分子气体输运系数的分子模拟计算
Using Molecular Simulation to Compute Transport Coefficients of Molecular Gases
摘要：
现有的气体动力学理论是基于一种分析方法，除了最简单的分子外，这种方法对所有分子都变得难以处理。本文提出了一种计算无限稀释极限下分子气体输运性质的简单数值方法。我们提出的方法是近似的，但我们的结果的扩散率$D$，粘度$η$和导热系数$λ$的硬球，Lennard-Jones颗粒和粗糙的硬球，同意与标准（最低阶）Chapman-Enskog的结果。我们还提出了一个Lennard-Jones二聚体模型的氮，没有分析结果。在多原子分子的情况下（我们认为正辛烷），我们的方法仍然很简单，并给出了很好的预测的扩散率和粘度。计算多原子分子的热导率需要近似处理其量子化的内部模式。我们表明，一个众所周知的近似，涉及$λ$到$D$和$η$，产生良好的结果。我们注意到，我们的方法应该产生$D$、$η$和$λ$的精确值的下限。有趣的是，粗糙硬球的最复杂的（高阶）Chapman-Enskog结果似乎违反了这个界限。
英文摘要：
The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the limit of infinite dilution. The approach that we propose is approximate, but our results for the diffusivity $D$, the viscosity $η$ and the thermal conductivity $λ$ of hard spheres, Lennard-Jones particles and rough hard spheres, agree well with the standard (lowest order) Chapman-Enskog results. We also present results for a Lennard-Jones-dimer model for nitrogen, for which no analytical results are available. In the case of poly-atomic molecules (we consider n-octane), our method remains simple and gives good predictions for the diffusivity and the viscosity. Computing the thermal conductivity of poly-atomic molecules requires an approximate treatment of their quantized internal modes. We show that a well-known approximation that relates $λ$ to $D$ and $η$, yields good results. We note that our approach should yield a lower limit to the exact value of $D$, $η$ and $λ$. Interestingly, the most sophisticated (higher-order) Chapman-Enskog results for rough hard spheres seem to violate this bound.
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