Pieprzyk Sławomir, Brańka Arkadiusz C, Heyes David M, Bannerman Marcus N
Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland.
Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.
Phys Rev E. 2024 May;109(5-1):054119. doi: 10.1103/PhysRevE.109.054119.
Hard-sphere (HS) shear, longitudinal, cross, and bulk viscosities and the thermal conductivity are obtained by molecular dynamics (MD) simulations, covering the entire density range from the dilute fluid to the solid crystal near close-packing. The transport coefficient data for the HS crystal are largely new and display, unlike for the fluid, a surprisingly simple behavior in that they can be represented well by a simple function of the density compressibility factor. In contrast to the other four transport coefficients (which diverge), the bulk viscosity in the solid is quite small and decreases rapidly with increasing density, tending to zero in the close-packed limit. The so-called cross viscosity exhibits a different behavior to the other viscosities, in being negative over the entire solid range, and changes sign from negative to positive on increasing the density in the fluid phase. The extent to which the viscosity tensor and thermal conductivity of the HS crystal can be represented by revised Enskog theory (RET) is investigated. The RET expressions are sums of an instantaneous (I), a kinetic (K), and a so-called α part. The I part of the transport coefficients evaluated directly by MD are statistically indistinguishable from those of the corresponding kinetic theory (Enskog and RET) expressions. For the K part the integral over the spatial two-particle distribution function at contact was determined and the α part was estimated using the direct correlation function and density functional theory approximations. All three parts were determined in this work which allowed the accuracy of RET for solid systems to be assessed rigorously. It is found that in the case of the thermal conductivity the predictions of RET are in excellent agreement with the MD results. Also, for the shear viscosity the agreement over the entire solid phase is quite good but is considerably worse for the three remaining viscosities in the solid phase.
通过分子动力学（MD）模拟获得了硬球（HS）的剪切黏度、纵向黏度、横向黏度、体黏度以及热导率，涵盖了从稀流体到接近密堆积的固体晶体的整个密度范围。HS晶体的输运系数数据大多是新的，并且与流体不同，显示出一种惊人的简单行为，即它们可以用密度压缩因子的简单函数很好地表示。与其他四个发散的输运系数相比，固体中的体黏度相当小，并且随着密度的增加而迅速减小，在密堆积极限下趋于零。所谓的横向黏度表现出与其他黏度不同的行为，在整个固体范围内为负，并且在流体相中随着密度的增加从负变为正。研究了HS晶体的黏度张量和热导率可以由修正的恩斯科格理论（RET）表示的程度。RET表达式是一个瞬时（I）部分、一个动力学（K）部分和一个所谓的α部分的总和。通过MD直接评估的输运系数的I部分在统计上与相应动力学理论（恩斯科格和RET）表达式的I部分无法区分。对于K部分，确定了接触处空间双粒子分布函数的积分，并使用直接相关函数和密度泛函理论近似估计了α部分。在这项工作中确定了所有三个部分，从而能够严格评估RET对固体系统的准确性。结果发现，在热导率方面，RET的预测与MD结果非常吻合。此外，对于剪切黏度，在整个固相范围内的一致性相当好，但对于固相中的其余三个黏度，一致性要差得多。
