Definition of frame-invariant Soret coefficients for ternary mixtures

TL;DR

This paper reviews and extends the concept of frame-invariant Soret coefficients from binary to ternary mixtures, emphasizing the importance of concentration prefactors for invariance under reference frame changes.

Contribution

It introduces a matrix-based concentration prefactor for defining frame-invariant Soret coefficients in ternary mixtures, extending the concept beyond binary systems.

Findings

Invariance of Soret coefficients achieved with appropriate prefactors.

Extension of invariance property to ternary and multi-component mixtures.

Guidelines for choosing dependent concentrations and using molar concentrations.

Abstract

The definition of the Soret coefficient of a binary mixture includes a concentration prefactor, $x(1-x)$ when mol fraction $x$ is used, or $w(1-w)$ when mass fraction $w$ is used. In this paper the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the Soret coefficient invariant upon change in the reference frame, either mass or molar. Then, it is shown how this invariance property can be extended to ternary mixtures by using an appropriate concentration prefactor in matrix form. The work is completed with some considerations of general non-isothermal diffusion fluxes, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, use of molar concentrations and, finally, extension to multi-component mixtures.