I - Semilinear Expressions for Transport Coefficients

Summary

Diffusion Coefficients and Thermal Conductivities

The heat flow and ambipolar diffusion equations that contain the higher-order transport effects, such as thermal diffusion and diffusion thermal heat flow, are presented in Section 5.14. The transport coefficients that appear in these equations have been calculated using both the linear (4.129a–g) and semilinear (4.132a,b) collision terms. Here, the more general semilinear transport coefficients are presented, which are valid for arbitrarily large temperature differences between the interacting species. These coefficients reduce to the linear coefficients in the limit of small temperature differences, i.e., when (T_s − T_t)/T_st ≪ l.

The general expressions for the ion and neutral heat flows are summarized as follows

where subscripts s and t refer to either ion or neutral species. The thermal conductivities and diffusion thermal coefficients in equations (I.1) and (I.2) are given by

where

Note that a simple change of subscripts in equations (1.3) to (1.10) yields the other transport coefficients that are needed.