Thermodynamic Theory of Diffusion and Thermodiffusion Coefficients in Multicomponent Mixtures

Transport coefficients (like diffusion and thermodiffusion) are the key parameters to be studied in non-equilibrium thermodynamics. For practical applications, it is important to predict them based on the thermodynamic parameters of a mixture under study: pressure, temperature, composition, and thermodynamic functions, like enthalpies or chemical potentials. The current study develops a thermodynamic framework for such prediction. The theory is based on a system of physically interpretable postulates; in this respect, it is better grounded theoretically than the previously suggested models for diffusion and thermodiffusion coefficients. In fact, it translates onto the thermodynamic language of the previously developed model for the transport properties based on the statistical fluctuation theory. Many statements of the previously developed model are simplified and amplified, and the derivation is made transparent and ready for further applications. The n(n+1)/2 independent Onsager coefficients are reduced to 2n+1 determining parameters: the emission functions and the penetration lengths. The transport coefficients are expressed in terms of these parameters. These expressions are much simplified based on the Onsager symmetry property for the phenomenological coefficients. The model is verified by comparison with the known expressions for the diffusion coefficients that were previously considered in the literature.

Thermoelectric Thomson Relations Revisited for a Linear Energy Converter

In this paper we revisit the classic thermocouple model, as a Linear Irreversible Thermodynamic (LIT) energy converter. In this model we have two types of phenomenological coefficients: the first comes from some microscopic models, such as the coefficient associated with the electric conductivity, and the second comes from experimental facts, such as the coefficient associated with the Seebeck power. We show that in the last case, these coefficients can be related to the thermodynamic operation modes of the energy converter. These relations between the experimental phenomenological coefficients and the regimes of performance allow us to propose a first and a second Thomson-type relation, which give us 12 new relations between the Seebeck power, the Peltier heat and the Thomson heat. With this purpose we develop the idea of non-isothermal linear energy converters operated either “directly” (like a heat engine) or “inversely” (like a refrigerator). We analyze the energetics associated to these converters operating under steady states corresponding to different modes of performance, all of them satisfying the fundamental Onsager symmetry relations.

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of$O(N)$, where$N$is the number of parameters used to describe the outer flux surface or coil shapes.

A nonlinear thermodynamic model for a breakdown of the Onsager symmetry and the efficiency of thermoelectric conversion in nanowires

We consider non-equilibrium steady-state situations for thermoelectric systems with non-local and non-linear effects. We show that the Onsager symmetry relations for effective transport coefficients break down. We also estimate the consequences of such a breakdown for the efficiency of the thermoelectric energy conversion which, under some conditions, could be higher than in the usual linear regime with Onsager symmetry.