Concentration instability of sedimenting spheres in a second-order fluid
Concentration instability of sedimenting spheres in a second-order fluid
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DOI：
10.1063/1.4733700
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发表时间：
2012-07
影响因子：
4.6
通讯作者：
R. Vishnampet;D. Saintillan
中科院分区：
文献类型：
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作者：
R. Vishnampet;D. Saintillan
用理论和数值模拟方法研究了二阶流体中球形颗粒稀悬液的缓慢沉降。我们首先分析了一个孤立的球形颗粒在重力作用下在线性流场中的运动。在弱粘弹性极限（低底波拉数）下，计算了颗粒的速度，表明沉降运动与局部流场的非线性耦合导致了垂直于重力方向的侧向漂移。通过同样的效果，在流体动力学相互作用的颗粒的大规模悬浮液中，由弱水平密度波动驱动的平均流动也会导致水平漂移，这具有加强波动的效果，正如我们使用线性稳定性分析所证明的那样。基于这一机制，最初均匀的悬浮液预计会出现浓度波动，这一预测得到了先前在聚合物中的沉降实验的支持。
The slow sedimentation of a dilute suspension of spherical particles in a second-order fluid is investigated using theory and numerical simulations. We first analyze the motion of a single isolated spherical particle sedimenting under gravity when placed in a linear flow field. In the limit of weak viscoelasticity (low Deborah number), the velocity of the particle is calculated, and the nonlinear coupling of the settling motion with the local flow field is shown to result in a lateral drift in a direction perpendicular to gravity. By the same effect, the mean flow driven by weak horizontal density fluctuations in a large-scale suspension of hydrodynamically interacting particles will also result in a horizontal drift, which has the effect of reinforcing the fluctuations as we demonstrate using a linear stability analysis. Based on this mechanism, an initially homogeneous suspension is expected to develop concentration fluctuations, a prediction supported by previous experiments on sedimentation in polymer...