title: Functional constraints on phenomenological coefficients.
abstract: Thermodynamic fluxes (diffusion fluxes, heat flux, etc.) are often proportional to thermodynamic forces (gradients of chemical potentials, temperature, etc.) via the matrix of phenomenological coefficients. Onsager's relations imply that the matrix is symmetric, which reduces the number of unknown coefficients is reduced. In this article we demonstrate that for a class of nonequilibrium thermodynamic models in addition to Onsager's relations the phenomenological coefficients must share the same functional dependence on the local thermodynamic state variables. Thermodynamic models and experimental data should be validated through consistency with the functional constraint. We present examples of coupled heat and mass transport (thermodiffusion) and coupled charge and mass transport (electro-osmotic drag). Additionally, these newly identified constraints further reduce the number of experiments needed to describe the phenomenological coefficient.
authors.affiliation: Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00, Prague, Czech Republic.
authors.forename: Václav
authors.initials: V
authors.lastname: Klika
authors.affiliation: Mathematical Institute, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75 Prague, Czech Republic and Department of Chemical Engineering, University of Chemistry and Technology Prague, Technická 5, 16628 Prague 6, Czech Republic.
authors.forename: Michal
authors.initials: M
authors.lastname: Pavelka
authors.affiliation: Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Jay B
authors.initials: JB
authors.lastname: Benziger