Duality principle from rarefied to dense gas and extended thermodynamics with six fields
Duality principle from rarefied to dense gas and extended thermodynamics with six fields
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DOI：
10.1103/physrevfluids.2.013401
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发表时间：
2017-01-19
影响因子：
2.7
通讯作者：
Sugiyama, Masaru
中科院分区：
文献类型：
--
作者：
Arima, Takashi;Ruggeri, Tommaso;Sugiyama, Masaru
本文提出了一个耗散稠密气体的扩展热力学理论。特别是，我们研究了ET理论与六个领域，我们忽略剪切粘度和导热系数。我们假定稀薄气体和稠密气体之间的一个简单的对偶原理。这一原理是基于分子运动不同模式之间能量交换的微观分析。方程的基本系统满足所有的原则ET，即伽利略不变性，熵原理，和热力学稳定性（熵凸性），并在稀薄气体的ET理论，本构方程是完全由热和热量状态方程。该系统是最简单的欧拉系统后，但与欧拉系统相比，我们可能有一个整体光滑的解决方案，由于该系统是耗散对称双曲，并满足所谓的K条件。出现了两种非平衡温度，一种是由于分子的平移模，另一种是由于分子的内部模式，如旋转和振动。这种观点使我们能够更清楚地理解动压的起源。此外，我们评估的特征速度与双曲系统和地址的波动耗散关系的体积粘度。作为一个典型的例子，我们分析了货车德瓦尔斯流体的基础上，目前的理论。
We present an extended thermodynamics (ET) theory of dissipative dense gases. In particular, we study the ET theory with six fields, where we neglect shear viscosity and heat conductivity. We postulate a simple principle of duality between rarefied and dense gases. This principle is based on the microscopic analysis of the energy exchange between different modes of the molecular motion. The basic system of equations satisfies all principles of ET, that is, Galilean invariance, entropy principle, and thermodynamic stability (entropy convexity), and, as in the ET theory of rarefied gases, the constitutive equations are completely determined by the thermal and caloric equations of state. The system is simplest after the Euler system, but, in contrast to the Euler system, we may have a global smooth solution due to the fact that the system is dissipative symmetric hyperbolic and satisfies the so-called K condition. There emerge two nonequilibrium temperatures; one is due to the translational modes, and the other is due to the internal modes such as rotation and vibration of a molecule. This viewpoint allows us to understand the origin of the dynamic pressure in a more clear way. Furthermore we evaluate the characteristic velocities associated with the hyperbolic system and address the fluctuation-dissipation relation of the bulk viscosity. As a typical example, we analyze van der Waals fluids based on the present theory.