Consolidated theory of fluid thermodiffusion

Abstract

We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids by treating heat as a pseudo-component. 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 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 allows 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.