The characteristics of thermal diffusion

Abstract

When a gas mixture is contained in a vessel in which a steady temperature gradient is maintained, a concentration gradient is in general set up, whose amount is determined by the logarithm of the temperature ratio, and by k_T, the thermal diffusion ratio; the general theory of non-uniform gases gives successive approximations to k_T, and the first of these, [k_T]1, is accurate within a few per cent. The paper discusses the dependence of [k_T]1 on (a) the ratio of the molecular masses; (b) their concentration ratio (c₁ or c₂); (c) the two ratios of the molecular diameters, inferred from the coefficient of viscosity, to their joint diameter, inferred from the coefficient of diffusion; and (d) three parameters depending on the mode of interaction between the unlike molecules. When this interaction is according to the inverse-power law, the three parameters (d) are all expressible in terms of the mutual force index, and [k_T]1, is a function of five independent variables. The general nature of its dependence on these variables is discussed, with particular reference to the end values (for c₁ or c₂ zero) of the thermal diffusion factor α, given by k_T/c₁c₂;these end values involve fewer variables (less by two) than the general values, and their functional character can be represented graphically. It is shown that k_T may be zero not only when c₁ or c₂ is zero, but also for at most one intermediate mixture ratio. Formulae for [k_T]1 appropriate to various special cases are also given.