Heyes D M, Pieprzyk S, Brańka A C
Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.
Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland.
J Chem Phys. 2022 Sep 21;157(11):114502. doi: 10.1063/5.0101728.
The bulk viscosity, η, of the hard sphere (HS) fluid is computed by equilibrium and nonequilibrium molecular dynamics (NEMD) simulations, the latter using an adaptation of the time-stepping method for continuous potential systems invented by Hoover et al. [Phys. Rev. A 21, 1756 (1980)], which employs an imposed cyclic density variation on the system by affine scaling of the particle coordinates. The time-stepping method employed for HS is validated against exact event-driven hard sphere methodology for a series of equilibrium quantities over a wide density range, including the pressure, singular parts of the hard sphere viscosities, and the nonsingular parts of the shear viscosity time correlation functions. The time steps used are typically only a little smaller than those employed in continuous potential simulations. Exact pressure tensor fluctuation expressions are derived for the singular (or infinite limiting frequency) equilibrium parts of the viscosities, which were employed in the simulations. The values obtained agree well with the predictions of the Enskog theory for all densities considered. The bulk viscosity obtained by NEMD is shown to be noticeably frequency dependent for densities in excess of ∼0.8, decaying approximately exponentially to the Enskog and equilibrium simulation values at all densities considered for frequencies in excess of ∼5 in hard sphere units. Temperature profiles during the cycle and the effects of strain amplitude on the computed frequency dependent bulk viscosity are presented. The bulk viscosity increases with the maximum density amplitude.
通过平衡分子动力学和非平衡分子动力学（NEMD）模拟计算了硬球（HS）流体的体黏度η，后者采用了胡佛等人[《物理评论A》21, 1756 (1980)]发明的适用于连续势系统的时间步长法的一种变体，该方法通过对粒子坐标进行仿射缩放对系统施加周期性密度变化。针对一系列平衡量，在很宽的密度范围内，将用于HS的时间步长法与精确的事件驱动硬球方法进行了验证，这些平衡量包括压力、硬球黏度的奇异部分以及剪切黏度时间关联函数的非奇异部分。所使用的时间步长通常仅比连续势模拟中使用的时间步长略小一点。推导了黏度奇异（或无限极限频率）平衡部分的精确压力张量涨落表达式，并将其用于模拟中。对于所有考虑的密度，得到的值与恩斯科格理论的预测结果吻合良好。结果表明，对于密度超过约0.8的情况，通过NEMD得到的体黏度明显依赖于频率，在硬球单位下，对于频率超过约5的情况，它大约呈指数衰减至恩斯科格理论值和所有考虑密度下的平衡模拟值。给出了循环过程中的温度分布以及应变幅度对计算得到的频率依赖体黏度的影响。体黏度随最大密度幅度的增加而增大。
