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.1922.0078
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发表时间：
1922-11-01
期刊：
影响因子：
--
通讯作者：
Jeffery, GB
中科院分区：
文献类型：
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作者：
Jeffery, GB
在物理科学和生物科学中，我们经常关注流体或等离子体的性质，其中小颗粒或微粒悬浮在流体中，并被流体的运动携带。颗粒的存在将影响悬浮液的本体性质，特别是其粘度将增加。从这个观点出发，爱因斯坦对这个问题进行了最完整的数学处理，他考虑了球形粒子的情况，并给出了一个简单的粘度增加公式。我们把这项工作推广到椭球形粒子的情况。第二部分的文件是占领与必要的解决方案的运动方程的流体。一个粘性流体的运动问题，由于一个椭球体在平行于它的一个轴的方向上以很小的平移速度移动通过它，已经由Oberbeck解决了，而一个椭球体围绕它的一个轴旋转的相应问题由Edwards解决了。在这两种情况下，运动方程都是通过忽略涉及速度平方的项来近似的。可以看出，后验的，该近似的有效性的条件是，产品的速度的椭圆体由其线性尺寸应小于“运动系数，粘度”的流体相比。因此，对于我们现在的问题，它要么对足够慢的运动，要么对足够小的粒子都是满足的。
In both physical and biological science, we are often concerned with the properties of a fluid, or plasma, in which small particles or corpuscles are suspended and carried about by the motion of the fluid. The presence of the particles will influence the properties of the suspension in bulk, and, in particular, its viscosity will be increased. The most complete mathematical treatment of the problem, from this point of view, has been that given by Einstein, who considered the case of spherical particles and gave a simple formula for the increase in the viscosity. We have extended this work to the case of particles of ellipsoidal shape. The second section of the paper is occupied with the requisite solution of the equations of motion of the fluid. The problem of the motion of a viscous fluid, due to an ellipsoid moving through it with a small velocity of translation in a direction parallel to one of its axes, has been solved by Oberbeck, and the corresponding problem for an ellipsoid rotating about one of its axes by Edwards. In both cases the equations of motion are approximated by neglecting the terms involving the squares of the velocities. It may be seen,a posteriori, that the condition for the validity of this approximation is that the product of the velocity of the ellipsoid by its linear dimensions shall be small compared with the “kinematic coefficient, of viscosity” of the fluid. In relation to our present problem, it will therefore be satisfied either for sufficiently slow motions,orfor sufficiently small particles.