Moratto Valdemar, Kremer Gilberto M
Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 May;91(5):052139. doi: 10.1103/PhysRevE.91.052139. Epub 2015 May 26.
In this work we study an r-species mixture of gases within the relativistic kinetic theory point of view. We use the relativistic covariant Boltzmann equation and incorporate the Schwarzschild metric. The method of solution of the Boltzmann equation is a combination of the Chapman-Enskog and Grad representations. The thermodynamic four-fluxes are expressed as functions of the thermodynamic forces so the generalized expressions for the Navier-Stokes, Fick, and Fourier laws are obtained. The constitutive equations for the diffusion and heat four-fluxes of the mixture are functions of thermal and diffusion generalized forces which depend on the acceleration and the gravitational potential gradient. While this dependence is of relativistic nature for the thermal force, this is not the case for the diffusion forces. We show also that the matrix of diffusion coefficients is symmetric, implying that the thermal-diffusion equals the diffusion-thermal effect, proving the Onsager reciprocity relations. The entropy four-flow of the mixture is also expressed in terms of the thermal and diffusion generalized forces, so its dependence on the acceleration and gravitational potential gradient is also determined.
在这项工作中，我们从相对论动力学理论的角度研究了一种r种气体的混合物。我们使用相对论协变玻尔兹曼方程并纳入史瓦西度规。玻尔兹曼方程的求解方法是查普曼-恩斯科格表示法和格拉德表示法的结合。热力学四通量被表示为热力学力的函数，从而得到了纳维-斯托克斯、菲克和傅里叶定律的广义表达式。混合物的扩散和热四通量的本构方程是热和扩散广义力的函数，这些广义力取决于加速度和引力势梯度。虽然这种依赖关系对于热力来说具有相对论性质，但对于扩散力则并非如此。我们还表明，扩散系数矩阵是对称的，这意味着热扩散等于扩散热效应，从而证明了昂萨格互易关系。混合物的熵四流也用热和扩散广义力来表示，因此也确定了它对加速度和引力势梯度的依赖关系。
