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首页> 外文期刊>Journal of mathematical fluid mechanics >Translational Steady Fall of Symmetric Bodies in a Navier-Stokes Liquid, with Application to Particle Sedimentation
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Translational Steady Fall of Symmetric Bodies in a Navier-Stokes Liquid, with Application to Particle Sedimentation

机译：Navier-Stokes液体中对称物体的平移平稳下降及其在颗粒沉降中的应用

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摘要

Let B be a homogeneous body of revolution around an axis a, with fore-and-aft symmetry. Typical examples are bodies of constant density having the shape of cylinders of circular cross-section, of prolate and oblate spheroids, etc. In this paper we prove that, provided a certain geometric condition is satisfied, the only possible orientations that B can eventually achieve when dropped in a Navier-Stokes fluid under the action of the acceleration of gravity g and at a small and nonzero Reynolds number, is with a either parallel or perpendicular to g. This result is obtained by a rigorous calculation of the torque exerted by the fluid on the body. We also show that the above geometric condition is certainly satisfied if B is a prolate spheroid. Moreover, in this case, we prove, by a "quasi-steady" argument, that, at first order in λ, the configuration with a perpendicular to g is stable to small disorientation, while the other is unstable, in accordance with experiments.
机译：设B为绕轴a前后对称的均匀旋转体。典型的例子是具有圆形横截面的圆柱形状，长圆形和扁球形的等密度的恒密度物体。在本文中，我们证明，只要满足一定的几何条件，B最终可以实现的唯一可能取向当在重力加速度g的作用下以较小且非零的雷诺数落入Navier-Stokes流体时，其与g平行或垂直。通过对流体在人体上施加的扭矩进行严格计算，可以获得该结果。我们还表明，如果B为扁长球体，则上述几何条件肯定得到满足。而且，在这种情况下，根据实验，我们通过“拟稳态”论证证明，在λ的一阶处，垂直于g的构型对于较小的取向差是稳定的，而另一个则不稳定。

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