Klika Václav, Pavelka Michal, Benziger Jay B
Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00, Prague, Czech Republic.
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.
Phys Rev E. 2017 Feb;95(2-1):022125. doi: 10.1103/PhysRevE.95.022125. Epub 2017 Feb 21.
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.
热力学通量（扩散通量、热通量等）通常通过唯象系数矩阵与热力学力（化学势梯度、温度等）成正比。昂萨格关系表明该矩阵是对称的，这使得未知系数的数量减少。在本文中，我们证明对于一类非平衡热力学模型，除了昂萨格关系外，唯象系数对局部热力学状态变量必须具有相同的函数依赖关系。热力学模型和实验数据应通过与函数约束的一致性来验证。我们给出了热质耦合传输（热扩散）和电荷与质量耦合传输（电渗拖拽）的例子。此外，这些新确定的约束进一步减少了描述唯象系数所需的实验数量。
