J. Non-Equilib. Thermodyn. 2020; 45(1): 27–38 Research Article Antonio Bertei*, Andrea Lamorgese, and Roberto Mauri Constitutive Relations of Thermal and Mass Difusion https://doi.org/10.1515/jnet-2019-0055 Received July 17, 2019; revised October 17, 2019; accepted October 23, 2019 Abstract: Non-equilibrium thermodynamics provides a general framework for the description of mass and thermal difusion, thereby including also cross-thermal and material difusion efects, which are generally modeled through the Onsager coupling terms within the constitutive equations relating heat and mass fux to the gradients of temperature and chemical potential. These so-called Soret and Dufour coefcients are not uniquely defned, though, as they can be derived by adopting one of the several constitutive relations satisfy- ing the principles of non-equilibrium thermodynamics. Therefore, mass difusion induced by a temperature gradient and heat conduction induced by a composition gradient can be implicitly, and unexpectedly, pre- dicted even in the absence of coupling terms. This study presents a critical analysis of diferent formulations of the constitutive relations, with special focus on regular binary mixtures. It is shown that, among the difer- ent formulations presented, the one which adopts the chemical potential gradient at constant temperature as the driving force for mass difusion allows for the implicit thermo-difusion efect to be strictly absent while the resulting Dufour efect is negligibly small. Such a formulation must be preferred to the other ones since cross-coupling efects are predicted only if explicitly introduced via Onsager coupling coefcients. Keywords: constitutive relations, chemical potential, regular mixtures, thermo-difusion 1 Introduction Mass difusion and heat conduction are central phenomena in many subjects of physics and engineering, including evaporation [1, 2], phase separation [3, 4], distillation [5], drying [6], and many other applications and processes. Mass difusion deals with the transport of chemical species, typically (but not necessarily) from regions of high concentration to regions of low concentration until chemical equilibrium is reached with uniform chemical potentials. Heat conduction refers to how internal energy is transferred within a medium to establish thermal equilibrium, typically moving from high temperature to low temperature. The most simplistic phenomenological constitutive equations for mass and heat transfer, namely, Fick and Fourier laws, provide a linear relationship between fuxes and driving forces, or more specifcally, be- tween mass fux and concentration gradient for mass transfer and between heat fux and temperature gradi- ent for heat transfer [7]. Due to such a similar mathematical formulation, the term “difusion” is used to refer to both mass difusion and thermal difusion (i. e., heat conduction) [7]. The genesis of such constitutive difusion equations, which were originally formulated based on empir- ical arguments, can be systematized through non-equilibrium thermodynamics [8–10]. In particular, non- equilibrium thermodynamics provides a general framework for the mesoscopic description of irreversible phenomena, such as (but not limited to) mass and thermal difusion. As recalled later on in the paper, the constitutive equations of mass and thermal difusion emerge naturally (but not univocally) from the entropy formulation of the second law of thermodynamics [8–11]. More specifcally, according to the entropy produc- *Corresponding author: Antonio Bertei, Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 2, 56122 Pisa, Italy, e-mail: antonio.bertei@unipi.it, ORCID: https://orcid.org/0000-0002-3202-6825 Andrea Lamorgese, Roberto Mauri, Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 2, 56122 Pisa, Italy, e-mails: andrea.lamorgese@unipi.it, roberto.mauri@unipi.it