arXiv 2004.139442020-04-29physics.flu-dyncond-mat.softphysics.bio-ph

球形蠕动体浓悬浮液的流变学：简单剪切流中的单分子层

Rheology of a concentrated suspension of spherical squirmers: monolayer in simple shear flow

T. Ishikawa, D. R. Brumley, T. J. Pedley

备注：: 24 pages, 13 figures, 1 table

摘要：

一个集中的，垂直单层相同的球形蠕动，这可能是底部重，并受到线性剪切流，模拟计算两种不同的方法：斯托克斯动力学，和润滑理论为基础的方法。惯性可以忽略不计。目的是计算有效剪切粘度，并且在可能的情况下，计算法向应力差作为球体面积分数$ϕ$、蠕动参数$β$的函数（与蠕动者的主动应力波与其游动速度的比率成比例），游动速度与剪切流的典型速度的比率$Sq$，底部重度参数$G_{bh}$，剪切流与水平线形成的角度$α$，以及两个参数，这两个参数定义了在计算上需要的排斥力，以防止当它们的距离小于临界值$εa$时蠕动体重叠，其中$ε$非常小，而$a$是球体半径。斯托克斯动力学方法允许计算$ϕ$值至$0.75$值的流变学量;润滑理论方法可用于计算$ϕ> 0.5$。这项工作的一个主要发现是，尽管有非常不同的假设，两种方法的计算给出重叠的结果作为$ϕ$的函数的粘度范围$0.5 < ϕ< 0.75$。这表明，润滑理论，仅基于近场相互作用，包含了大部分相关的物理，并考虑到更远的粒子比最近的相互作用是不必要的描述占主导地位的物理。

英文摘要：

A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom-heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. Inertia is negligible. The aim is to compute the effective shear viscosity and, where possible, the normal stress differences as functions of the areal fraction of spheres $ϕ$, the squirming parameter $β$ (proportional to the ratio of a squirmer's active stresslet to its swimming speed), the ratio $Sq$ of swimming speed to a typical speed of the shear flow, the bottom-heaviness parameter $G_{bh}$, the angle $α$ that the shear flow makes with the horizontal, and two parameters that define the repulsive force that is required computationally to prevent the squirmers from overlapping when their distance apart is less than a critical value $εa$, where $ε$ is very small and $a$ is the sphere radius. The Stokesian dynamics method allows the rheological quantities to be computed for values of $ϕ$ up to $0.75$; the lubrication-theory method can be used for $ϕ> 0.5$. A major finding of this work is that, despite very different assumptions, the two methods of computation give overlapping results for viscosity as a function of $ϕ$ in the range $0.5 < ϕ< 0.75$. This suggests that lubrication theory, based on near-field interactions alone, contains most of the relevant physics, and that taking account of interactions with more distant particles than the nearest is not essential to describe the dominant physics.

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