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Nonequilibrium thermodynamics of multicomponent fluids

多组分流体的非平衡热力学

基本信息

批准号：
09640458
负责人：
KITAHARA Kazuo
金额：
$ 1.15万
依托单位：
International Christian University (1998)Tokyo Institute of Technology (1997)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

We obtained the general evolution equations for the density and mass flux of each component of a multicomponent fluid on the basis of conservation laws and irreversibility, which are required from the thermodynamic laws, as summarized in the Miyazaki-Kitahara-Bedeaux paper and in the book. The idea is that in a multicomponent fluid, internal energy is no more a conservative quantity, but the total energy including the kinetic energy of mass fluxes is conserved. Thus the Gibbs relation is generalized in terms of total energy density. Then the momentum densities ( mass flux densities) enter into the Gibbs relation. Then we derived linear irreversible thermodynamics in terms of intensive parameters, which appear in the generalized Gibbs relation. Furthermore, assuming the reversible part of the evolution equation has a symplectic property, which automatically satisfies the condition of no entropy production, we derived the reversiblepart of the evolution equation, which was not known for the mass flux of multicomponent fluids. Since our formulation is based on the entorpy concept, we generalized Boltzmann-Einstein principle to none quilibrium fluctuation of multicomponent fluids. Especially, thespatial correlation in nonequilibrium reaction-diffusion systems was studied in detail together with computer simulations. Finally, in the frame of linear hydrodynamics, we proved the thermodynamic results are correct from the microscopic Liouville formalism.

我们得到的一般演化方程的密度和质量通量的每一个组成部分的多组分流体的基础上的守恒定律和不可逆性，这是需要从热力学定律，总结在宫崎北原贝多纸和书。其思想是，在多组分流体中，内能不再是保守量，但总能量包括质量通量的动能是守恒的。因此，吉布斯关系是广义的总能量密度。然后动量密度（质量通量密度）进入吉布斯关系。在此基础上，我们导出了广义吉布斯关系式中的强度参数表示的线性不可逆热力学。此外，假设演化方程的可逆部分具有辛性质，自动满足无熵产生的条件，我们推导出了演化方程的可逆部分，这在多组分流体的质量通量中是未知的。由于我们的公式是基于内托概念，我们推广玻尔兹曼-爱因斯坦原理的非平衡多组分流体的波动。特别是对非平衡反应扩散系统中的空间相关性进行了详细的研究，并进行了计算机模拟。最后，在线性流体力学的框架下，从微观刘维尔形式证明了热力学结果的正确性。