Cates M E, Desplat J-C, Stansell P, Wagner A J, Stratford K, Adhikari R, Pagonabarraga I
School of Physics, University of Edinburgh, UK.
Philos Trans A Math Phys Eng Sci. 2005 Aug 15;363(1833):1917-35. doi: 10.1098/rsta.2005.1619.
We describe some scaling issues that arise when using lattice Boltzmann (LB) methods to simulate binary fluid mixtures--both in the presence and absence of colloidal particles. Two types of scaling problem arise: physical and computational. Physical scaling concerns how to relate simulation parameters to those of the real world. To do this effectively requires careful physics, because (in common with other methods) LB cannot fully resolve the hierarchy of length, energy and time-scales that arise in typical flows of complex fluids. Care is needed in deciding what physics to resolve and what to leave unresolved, particularly when colloidal particles are present in one or both of two fluid phases. This influences steering of simulation parameters such as fluid viscosity and interfacial tension. When the physics is anisotropic (for example, in systems under shear) careful adaptation of the geometry of the simulation box may be needed; an example of this, relating to our study of the effect of colloidal particles on the Rayleigh-Plateau instability of a fluid cylinder, is described. The second and closely related set of scaling issues are computational in nature: how do you scale-up simulations to very large lattice sizes? The problem is acute for systems undergoing shear flow. Here one requires a set of blockwise co-moving frames to the fluid, each connected to the next by a Lees-Edwards like boundary condition. These matching planes lead to small numerical errors whose cumulative effects can become severe; strategies for minimizing such effects are discussed.
我们描述了在使用格子玻尔兹曼（LB）方法模拟二元流体混合物时出现的一些尺度问题——包括存在和不存在胶体颗粒的情况。出现了两种类型的尺度问题：物理尺度问题和计算尺度问题。物理尺度问题涉及如何将模拟参数与现实世界的参数相关联。要有效地做到这一点需要仔细考虑物理原理，因为（与其他方法一样）LB 无法完全解析复杂流体典型流动中出现的长度、能量和时间尺度的层次结构。在决定解析哪些物理过程以及哪些不解析时需要谨慎，特别是当胶体颗粒存在于两种流体相中的一种或两种中时。这会影响诸如流体粘度和界面张力等模拟参数的控制。当物理过程是各向异性时（例如，在剪切作用下的系统中），可能需要仔细调整模拟盒的几何形状；本文描述了一个与此相关的例子，它与我们对胶体颗粒对流体圆柱体瑞利 - 普拉托不稳定性影响的研究有关。第二组且密切相关的尺度问题本质上是计算性的：如何将模拟扩展到非常大的晶格尺寸？对于经历剪切流的系统，这个问题很尖锐。在这里，需要为流体设置一组逐块共同移动的框架，每个框架通过类似李斯 - 爱德华兹的边界条件与下一个框架相连。这些匹配平面会导致小的数值误差，其累积效应可能会变得很严重；本文讨论了将此类效应最小化的策略。
