Consolidated theory of fluid thermodiffusion

TL;DR

This paper introduces a comprehensive thermodiffusion model based on Onsager--Stefan--Maxwell equations that accurately describes heat and mass transfer in multicomponent fluids, preserving thermodynamic consistency and enabling detailed simulations.

Contribution

It develops a unified, thermodynamically consistent framework for multicomponent thermodiffusion that extends classical laws and provides practical tools for simulations and data tabulation.

Findings

The new equations preserve the structure of isothermal Stefan--Maxwell laws.

The transport-coefficient matrix is symmetric with simple spectral properties.

Numerical simulations demonstrate the framework's applicability to ternary gas diffusion.

Abstract

We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the isothermal Stefan--Maxwell equations, separating the thermodynamic forces that drive diffusion from the force that drives heat flow. The Onsager--Stefan--Maxwell transport-coefficient matrix is symmetric, and the second law of thermodynamics imbues it with simple spectral characteristics. This new approach allows for heat to be considered as a pseudo-species and proves equivalent to both the intuitive extension of Fick's law and the generalized Stefan--Maxwell equations popularized by Bird, Stewart, and Lightfoot. A general inversion process facilitates the unique formulation of flux-explicit transport equations relative to any choice of convective reference velocity. Stefan--Maxwell diffusivities and thermal diffusion factors are tabulated for gaseous mixtures containing helium, argon, neon, krypton, and xenon. The framework is deployed to perform numerical simulations of steady three-dimensional thermodiffusion in a ternary gas.