The /D/ matrix for multicomponent diffusion
Multicomponent diffusion process calculation using eigenvalues of Onsager diffusion matrix
Cooper, A. R., Jr.↗
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Diffusion analysis for two-phase metal-matrix composite
Diffusion controlled filament matrix interaction in a metal matrix composite, where the filaments and matrix comprise a two phase binary alloy system, was mathematically modeled. The problem of a diffusion controlled, two phase moving interface by means of a one dimensional, variable grid, finite difference technique was analyzed. Concentration dependent diffusion coefficients and equilibrium solubility limits were used, and the change in filament diameter and compositional changes in the matrix were calculated as a function of exposure time at elevated temperatures. With the tungsten nickel (W-Ni) system as a model composite system, unidirectional composites containing from 0.06 to 0.44 initial filament volume fraction were modeled. Compositional changes in the matrix were calculated by superposition of the contributions from neighboring filaments. Alternate methods for determining compositional changes between first and second nearest neighbor filaments were also considered. The results show the relative importance of filament volume fraction, filament diameter, exposure temperature, and exposure time as they affect the rate and extent of filament matrix interaction.
Tenney, D. R.↗
Continuous and cyclic thermal exposure induced degradation in boron reinforced 6061 aluminum composites
Boron reinforced 6061 aluminum (B/Al) composite was continuously exposed at 728 K for up to 240 hours and cyclically exposed between 293 K and 728 K for up to 6000 three-minute cycles. Room temperature tensile strengths were measured and the specimens were metallographically examined. The data suggest that, in addition to AlB2 formation, magnesium in the matrix diffused to the reaction layer and formed (Al,Mg)B2. This formation could weaken the matrix and embrittle the reaction layer. Continuous exposure degraded the strength of the B/Al specimens about 28% in 240 hours. However, the fracture mode, one indicative of high strength interfaces, did not change. The strength degradation was attributed to crack initiation in the brittle reaction layer causing stress concentrations in the fibers. Cyclic exposure degraded the strength of the B/Al about 34% in 6000 cycles. The fracture mode of the cyclic exposure specimens showed transition toward a mode characteristic of low interfacial strength. The lower interfacial strengths were attributed to stress fields induced by differential thermal expansion. Cyclic exposure degraded the strength of the B/Al specimens more than continuous exposure for similar cumulative exposure times.
Olsen, G. C.↗
The effect of alloy composition on the mechanism of stress-corrosion cracking of titanium alloys in aqueous environments
A detailed study was made of the relation between the size distribution of Ti3Al particles in a Ti-8Al alloy and the tensile properties measured in air and in saltwater. The size distribution of Ti3Al was varied by isothermal aging for various times at temperatures in the range 770 to 970 K (930 to 1290 F). The aging kinetics were found to be relatively slow. Quantitative measurements of the particle coarsening rate at 920 K (1200 F) showed good agreement with the predicted behavior for coarsening controlled by matrix diffusion, and suggested that the specific free energy of the Ti3Al alpha interface in negligible small. In all cases, the Ti3Al particles were sheared by the glide dislocations. It was concluded that there is a definite correlation between the presence of deformable Ti3Al particles and an alloy's susceptibility to aqueous stress corrosion cracking. Furthermore, the appearance of the surface slip lines and the dislocation substructure in deformed specimens suggest that the specific effect of the Ti3Al particles is to cause a nonhomogeneous planar slip character and an enhanced chemical potential of the slip bands.
Wood, R. A.↗
Analytical solutions of a class of multidimensional Fokker-Planck equations
Analytical representations of the solutions of Kolmogorov's forward (i.e., Fokker-Planck) and backward partial differential equations are obtained by employing Girsanov's (1960) transformation. The equations considered are restricted to those with the drift vector being the gradient of a function and the diffusion matrix being nonsingular and dependent upon time only.
Zhang, Weijian↗
Fuel Cells Utilizing Oxygen From Air at Low Pressures
A fuel cell stack has been developed to supply power for a high-altitude aircraft with a minimum of air handling. The fuel cell is capable of utilizing oxygen from ambient air at low pressure with no need for compression. For such an application, it is advantageous to take oxygen from the air (in contradistinction to carrying a supply of oxygen onboard), but it is a challenging problem to design a fuel-cell stack of reasonable weight that can generate sufficient power while operating at reduced pressures. The present fuel-cell design is a response to this challenge. The design features a novel bipolar plate structure in combination with a gas-diffusion structure based on a conductive metal core and a carbon gas-diffusion matrix. This combination makes it possible for the flow fields in the stack to have a large open fraction (ratio between open volume and total volume) to permit large volumes of air to flow through with exceptionally low backpressure. Operations at reduced pressure require a corresponding increase in the volume of air that must be handled to deliver the same number of moles of oxygen to the anodes. Moreover, the increase in the open fraction, relative to that of a comparable prior fuel-cell design, reduces the mass of the stack. The fuel cell has been demonstrated to operate at a power density as high as 105 W/cm2 at an air pressure as low as 2 psia (absolute pressure 14 kPa), which is the atmospheric pressure at an altitude of about 50,000 ft ( 15.2 km). The improvements in the design of this fuel cell could be incorporated into designs of other fuel cells to make them lighter in weight and effective at altitudes higher than those of prior designs. Potential commercial applications for these improvements include most applications now under consideration for fuel cells.
Cisar, Alan↗
Extrapolation techniques applied to matrix methods in neutron diffusion problems
A general matrix method is developed for the solution of characteristic-value problems of the type arising in many physical applications. The scheme employed is essentially that of Gauss and Seidel with appropriate modifications needed to make it applicable to characteristic-value problems. An iterative procedure produces a sequence of estimates to the answer; and extrapolation techniques, based upon previous behavior of iterants, are utilized in speeding convergence. Theoretically sound limits are placed on the magnitude of the extrapolation that may be tolerated. This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.
Mccready, Robert R↗
Matrix equations of radiation diffusion, 4
The matrices A sup (-1) and T (tau sub O = 0.1 - 1.0) are tabulated, permitting a source function and emission line profile to be easily calculated. It is assumed that the radiation diffuses with complete redistribution in frequency.
Kostyk, R. I.↗
Extrapolation techniques applied to matrix methods in neutron diffusion problems
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Mccready, Robert R↗
Tables of auxiliary functions for the nonconservative Rayleigh phase matrix in semi-infinite atmospheres
Tables of scattering functions and albedo for semiinfinite atmospheres according to nonconservative Rayleigh phase matrix for diffuse radiation computation
Abhyankar, K. D.↗
Optical Sensors for Biomolecules Using Nanoporous Sol-Gel Materials
An important consideration for space missions to Mars is the ability to detect biosignatures. Solid-state sensing elements for optical detection of biological entities are possible using sol-gel based biologically active materials. We have used these materials as optical sensing elements in a variety of bioassays, including immunoassays and enzyme assays. By immobilizing an appropriate biomolecule in the sol-gel sensing element, we have successfully detected analytes such as amino acids and hormones. In the case of the amino acid glutamate, the enzyme glutamate dehydrogenase was the immobilized molecule, whereas in the case of the hormone cortisol, an anti-cortisol antibody was immobilized in the sensing element. In this previous work with immobilized enzymes and antibodies, excellent sensitivity and specificity were demonstrated in a variety of formats including bulk materials, thin films and fibers. We believe that the sol-gel approach is an attractive platform for bioastronautics sensing applications because of the ability to detect a wide range of entities such as amino acids, fatty acids, hopanes, porphyrins, etc. The sol-gel approach produces an optically transparent 3D silica matrix that forms around the biomolecule of interest, thus stabilizing its structure and functionality while allowing for optical detection. This encapsulation process protects the biomolecule and leads to a more "rugged" sensor. The nanoporous structure of the sol-gel matrix allows diffusion of small target molecules but keeps larger, biomolecules immobilized in the pores. We are currently developing these biologically active sol-gel materials into small portable devices for on-orbit cortisol detection
Fang, Jonathan↗
Oxidation of Silicon Particles Suspended in Mullite Matrix With Dual-Mode Vacancy Diffusion of Oxygen
Mullite bond coats filled with silicon particles have recently been proposed for the next generation of environmental barrier coatings (EBCs). The sacrificial oxidation of the silicon particles eliminates some of the environmental durability issues associated with traditional EBC designs. To investigate this novel design approach, a mathematical formulation and resulting numerical method have been developed for simulating the oxidation of silicon particles embedded in a mullite matrix. The focus is on the oxidation of the silicon in a dry oxygen environment where the oxidant is presumably oxygen. Oxygen transport from the exterior environment through the mullite is assumed to occur via two lattice defect diffusion mechanisms. As a result, the rate of oxygen transport is dictated by the self-diffusivity of the lattice defects. The numerical method is implemented using the COMSOL Multiphysics® program (COMSOL, Inc.). The method is applied to simulate the oxidation of silicon particles in a mullite pellet in recent oxidation experiments. Numerical results compare favorably with the oxidation behavior observed in the oxidation experiments. The numerical method is also used to investigate the effects of various features of the mullite-silicon particle system on the oxidation behavior.
silicon oxidation↗
Dynamics of moisture diffusion through a partially liquid filled porous matrix.
Models for unsteady water transport in fuel cell configurations of Bacon-Pratt and Whitney type are derived. Tests with a specially constructed isothermal cell producing no water and order of magnitude analysis show that diffusion through the liquid alone cannot account for the observed behavior. An analytical solution which includes diffusion in both the liquid and the gas spaces of the matrix is in better agreement with the data than models which consider diffusion in either the liquid or in the gas phase alone.
Murty, B. G. K.↗
Matrix Resin Characterization in Cured Graphite Composites Using Diffuse Reflectance-Ftir
The chemical characterization of cured graphite fiber reinforced polymer matrix composites is complicated by the fact that the resins are insoluble and the composites are apaque. Standard analyses which depend either on the ability to dissolve the sample or to detect transmitted radiation are impossible. As a result, data reported on environmentally exposed composites primarily concern macroscopic information such as weight loss or changes in selected mechanical properties. Diffuse reflectance in combination with fourier transform infrared spectroscopy was developed to gain a basic chemical understanding of composite and adhesive behavior. Several composite and adhesive materials were characterized before and after environmental exposure. In each case significant changes in resin molecular structure were observed and correlated with changes in mechanical properties, providing new insights into material performance.
Young, P. R.↗
Oxygen Diffusion and Reaction Kinetics in Continuous Fiber Ceramic Matrix Composites
Previous stressed oxidation tests of C/SiC composites at elevated temperatures (350 C to 1500 C) and sustained stresses (69 MPa and 172 MPa) have led to the development of a finite difference cracked matrix model. The times to failure in the samples suggest oxidation occurred in two kinetic regimes defined by the rate controlling mechanisms (i.e. diffusion controlled and reaction controlled kinetics). Microstructural analysis revealed preferential oxidation along as-fabricated, matrix microcracks and also suggested two regimes of oxidation kinetics dependent on the oxidation temperature. Based on experimental results, observation, and theory, a finite difference model was developed. The model simulates the diffusion of oxygen into a matrix crack bridged by carbon fibers. The model facilitates the study of the relative importance of temperature, the reaction rate constant, and the diffusion coefficient on the overall oxidation kinetics.
Halbig, Michael C.↗
A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment
The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.
Tenney, D. R.↗
A Hybrid Parallel Preconditioning Algorithm For CFD
A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.
Barth,Timothy J.↗
Creep of oxide dispersion strengthened materials /with special reference to T-D nichrome/
Analyses of oxide dispersion strengthened (ODS) alloys shows that their characteristics are mainly due to the creep behavior of the matrix material. Diffusion-controlled slip creep is established as the rate-controlling process in the alloys investigated, with the glide and climb of edge dislocations associated with the subgrain structure as barriers being the specific rate-controlling step. It is found that the stable subgrain size in ODS alloys is usually associated with the spacing between particles 500-1000 A in size, and that their creep behavior is distinguished from that of the matrix material by the existence of a threshold stress that is not well defined microscopically but appears to be related to particles of less than 500 A size.
Lin, J.↗