论文标题
在液体限制的情况下，在圆柱体上的stokes力
Stokes force on a cylinder in the presence of fluid confinement
论文作者
论文摘要
在本说明中，我们介绍了流体在振荡圆柱上施加的力的计算。尽管在几个教科书中处理了类似问题的计算，但在这些教科书中不存在圆柱体的情况。由于经过修改的贝塞尔功能在1851年没有定义，当斯托克斯进行了此计算时，斯托克斯无法以封闭形式表达其结果，但他给出了渐近公式在两个极限$ a \llδ$和$ a \ggΔ$中有效，而$ a $ a $ a $ a $是cinlinder radius and $δ$是visocococious Pristation Pervess。封闭式结果由Stuart在1963年给出。我们回想起了这一计算，我们将Stokes的渐近公式与这些确切的结果进行了比较。使用经过修改的贝塞尔功能，当流体受到半径$ b $共享相同轴的外部气缸限制时，可以计算力：我们审查了以前的出版物，这些出版物已经处理了该问题，并且我们提出了该力量的精确计算，该计算在$Δ/a $中也以$Δ/a $的功能开发，并具有扩展系数的扩展系数，该系数的功能是radio $ $ $ $ $ g a a/b y a a/b y a a/b y a a/b y a a/b a a/b a a/b a a/b a a/b y a a/b a a/b a a/b y a a/b a a/b。
In this note, we present Stokes' calculation of the force exerted by the fluid on an oscillating cylinder. While the calculation of the similar problem in the case of the sphere is treated in several textbooks, the case of the cylinder is absent from these textbooks. Because modified Bessel functions were not defined in 1851 when Stokes made this calculation, Stokes was not able to express his results in closed forms but he gave asymptotic formulas valid in the two limits $a\ll δ$ and $a \gg δ$, where $a$ is the cylinder radius and $δ$ is the viscous penetration depth. The closed form results were given by Stuart in 1963. We recall this calculation and we compare Stokes' asymptotic formulas to these exact results. Using modified Bessel functions, it is possible to calculate the force when the fluid is confined by an external cylinder of radius $b$ sharing the same axis: we review previous publications which have treated this problem and we present an exact calculation of this force which is also developed in powers of $δ/a$, with the expansion coefficients being functions of the ratio $γ= a/b$ of the cylinder radii.
