tests had an uptake of 35.6% of the original. Saturated aluminum samples submerged in distilled water for 12 hours in between tests had an uptake of 82.2% of the original sample. Previously saturated aluminum tested with HCl and a 50% RH air flow resulted in similar uptake characteristics in multiple repeated tests. The experiments show the profound effect water vapor has on HCl uptake onto aluminum surfaces. In the samples subjected to water vapor or liquid water, capillary condensation and capillary diffusion alters the transport of HCl significantly. A model was proposed that developed a relationship between RH and the coefficient of HCl diffusion in aluminum chloride. This produced an “S-shaped” curve with diffusion coefficient as a function of RH, with 45% RH represented as the point where the diffusion coefficient is halfway between no water saturation and 100% water saturation in the aluminum chloride product layer. No difference in uptake characteristics for the experiment or model were realized between 50% and 62% RH. The results from the large-scale microgravity experiment, Saffire, are discussed as they pertain to the fate of HCl throughout a spacecraft. HCl was released, both as a standalone event, and in concurrence with the burning of a structured cloth. These events only produced a small response in the far field HCl sensor, while a PMMA burn that did not produce HCl had a significantly greater response. A ground-based large-scale facility was constructed to flow acid gas at the scale and configuration realized in the Saffire experiments. A CFD model of this duct was constructed to test kinetic parameters developed in this work at a larger scale and different geometric configuration and to predict the results of the large-scale facility. The models developed in this work were used to interpret the results of the microgravity tests and lead the discussion on what further experiments and models are needed in order to predict the fate of acid gas in a spacecraft environment. To summarize, the major contributions of this work are as follows: the capacity to uptake HCl, with and without the presence of water vapor, was measured for a variety of real spacecraft surfaces. Several different models (single reactor-scale, multiscale, spacecraft-scale) were developed and with the aid of modeling, the rate of uptake for those surfaces was also predicted and validated. The kinetic parameters determined from the small-scale reactor experiments and models were used to predict large-scale and microgravity tests. Conclusions from this research will be used in the design of spacecraft vehicles and large-scale microgravity fire safety experiments. The models built by this work will aid designers in sensor placement and could be used to predict acid gas transport from fires in partial gravity, as would be seen in Lunar and Martian habitats.
Measurements of Saturn's He 584 A dayglow and the CH4 density profile deduced from stellar occultation data near the homopause have been combined to infer an eddy diffusion coefficient of 8 + or - 4 x 10 to the 7th sq cm/s and a temperature of 125 + 40 or - 25 K near the homopause at Voyager 2 encounter. It appears that the eddy diffusion coefficient may have increased between the Voyager encounters. Saturn's H Ly-alpha dayglow is qualitatively compatible with this increase and the interpretation of the He 584 A dayglow and CH4 absorption measurement.
The discovery of a microsignatury of trapped radiation in the Amalthea orbit as detected by Pioneer 11 in a flyby of Juptier in 1974 is reported and its implications for the radial diffusion coefficient in Jupiter's inner magnetosphere are discussed. A low energy telescope registered the absorption of low-energy protons as a function of the magnetic L shell durig inbound and outbound trajectories. Drift velocities of the 1 MeV particles were calculated. No correspondingly heightened effects were observed from high-energy electrons or heavier nuclei. Further analysis of the 0.5-8.7 MeV protons showed data to be consistent erosion of the particle drift shadows by a diffusion process. A limit was calculated for the highest diffusion coefficient value for the 1 MeV protons at the Amalthea orbit. The results indicate that the diffusion is driven by fluctuating electric or magnetic fields.