Eu Byung Chan
Department of Chemistry, McGill University, 801 Sherbrooke St. West, Montreal, Quebec H3A 2K6, Canada.
J Chem Phys. 2008 Sep 7;129(9):094502. doi: 10.1063/1.2971039.
In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.
在不可逆热力学和流体力学的传统理论中，比容和摩尔体积在纯流体中一直被交替使用，但在本研究中我们表明它们应相互区分，并赋予独特的统计力学表示。在本文中，我们通过使用Voronoi体积及其平均值（可视为摩尔域（体积））以及体积通量的统计力学表示，给出了分子域（体积或空间）的统计力学表示的通用公式。通过使用它们的统计力学公式，从流体的广义玻尔兹曼方程推导出体积输运的演化方程。体积输运演化方程的近似解给出了分子域的动力学理论公式、摩尔域（体积）和体积通量的本构方程以及与体积输运相关的能量耗散。与前文得到的流体平均速度的本构方程一起，体积输运演化方程不仅为流体中的不可逆现象提供了新的视角和深入理解，而且能够以流体动力学和不可逆热力学中前所未有的方式应用于研究流体流动问题。它们在广义流体动力学中的作用将在后续讨论。
