Constitutive relations of thermal and mass diffusion

Non-equilibrium thermodynamics provides a general framework for the description of mass and thermal diffusion, thereby including also cross-thermal and material diffusion effects, which are generally modeled through the Onsager coupling terms within the constitutive equations relating heat and mass flux to the gradients of temperature and chemical potential. These so-called Soret and Dufour coefficients are not uniquely defined, though, as they can be derived by adopting one of the several constitutive relations satisfying the principles of non-equilibrium thermodynamics. Therefore, mass diffusion induced by a temperature gradient and heat conduction induced by a composition gradient can be implicitly, and unexpectedly, predicted even in the absence of coupling terms. This study presents a critical analysis of different formulations of the constitutive relations, with special focus on regular binary mixtures. It is shown that, among the different formulations presented, the one which adopts the chemical potential gradient at constant temperature as the driving force for mass diffusion allows for the implicit thermo-diffusion effect to be strictly absent while the resulting Dufour effect is negligibly small. Such a formulation must be preferred to the other ones since cross-coupling effects are predicted only if explicitly introduced via Onsager coupling coefficients.