Remarks concerning the Phase Rule

Rysselberghe, Pierre Van

doi:10.1021/j150336a009

Cited by 4 publications

(2 citation statements)

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“…Transport in the nonlinear region, has been largely studied both experimentally and theoretically. In particular, many theories, based on the Fourier expansion of the transport coefficients in terms of the thermodynamic forces, have been proposed (see, for example, refs [7], [8] and [9]). The theoretical predictions are however in disagreement with the experiments and this is mainly due to the fact that, in the series expansion, the terms of superior order are greater than those of inferior order.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear closure relations theory for transport processes in nonequilibrium systems

Sonnino

2009

Phys. Rev. E

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A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ("Onsager") transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

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Section: Introductionmentioning

confidence: 99%

Nonlinear closure relations theory for transport processes in nonequilibrium systems

Sonnino

2009

Phys. Rev. E

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“…According to the Clausius-Mossotti equation [19], dielectric constant is proportional to the density of complex, to which the permittivity test results at different frequencies with temperature variation conform. The permittivity behaviors of complex 1 and 2 are normal and in terms of the overall structures.…”

Section: Dielectric Constantsmentioning

confidence: 99%