A STRONG INTERACTION THEORY FOR THE CREEPING MOTION OF A SPHERE BETWEEN PLANE PARALLEL BOUNDARIES .2. PARALLEL MOTION
A STRONG INTERACTION THEORY FOR THE CREEPING MOTION OF A SPHERE BETWEEN PLANE PARALLEL BOUNDARIES .2. PARALLEL MOTION
复制标题
DOI：
10.1017/s0022112080000882
复制
发表时间：
1980-01-01
影响因子：
3.7
通讯作者：
WEINBAUM, S
中科院分区：
文献类型：
--
作者：
GANATOS, P;PFEFFER, R;WEINBAUM, S
在以下条件下，提出了两个平面平行壁之间任意尺寸和位置的球体的三维蠕动运动的精确解：（a）平行于两个静止壁的纯平移，（b）绕平行于壁的轴的纯旋转，（c）由边界之一的运动引起的经过刚性保持球体的库埃特流，以及（d）经过通道中刚性保持球体的二维泊肃叶流。结合的解析和数值求解程序是 Ganatos、Pfeffer 和 Weinbaum (1978) 开发的三维边界配置理论有界流的首次应用。通过与 Goldman、Cox 和 Brenner (1967a, b) 的精确双极坐标解进行详细比较来测试求解技术的准确性，该解针对平行于单个平面壁平移、邻近壁旋转或存在剪切场的球体上的阻力和扭矩。在所有情况下，聚合配置解与所有测试间距的精确解完全一致。新的搭配解决方案还用于使用反射技术的方法来测试现有解决方案的准确性，该解决方案用于平行于两个墙壁的球体运动。 Ho 和 Leal (1974) 的一阶反射理论与当前球体距两壁半径为 5 个或更多半径时的阻力结果提供了合理的一致性。在更近的间距下，一阶反射理论非常不准确，并且对于大范围的球体位置预测球体上的扭矩的方向是错误的。与Faxen(1923)经典高阶反射解法的比较表明，当球心距离任一边界小于两个半径时，多重反射级数解的收敛性很差。流体速度场也得到了解。这些解决方案表明，对于某些壁间距和颗粒位置，会在球体附近形成闭合流线的分离区域，从而反转作用在平移球体上的扭矩方向。
Exact solutions are presented for the three-dimensional creeping motion of a sphere of arbitrary size and position between two plane parallel walls for the following conditions: (a) pure translation parallel to two stationary walls, (b) pure rotation about an axis parallel to the walls, (c) Couette flow past a rigidly held sphere induced by the motion of one of the boundaries and (d) two-dimensional Poiseuille flow past a rigidly held sphere in a channel. The combined analytic and numerical solution procedure is the first application for bounded flow of the three-dimensional boundary collocation theory developed in Ganatos, Pfeffer & Weinbaum (1978). The accuracy of the solution technique is tested by detailed comparison with the exact bipolar co-ordinate solutions of Goldman, Cox & Brenner (1967a, b) for the drag and torque on a sphere translating parallel to a single plane wall, rotating adjacent to the wall or in the presence of a shear field. In all cases, the converged collocation solutions are in perfect agreement with the exact solutions for all spacings tested. The new collocation solutions have also been used to test the accuracy of existing solutions for the motion of a sphere parallel to two walls using the method of reflexions technique. The first-order reflexion theory of Ho & Leal (1974) provides reasonable agreement with the present results for the drag when the sphere is five or more radii from both walls. At closer spacings first-order reflexion theory is highly inaccurate and predicts an erroneous direction for the torque on the sphere for a wide range of sphere positions. Comparison with the classical higher-order method of reflexions solutions of Faxen (1923) reveals that the convergence of the multiple reflexion series solution is poor when the sphere centre is less than two radii from either boundary.Solutions have also been obtained for the fluid velocity field. These solutions show that, for certain wall spacings and particle positions, a separated region of closed streamlines forms adjacent to the sphere which reverses the direction of the torque acting on a translating sphere.