# CALCULATION OF COMBINED DIFFUSION COEFFICIENTS FROM THE SIMPLIFIED THEORY OF TRANSPORT PROPERTIES

**V. Rat**

PCTS -CNRS UMR 6638, University of Limoges, 123 av. A. Thomas, 87060 Limoges cedex, France

**P. Andre**

Laboratoire Arc Electrique et Plasmas Thermiques CNRS FRE 3120, Phys. Bât. 5 - Université Blaise Pascal, Aubière Cedex, France; and P.R.E.S. Clermont Université, Clermont-Ferrand Cedex 1, France

**Jacque Aubreton**

SPCTS University of Limoges, 123 av. A. Thomas, 87060 Limoges cedex, France

**M. F. Elchinger**

SPCTS University of Limoges, 123 av. A. Thomas, 87060 Limoges cedex, France

**Pierre Fauchais**

Laboratoire Sciences des Procedes Ceramiques et de Traitements de Surface UMR CNRS 6638 University of Limoges 123 avenue Albert Thomas, 87060 LIMOGES - France

**A. Lefort**

Laboratoire Arc Electrique et Plasmas Thermiques, Université Blaise Pascal, CNRS UMR 6069, 24 avenue des Landais, F63177 Aubiére Cedex, France

## Abstract

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 T_{e} tends towards T_{h}, 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.