Calculation of combined diffusion coefficients from the simplified theory of transport properties

The aim of this study is to check if it is possible to use the combined dif fusion coefficients introduced by Murphy at equilibrium in a two-temperatur e model (electron temperature T-e different from that of heavy species T-h) , such as that defined by Devoto and Bonnefoi for transport properties. On the one hand, the two-temperature (2-T) theory of transport properties was established by Devote and Bonnefoi by separating electrons and heavy specie s because of their mass difference. Their simplified theories allow the cal culation of transport coefficients (except diffusion) out of thermal equili brium, but it has to be noted that when T, tends toward T-h, the results ar e those obtained with an equilibrium calculation. On the other hand, Murphy 's combined diffusion coefficients describe the diffusive mixing of two non reactive ionized gases at equilibrium. First, the exact combined diffusion coefficients of Murphy ale calculated for an Ar-N-2 (50 wt.%) mixture at at mospheric pressure. Expressions of combined diffusion coefficients are then obtained by using the simplified theory of Bonnefoi at thermal equilibrium . The results of the calculation of combined diffusion coefficients from th e simplified theory of transport proper ties, assuming T-e = T-h, are compa red with those of Murphy at equilibrium. rt is shown that large discrepanci es occur as soon as the ionization degree is over 10%. These results prove that the simplified 2-T theory of transport coefficients cannot be used for the treatment of diffusion, probably because the mass flux of electrons is no longer constrained. Thus, a new theory of transport coefficients has to be developed taking into account the coupling of electrons and heavy speci es.