Mobility of a Small Sphere in a Viscous Fluid Confined in a Rigid Circular Cylinder of Finite Length
Mobility of a Small Sphere in a Viscous Fluid Confined in a Rigid Circular Cylinder of Finite Length
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有限长度刚性圆柱体中粘性流体中小球体的运动性
DOI：
10.1143/jpsj.56.2713
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发表时间：
1987
影响因子：
1.7
通讯作者：
O. Sano
中科院分区：
文献类型：
--
作者：
O. Sano
从理论上研究了圆柱长度有限对小球沿着中心线平移运动的影响。假设占据该区域的流体是粘性和不可压缩的，并且分析基于斯托克斯方程。采用反射法，得到了球所受力的一阶修正。对于较长的圆柱体，只有当球体非常接近端壁时，端部对力的影响才很重要，而对于长度与半径相同数量级的圆柱体，端部和侧壁起着同样重要的作用。在容纳相同量流体体积的圆柱形盒中，对于其长度/直径比约为0.56的圆柱体，中心处的附加阻力变得最小。还显示了流线。
A theoretical study is made on the effect of finiteness of the length of a circular cylinder on the translational motion of a small sphere along its centerline. Fluid occupying that region is assumed viscous and incompressible, and the analysis is based on the Stokes equations. The method of reflections is employed and first-order correction of the force experienced by the sphere is obtained. For longer cylinders, end-effects on the force are important only when the sphere is very close to the endwalls, while for cylinders whose length is the same order of magnitude as its radius, end-and sidewalls play equally significant roles. Among cylindrical boxes containing the same amount of fluid volume, additional resistance force at the center becomes minimum for a cylinder with its length/diameter ratio of about 0.56. Streamlines are also shown.