Gauge-invariant approach to thermodiffusion in a liquid binary mixture

The paper aims at a molecular understanding of thermodiffusion (the Ludwig–Soret effect) in a liquid binary mixture. To this end, we first review the capabilities of the Maxwell–Stefan description of interdiffusion, which in a liquid rests upon the use of a thermodynamic force. The latter is defined here as a force per particle which generalizes the mechanical force and obeys Newton’s third law. Moreover, the force is required to be invariant under changes of the energy and entropy gauges. The gauge-invariant force thus defined is found to account for ordinary diffusion and barodiffusion, but not for thermodiffusion. The force driving thermodiffusion arises from Onsager’s reciprocity theorem in non-equilibrium thermodynamics: it is shown to be proportional to the covariance of enthalpy and velocity. In case that intermolecular collisions are elastic, an explicit kinetic expression is given of the force driving thermodiffusion; it involves the interaction cross-section of the two components and the mean-free-path function of the liquid mixture. That expression is equivalent to, but much simpler than, the Chapman–Enskog result in gaseous mixtures, and it qualitatively accounts for observations performed in liquid mixtures. The role of the internal degrees of freedom of the molecules is brought out. Finally, two pragmatic rules for devising models of thermodiffusion are enunciated.