A Comprehensive Theory of the Soret Effect in a Multicomponent Mixture

Abstract

A comprehensive theory for the Soret effect (also called: Ludwig-Soret effect and thermal diffusion) is presented which incorporates both the thermodynamic contribution and the kinetic contribution. The new theory is an extension of a theory presented in our previous paper (J. Chem. Phys. (1989) 90, 6541) in which the thermodynamic contribution only was modelled. The single assumption of the theory is that the Soret effect in the steady state is the macroscopic state accomplished by a maximum number of microstates with respect to the ideal gas state. The methodology of the new theory, which can be used to model other cross-effects in irreversible thermodynamics, is further validated by application to the textbook case of gravity equilibrium in an isothermal fluid column. As a result, the Soret effect in a multicomponent mixture can be calculated by using input from an equation-of-state of the mixture and kinetic gas theory.

However, it is crucial to critically examine the input data derived from an equation-of-state, particularly if calculations are compared to measurements to draw conclusions about the validity of the theory. The present equations-of-state, even those that are calibrated for use in the chemical and petroleum industry, require modification for the calculation of the Soret effect, because of a higher demand in accuracy. Further research to improve the accuracy of the equation-of-state is recommended, particularly for near-critical conditions. In addition, it is also important to examine which frame of reference (center of volume or center of mass) applies to a particular measurement or practical application, because the frame of reference determines which mathematical expression for the thermal diffusion factor must be used.