Diffusion in equilibrium mixtures of ionized gases

Calculation and application of combined diffusion coefficients in thermal plasmas

The combined diffusion coefficient method is widely used to treat the mixing and demixing of different plasma gases and vapours in thermal plasmas, such as welding arcs and plasma jets. It greatly simplifies the treatment of diffusion for many gas mixtures without sacrificing accuracy. Here, three subjects that are important in the implementation of the combined diffusion coefficient method are considered. First, it is shown that different expressions for the combined diffusion coefficients, arising from different definitions for the stoichiometric coefficients that assign the electrons to the two gases, are equivalent. Second, an approach is presented for calculating certain partial differential terms in the combined temperature and pressure diffusion coefficients that can cause difficulties. Finally, a method for applying the combined diffusion coefficients in computational models, which typically require diffusion to be expressed in terms of mass fraction gradients, is given.

Elemental transport coefficients in viscous plasma flows near local thermodynamic equilibrium

We propose a convenient formulation of elemental transport coefficients in chemically reacting and plasma flows locally approaching thermodynamic equilibrium. A set of transport coefficients for elemental diffusion velocities, heat flux, and electric current is introduced. These coefficients relate the transport fluxes with the electric field and with the spatial gradients of elemental fractions, pressure, and temperature. The proposed formalism based on chemical elements and fully symmetric with the classical transport theory based on chemical species, is particularly suitable to model mixing and demixing phenomena due to diffusion of chemical elements. The aim of this work is threefold: to define a simple and rigorous framework suitable for numerical implementation, to allow order of magnitude estimations and qualitative predictions of elemental transport phenomena, and to gain a deeper insight into the physics of chemically reacting flows near local equilibrium.

Analytical formulation of chemical derivatives in equilibrium plasma flows

Chemical derivatives are used in the mathematical modeling of transport phenomena in equilibrium plasma flows when chemical element diffusion and mixing or demixing effects are accounted for. They measure the variation of mixture chemical composition in response to changes in element fractions, pressure, or temperature. Currently, these quantities are calculated numerically, using finite differences. This approach, other than being computationally expensive and prone to numerical error, does not provide any insight into flow physics. Our work is aimed at introducing a fully analytical method for the calculation of chemical derivatives which bypasses the computational cost. It also provides a simple means of estimating their order of magnitude.

Probing instabilities in arc plasma devices using binary gas mixtures

This paper presents an experimental approach to identify the sources of instabilities in arc plasma devices. The phenomena of demixing in arcs have been utilized to explore the characteristics of different instabilities. Problems in explaining the observed behavior with our current understanding of the phenomena are discussed. Hydrogen is used as a secondary gas with argon as the primary plasma gas for this study. Results indicate that the observed behavior such as steady, takeover, and restrike modes of instabilities in arcs may essentially originate from the thin boundary layer over the anode wall primarily at the location of the anodic arc root. The bulk core flow apparently does not play any significant role in such instabilities. Arc currents rather than flow rates control the behavior of the instabilities in frequency space. Bifurcation of the system behavior and evidence for the existence of quadratic zones in flow space of binary gas mixtures separating steady and unsteady behavior are discussed.

Closed form for the equations of chemically reacting flows under local thermodynamic equilibrium

We present a closed form for the governing equations of chemically reacting flows under local thermodynamic equilibrium, which rigorously takes into account effects of elemental (de)mixing. To this end, we show that when chemistry is fast, the diffusion fluxes of elements and species enthalpies can be expressed as explicit linear functions of gradients of elemental mass fractions and temperature. Our formulation is a natural extension of classical work on local equilibrium flows by other authors and yields results equivalent with a recent fully rigorous mathematical theory in a straightforward and physically appealing manner. The obtained set of equations is well-suited for numerical implementations and does not require the computationally expensive evaluation of thermodynamic derivatives using finite differences. The new transport coefficients that appear in the equations allow quantitative predictions and help to gain deeper insight into the physics of chemically reacting flows at and near local equilibrium.

Diffusion in two-temperature thermal plasmas

Combined diffusion coefficients, which allow species to be grouped into their parent gases, are derived in a thermal plasma in which the kinetic temperature of the electrons is different from that of the heavy species. As in previous calculations of combined diffusion coefficients for a one-temperature plasma, chemical equilibrium is assumed, and a plasma in a mixture of two homonuclear nonreacting gases is treated. Expressions for ambipolar diffusion in a two-temperature plasma are derived. Coupling between the electrons and the heavy species is retained in the calculations. It is confirmed that the values of the diffusion coefficients are consistent with mass conservation, in contrast to previous calculations that were based on a theory in which the electrons and heavy species were decoupled. Illustrative results are presented for a thermal plasma in different mixtures of argon and hydrogen at 1 bar, for temperatures up to 25 000 K and different ratios of electron to heavy species temperature.

Transport properties in a two-temperature plasma: theory and application

An alternate derivation of transport properties in a two-temperature plasma has been performed. Indeed, recent works have shown that the simplified theory of transport properties out of thermal equilibrium introduced by Devoto and then Bonnefoi, very often used in two-temperature modeling, is questionable and particularly does not work when calculating the combined diffusion coefficients of Murphy. Thus, in this paper, transport properties are derived without Bonnefoi's assumptions in a nonreactive two-temperature plasma, assuming chemical equilibrium is achieved. The electron kinetic temperature T(e) is supposed to be different from that of heavy species T(h). Only elastic processes are considered in a collision-dominated plasma. The resolution of Boltzmann's equation, thanks to the Chapman-Enskog method, is used to calculate transport coefficients from sets of linear equations. The solution of these systems allows transport coefficients to be written as linear combinations of collision integrals, which take into account the interaction potential for a collision between two particles. These linear combinations are derived by extending the definition and the calculation of bracket integrals introduced by Chapman et al. to the thermal nonequilibrium case. The obtained results are rigorously the same as those of Hirschfelder et al. at thermal equilibrium. The derivation of diffusion velocity and heat flux shows the contribution of a new gradient, that of the temperature ratio straight theta=T(e)/T(h). An application is presented for a two-temperature argon plasma. First, it is shown that the two-temperature linear combinations of collision integrals are drastically modified with respect to equilibrium. Secondly, the two-temperature simplified theory of transport coefficients of Devoto and Bonnefoi underestimates the electron thermal conductivity with respect to the accurate value at T(e)=20 000 K. Lastly, contrary to the simplified theory of transport coefficients, the diffusion coefficients satisfy the symmetry conditions. An example is given at T(e)=6000 K for different values of straight theta for the diffusion coefficient between electrons and heavy species D(e-Ar) as well as for that between argon atoms and argon ions D(Ar-Ar+).