AN IMPROVED SLENDER-BODY THEORY FOR STOKES-FLOW
AN IMPROVED SLENDER-BODY THEORY FOR STOKES-FLOW
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DOI：
10.1017/s0022112080000687
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发表时间：
1980-01-01
影响因子：
3.7
通讯作者：
JOHNSON, RE
中科院分区：
文献类型：
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作者：
JOHNSON, RE
本研究研究了粘性不可压缩流体中经过具有有限中心线曲率的细长体的流动，没有任何明显的惯性效应。我们考虑具有任意中心线配置、圆形横截面和靠近主体端部近似椭圆形的纵向横截面（即长椭球体端部）的细长主体。使用方便的逐步过程，可以满足物体表面上的无滑移边界条件，使细长参数 (ε) 的阶数比以前更高。事实上，通过在身体中心线上分布适当的斯托克斯、势双峰、旋转、源、应力和四极，可以满足误差项为 O(ε2) 的边界条件。这里使用的方法产生了一个沿整个身体长度（包括末端）有效的积分方程，其解决定了斯托克斯雷强度或相当于每单位长度的力，最高可达 O(ε2) 项。还发现了对斯托克斯雷强度的 O(ε2) 校正。该理论用于检查部分环面和有限长度螺旋的运动。对于螺旋体，使用 Gray & Hancock 和 Lighthill 的力系数对本理论和阻力理论进行了比较。对于所考虑的运动，格雷和汉考克力系数通常会低估每单位长度的力，而莱特希尔系数提供了良好的一致性，除了身体末端附近。
The present study examines the flow past slender bodies possessing finite centre-line curvature in a viscous, incompressible fluid without any appreciable inertia effects. We consider slender bodies having arbitrary centre-line configurations, circular transverse cross-sections, and longitudinal cross-sections which are approximately elliptic close to the body ends (i.e. prolate-spheroidal body ends). The no-slip boundary condition on the body surface is satisfied, using a convenient stepwise procedure, to higher orders in the slenderness parameter (ε) than has previously been possible. In fact, the boundary condition is satisfied up to an error term of O(ε2) by distributing appropriate stokeslets, potential doublets, rotlets, sources, stresslets and quadrupoles on the body centre-line. The methods used here produce an integral equation valid along the entire body length, including the ends, whose solution determines the stokeslet strength or equivalently the force per unit length up to a term of O(ε2). The O(ε2) correction to the stokeslet strength is also found. The theory is used to examine the motion of a partial torus and a helix of finite length. For helical bodies comparisons are made between the present theory and the resistive-force theory using the force coefficients of Gray & Hancock and Lighthill. For the motion considered the Gray & Hancock force coefficients generally underestimate the force per unit length, whereas Lighthill's coefficients provide good agreement except in the vicinity of the body ends.