Thermal Diffusion Coefficient in Multi-component Mixture Expressed in Terms of Binary Thermal Diffusion Factors and Binary Diffusion Coefficients

Abstract

The thermal diffusion coefficients D_i ^T(v) in multi(v)-component mixture are given as the ratio of two determinants by Hirschfelder et al. In order to express thermal diffusion coefficients as a linear function of binary thermal diffusion factor α_Tij ⁽²⁾, we enumerate four candidates of the function extended from the relation between thermal diffusion coefficient and thermal diffusion factor in binary mixture. The four candidates were checked analytically by two points: (1) it must be equal to the relation for binary mixture when the system can be regarded nearly as binary mixture, and (2) summation of thermal diffusion coefficients must be zero, and only the following passed the check:

where ρ is the total density. C the total molar concentration, D _ij ⁽²⁾ the binary diffusion coefficient, M _k, and X _k, are molar weight and mole fraction of the k-th component, respectively. For 3-component argon 36–38-40 isotope mixture and for 4-component xenon isotope 129–131-132-134 mixture, the temperature and composition dependences obtained from this linear relation were equal to those from the thermal diffusion coefficients given by Hirschfelder et al.

KEYWORDS:

• thermal diffusion coefficient
• thermal diffusion factor
• diffusion coefficient
• multi-component mixture
• argon isotopes
• xenon isotopes
• thermal diffusion column
• thermal diffusivity
• temperature dependence
• composition dependence