流体动力相互作用的乌藨子模型再访。I.球面和哑铃的周期排列
The Raspberry Model for Hydrodynamic Interactions Revisited. I. Periodic Arrays of Spheres and Dumbbells
摘要：
所谓的“乌藨子”模型是指用于模拟胶体颗粒悬浮液动力学的混合格子-玻尔兹曼和朗之万分子动力学方案，最初由[V. Lobaskin和B. Dünweg，New J.Phys.6，54（2004）]，其中离散表面点用于实现流体-颗粒耦合。该技术已被用于许多胶体行为的模拟研究。然而，在使用这种模式方面存在一些基本问题。在本文中，我们研究的准确性与树莓方法是能够重现斯托克斯水平的流体动力学相互作用相比，在简单的立方晶体中的固体球体的解析表达式。为此，我们考虑传统上用于建立这些属性的数值实验的质量，我们讨论了它们的缺点。我们发现，有一个简单的树莓模型复制的平移和旋转的流动性之间的差异，并提出了一种方法来解决这个问题，通过增加内部耦合点。最后，我们研究了一个非凸的形状，即一个胶体哑铃，并表明，填充乌藨子模型复制所需的流体动力学行为在散装这个更复杂的形状。我们的研究在[J. de Graaf，et al.，J. Chem.Phys.143，084107（2015）]，其中我们考虑了两个平行板的限制几何形状中的乌藨子模型。
英文摘要：
The so-called 'raspberry' model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by [V. Lobaskin and B. Dünweg, New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy the problem by adding internal coupling points. Finally, we examine a non-convex shape, namely a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in [J. de Graaf, et al., J. Chem. Phys. 143, 084107 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.
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