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 diffusion coefficients introduced by Murphy at equilibrium in a two-temperature model (electron temperature T(e) different from that of heavy species T(h)) such as that defined by Devoto or Bonnefoi for transport properties. Murphy's coefficients describe the diffusive mixing of two non reactive ionized gases while the Devoto's or Bonnefoi's simplified theories allow the calculation of transport coefficients (except diffusion) out of thermal equilibrium. It has to be noticed that in the latter case when Te tends towards Til, the results are those obtained with an equilibrium calculation. The two-temperature (2-T) theory of transport properties was established by separating electrons and other species because of their mass difference. First, the exact combined diffusion coefficients of Murphy are calculated for an Ar-N(2) (50wt%) mixture at atmospheric pressure. Then, expressions of combined diffusion coefficients are obtained using the simplified theory of Bonnefoi. The results of the calculation of combined diffusion coefficients from the simplified theory of transport properties, assuming equilibrium is achieved (T(e) = T(h)), is compared with those of Murphy at equilibrium. It is shown that large discrepancies occur when ionization is important. These results prove that the simplified 2-T theory cannot be used for the treatment of diffusion. Thus, a new theory of transport coefficients has to be developed taking into account the coupling of electrons and heavy species and work is in progress.