The Motion of Ellipsoidal Particles in a Viscous Fluid
The Motion of Ellipsoidal Particles in a Viscous Fluid
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DOI：
10.1098/rspa.1923.0040
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发表时间：
1923-04
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影响因子：
--
通讯作者：
G. Taylor
中科院分区：
文献类型：
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作者：
G. Taylor
在最近的一篇论文中，G. B。杰弗瑞曾讨论过浸没在运动的粘性流体中的椭球粒子的运动方程。他已经完全解决了这个问题的情况下，球状颗粒沉浸在一个非常粘滞的流体是平行于一个平面的均匀剪切运动。该解表明，运动取决于粒子释放的初始条件。这种运动是周期性的，似乎没有一个粒子使自己的轴处于任何特定方向的倾向。事实上，质点承担了流体的旋转，它的对称轴线描述了一种围绕涡丝方向的椭圆锥，也就是说，围绕垂直于流体运动发生的平面的方向。虽然忽略了运动方程中的惯性项的分析，没有给出轴在任何特定方向上设置自己的任何趋势，杰弗里博士认为，最终轴可能会采取某种特殊的位置，他提出了一个“最小能量“假设，这导致了以下明确的，但未经证明和证实的结果：受这一假设限制的长椭球体，其长轴与涡线平行，因此与流体的不受干扰运动发生的平面垂直。然后，它将与流体一起旋转，而流体将相对于它以稳定的运动移动。
In a recent paper* Dr. G. B. Jeffery has discussed the equations of motion of ellipsoidal particles immersed in a moving viscous fluid. He has solved the problem completely in The case of spheroidal particles immersed in a very viscous fluid which is moving parallel to a plane with a uniform shearing motion. his so1ution shows that the motion depends on the initial conditions of release of the Particle. The motion is periodic, and there appears to be no tendency for a particle to set itself so that its axis 1ies in any Particular direction. The Particle, in fact, takes up the rotation of the fluid, and its axis of symmetry describes a kind of elliptic cone round the direction of the vortex filaments, that is, round the direction which is perpendicular to the plane in which the motion of the fluid takes places. Though the ana1ysis, which neglects the inertia terms in the equations of motion, gives no indication of any tendency for the axis to set itself in any particular direction, Dr. Jeffery considers that ultimate1y the axis would probably adopt some special position, and he puts forward a " minimum energy ” hypothesis, which leads to the following definite, though unproved and unverified, results:— 1. A prolate spheroid, subject to the restriction imposed by this hypothesis, would set itself so that its long axis was Parallel to the vortex lines, and therefore perpendicular to the plane in which this undisturbed motion of the fluid takes places. It would then rotate with the fluid, which would move in steady motion relative to it.