Rosén Tomas, Kotsubo Yusuke, Aidun Cyrus K, Do-Quang Minh, Lundell Fredrik
KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden.
Wallenberg Wood Science Center, Royal Institute of Technology, SE-100 44 Stockholm, Sweden.
Phys Rev E. 2017 Jul;96(1-1):013109. doi: 10.1103/PhysRevE.96.013109. Epub 2017 Jul 18.
The motion of a single ellipsoidal particle in simple shear flow can provide valuable insights toward understanding suspension flows with nonspherical particles. Previously, extensive studies have been performed on the ellipsoidal particle with rotational symmetry, a so-called spheroid. The nearly prolate ellipsoid (one major and two minor axes of almost equal size) is known to perform quasiperiodic or even chaotic orbits in the absence of inertia. With small particle inertia, the particle is also known to drift toward this irregular motion. However, it is not previously understood what effects from fluid inertia could be, which is of highest importance for particles close to neutral buoyancy. Here, we find that fluid inertia is acting strongly to suppress the chaotic motion and only very weak fluid inertia is sufficient to stabilize a rotation around the middle axis. The mechanism responsible for this transition is believed to be centrifugal forces acting on fluid, which is dragged along with the rotational motion of the particle. With moderate fluid inertia, it is found that nearly prolate triaxial particles behave similarly to the perfectly spheroidal particles. Finally, we also are able to provide predictions about the stable rotational states for the general triaxial ellipsoid in simple shear with weak inertia.
单个椭球形颗粒在简单剪切流中的运动，可为理解含非球形颗粒的悬浮流提供有价值的见解。此前，针对具有旋转对称性的椭球形颗粒（即所谓的球体）已开展了广泛研究。众所周知，在无惯性的情况下，近长椭球体（一个长轴和两个几乎等长的短轴）会执行准周期甚至混沌轨道运动。当颗粒惯性较小时，颗粒也会趋向于这种不规则运动。然而，此前尚不清楚流体惯性会产生何种影响，而这对于接近中性浮力的颗粒最为重要。在此，我们发现流体惯性强烈抑制混沌运动，仅非常微弱的流体惯性就足以稳定围绕中轴的旋转。据信，导致这种转变的机制是作用于流体的离心力，流体随颗粒的旋转运动而被拖动。发现当流体惯性适中时，近长三轴颗粒的行为与完美球体颗粒相似。最后，我们还能够对弱惯性简单剪切中一般三轴椭球体的稳定旋转状态进行预测。
