Padding J T, Louis A A
Department of Chemistry, Cambridge University, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 1):031402. doi: 10.1103/PhysRevE.74.031402. Epub 2006 Sep 8.
We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons-keeping in mind that there is no such thing as a free lunch-that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.
我们详细描述了如何实现一种粗粒度混合分子动力学和随机旋转动力学模拟技术，该技术能够捕捉胶体悬浮液中布朗力和流体动力的综合效应。强调了仔细调整模拟参数以正确解析该问题的多个时间和长度尺度的重要性。我们系统地分析了我们的粗粒化方案如何解析无量纲流体动力学数，例如表示惯性效应重要性的雷诺数Re、表示动量传输是类液体还是类气体的施密特数Sc、测量压缩性效应的马赫数、描述非连续分子效应重要性的克努森数以及描述对流和扩散传输相对效应的佩克莱数。在这些无量纲数处于正确范围内时，许多布朗和流体动力学时间尺度可以合并在一起，以最大限度地提高计算效率，同时仍能正确解析物理相关过程。我们还展示了如何控制一些数值伪像，如有限尺寸效应和溶剂诱导的吸引性耗尽相互作用。当所有这些因素都得到妥善考虑时，测量得到的胶体速度自相关函数以及相关的自扩散系数和摩擦系数与理论计算结果在数量上相匹配。相比之下，这些计算表明，尽管基本的朗之万方程看似简单诱人，但在捕捉胶体体系中速度自相关函数衰减率方面表现得非常糟糕，在短时间内严重低估，在长时间内严重高估。最后，我们详细讨论了如何将我们方法的参数映射到物理系统上，并从中提取更通用的经验教训——要记住没有免费的午餐——这些经验教训可能与其他粗粒化方案（如格子玻尔兹曼或耗散粒子动力学）相关。
