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+).

This paper presents the first application to an argon atmospheric plasma of a very recent derivation of a two-temperature (2T) transport properties theory, based on the Chapman-Enskog method expanded up to the fourth approximation, where only elastic processes are considered. The kinetic electron temperature Te is assumed to be different from that of heavy species Th, chemical equilibrium being achieved. This new theory, where electrons and heavy species are coupled, allows one to determine 2T diffusion coefficients which was not the case of the previous ones. First, basic definitions of transport fluxes are recalled and a binary diffusion coefficient approximation is defined which involves an asymmetric relationship between these coefficients. Second, a particular care is taken in choosing the most recent data of potential interactions or elastic differential cross sections in order to determine the collision integrals. Third, a convergence study of transport coefficients is led to evaluate the influence of the non-equilibrium parameter θ = Te/Th on this convergence. It is shown that changing θ does not modify the convergence of transport coefficients. Moreover, ordinary and thermal diffusion coefficients, electrical and electron translational thermal conductivities as well as viscosity are displayed as functions of the electron temperature for different values of θ = Te/Th. It is pointed out that the non-equilibrium parameter θ has a non-negligible influence on transport coefficients. Besides, recently, it has been shown that the 2T simplified theory of transport properties, very often used in modelling, does not allow one to achieve mass conservation. Consequently, a comparison is presented between the 2T simplified theory and this new approach. Significant differences are found in the electrical conductivity and the electron translational thermal conductivity.

Thermal plasma flows provide a uniquely high specific enthalpy source that is well suited to transformation of matter, often via phase changes. As a consequence, numerous thermal-plasma-based processes have been developed to, for example, destroy pollutants, modify surfaces (e.g. cutting and welding), synthesize nanostructures and deposit functionalized nanostructured coatings. In many cases, departures from equilibrium (both thermal and chemical) occur in regions of such plasmas; for example, in electrode erosion phenomena or in the injection of a liquid into a plasma jet. This paper reviews the treatment of non-equilibrium phenomena in thermal plasma flows, in particular the methods of calculation of the composition and transport coefficients of non-equilibrium plasmas, which are required for modelling the above processes. The focus is on two-temperature plasmas, in which electrons and heavy species are at different temperatures. Methods of calculation of the composition of plasmas both in local chemical equilibrium (LCE) and out of LCE are presented. A comparison of the different methods shows large discrepancies, even assuming LCE. Two-temperature transport coefficients obtained from simplified expressions, from the modified Chapman–Enskog method and from the Stefan–Maxwell relations are presented, as well as examples focusing on the influence of plasma composition. Different methods of calculation of the collision integrals required in determining the transport coefficients are also reviewed. Particular attention is paid to diffusion, in particular to the combined diffusion coefficient method, which simplifies treatment of plasmas in LCE. The method of calculation of the reactive thermal conductivity and the influence of excited states on transport coefficients are also addressed in some detail.