Rheology of a concentrated suspension of spherical squirmers: monolayer in simple shear flow
Rheology of a concentrated suspension of spherical squirmers: monolayer in simple shear flow
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DOI：
10.1017/jfm.2020.885
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发表时间：
2021-03-05
影响因子：
3.7
通讯作者：
Pedley, T. J.
中科院分区：
文献类型：
--
作者：
Ishikawa, T.;Brumley, D. R.;Pedley, T. J.
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）、剪切流与水平方向形成的角度α和两个参数，这两个参数定义了在计算上需要的排斥力，以防止当它们分开的距离小于临界值时蠕动体重叠。斯托克斯动力学方法允许计算φ值高达0.75的流变学量;润滑理论方法可用于φ> 0.5。对于不受重力影响的非底部重的蠕动体，发现有效剪切粘度随φ的增加比惰性球体更快，无论蠕动体是牵引体（β> 0）还是推动体（β < 0）;它也随β变化，尽管变化不大。然而，对于底部重的蠕动器，当G（bh）和α变化时，牵引器和推进器的行为是非常不同的，因为粘度甚至可以下降到低于在高G（bh）下推进器的悬浮流体的粘度。法向应力差对于惰性球体来说很小，对于底部重的蠕动体来说可以变得很大，随着β的增加而增加，并且随着流动方向α从0到π/2的变化而显著变化。一个主要的发现是，尽管有非常不同的假设，这两种计算方法给出了重叠的结果，粘度作为φ的函数，范围为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。
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 phi, the squirming parameter beta (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 alpha 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. The Stokesian dynamics method allows the rheological quantities to be computed for values of phi up to 0.75; the lubrication-theory method can be used for phi > 0.5. For non-bottom-heavy squirmers, which are unaffected by gravity, the effective shear viscosity is found to increase more rapidly with phi than for inert spheres, whether the squirmers are pullers (beta > 0) or pushers (beta < 0); it also varies with beta, although not by very much. However, for bottom-heavy squirmers the behaviour for pullers and pushers as G(bh) and alpha are varied is very different, since the viscosity can fall even below that of the suspending fluid for pushers at high G(bh). The normal stress differences, which are small for inert spheres, can become very large for bottom-heavy squirmers, increasing with beta, and varying dramatically as the orientation alpha of the flow is varied from 0 to pi/2. A major finding is that, despite very different assumptions, the two methods of computation give overlapping results for viscosity as a function of phi in the range 0.5 < phi < 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.