The /D/ matrix for multicomponent diffusion
Multicomponent diffusion process calculation using eigenvalues of Onsager diffusion matrix
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Multicomponent diffusion process calculation using eigenvalues of Onsager diffusion matrix
Multicomponent diffusion theory in glasses and application to tektites
Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.
Numerical solutions of the viscous-shock-layer equation where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium are presented. Also the effects of the diffusion model, surface catalysis, and mass injection on surface transport and flow parameters are considered. The flow is treated as a mixture of five inert and thermally perfect species. The viscous-shock-layer equations are solved by using an implicit-difference scheme. All calculations are for hyperboloids with included angles of 20 and 45. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented to show the effects of the chemical models; diffusion models; surface catalysis; and mass injection of air on heat transfer; skin friction; shock standoff distance; wall pressure distribution; and tangential velocity, temperature, and species profiles. The results show that an equilibrium analysis can substantially overpredict the heat-transfer rates for flow conditions experienced by earth-orbital entry vehicles. Moreover, at such conditions surface catalysis significantly influences heat-transfer and flow-field properties. If a binary rather than a multicomponent diffusion model is assumed, negligible errors in most flow properties result. Quantitative results are presented that show the effect of mass injection on flow properties within and downstream of the injection region.
Multicomponent reacting laminar boundary layer in chemical equilibrium solved using Stefan-Maxwell relations
The problem of energy and multicomponent ambipolar diffusion of plasma in the lower ionosphere of a planet with a weak magnetic field is considered.
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Multicomponent gas diffusion is reviewed with particular emphasis on gas flows near solid boundaries-the so-called Kramers-Kistemaker effect. The aim is to derive an appropriate momentum boundary condition which governs many gaseous species diffusing together. The many species' generalization of the traditional single gas condition, either as slip or stick (no-slip), is not obvious, particularly for technologically important cases of lower gas pressures and very dissimilar molecular weight gases. No convincing theoretical case exists for why two gases should interact with solid boundaries equally but in opposite flow directions, such that the total gas flow exactly vanishes. ln this way, the multicomponent no-slip boundary requires careful treatment The approaches discussed here generally adopt a microscopic model for gas-solid contact. The method has the advantage that the mathematics remain tractable and hence experimentally testable. Two new proposals are put forward, the first building in some molecular collision physics, the second drawing on a detailed view of surface diffusion which does not unphysically extrapolate bulk gas properties to govern the adsorbed molecules. The outcome is a better accounting of previously anomalous experiments. Models predict novel slip conditions appearing even for the case of equal molecular weight components. These approaches become particularly significant in view of a conceptual contradiction found to arise in previous derivations of the appropriate boundary conditions. The analogous case of three gases, one of which is uniformly distributed and hence non-diffusing, presents a further refinement which gives unexpected flow reversals near solid boundaries. This case is investigated alone and for aggregating gas species near their condensation point. In addition to predicting new physics, this investigation carries practical implications for controlling vapor diffusion in the growth of crystals used in medical diagnosis (e.g. mercuric iodide) and semiconductors.
Boundary equations obtained for a low Reynolds number, high enthalpy gas flow in regions of velocity slip and temperature jump are presented. The formulation treats, through a first-order distribution function used to include multicomponent diffusion, a multicomponent gas mixture that may be in nonequilibrium with finite-rate catalytic recombination occurring on the wall. In the boundary equations, which are obtained for use in flow-field calculations applicable to low-density flow regimes, a simplified gas/wall interaction is assumed wherein individual atoms or molecules either reflect specularly off the wall or stick and are fully accommodated. Fluxes in terms of evaluated integrals over the distribution function and integrals necessary for determining fluxes are given.
Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.
Computer program calculates rates of deposition by vapor or by small particles. Embodies comprehensive but tractable theory of rates of convective diffusion deposition developed on basis of assumption of multicomponent, chemically-frozen boundary layer. Program written in FORTRAN IV.
The computer program based on multicomponent chemically frozen boundary layer (CFBL) theory for calculating vapor and/or small particle deposition rates is documented. A specific application to perimter-averaged Na2SO4 deposition rate calculations on a cylindrical collector is demonstrated. The manual includes a typical program input and output for users.
Effective binary diffusion coefficients for multicomponent diffusion determined for potassium oxide and SrO in system potassium oxide-SrO- silicon dioxide
Experimental studies of self-diffusion isotopes in silicate melts often have quite large uncertainties when comparing one study to another. We designed an experiment in order to improve the precision of the results by simultaneously studying several elements (Mg, Ca, Sr, Ba) during the same experiment thereby greatly reducing the relative experimental uncertainties. Results show that the uncertainties on the diffusion coefficients can be reduced to 10 percent, allowing a more reliable comparison of differences of self-diffusion coefficients of the elements. This type of experiment permits us to study precisely and simultaneously several elements with no restriction on any element. We also designed an experiment to investigate the possible effects of multicomponent diffusion during Mg self-diffusion experiments by comparing cases where the concentrations of the elements and the isotopic compositions are different. The results suggest that there are differences between the effective means of transport. This approach should allow us to investigate the importance of multicomponent diffusion in silicate melts.
Simplified multicomponent diffusion calculations are made for the ionosphere of Venus. Large differences in temperature between electrons and ions and appreciable temperature gradients that are near those of recent measurements are used. Compositions for which binary thermal diffusion coefficients for ions are the same as multi-ion ones are examined as well as those that are quite different. An attempt to combine binary coefficients to give multi-ions ones has not been particularly successful.
Equations have been obtained for jump (or slip) in the wall values of species concentration, pressure, velocity, and temperature for the low-Reynolds-number high-altitude flight regime of a space vehicle. The analysis, based on the Chapman-Enskog method as applied by Shidlovskiy for a single-species gas, includes multicomponent diffusion with finite-rate surface catalytic recombination. A consistent set of equations is provided for multicomponent, binary, and single species mixtures.
Equations have been obtained for jump (or slip) in the wall values of species concentration, pressure, velocity, and temperature for the low-Reynolds-number high-altitude flight regime of a space vehicle. The analysis, based on the Chapman-Enskog method as applied by Shidlovskiy for a single-species gas, includes multicomponent diffusion with finite-rate surface catalytic recombination. A consistent set of equations is provided for multicomponent, binary, and single species mixtures.
The effects of MCrAl coating-substrate interdiffusion on oxidation life and the general mutliphase, multicomponent diffusion problem were examined. Semi-infinite diffusion couples that had sources representing coatings and sinks representing gas turbine alloys were annealed at 1,000, 1,095, 1,150, or 1,205 C for as long as 500 hours. The source and sink aluminum and chromium contents and the base metal (cobalt or nickel) determined the parabolic diffusion rate constants of the couples and predicted finite coating lives. The beta source strength concept provided a method (1) for correlating beta recession rate constants with composition; (2) for determining reliable average total, diffusion, and constitutional activation energies; and (3) for calculating interdiffusion coefficients.