SLOW VISCOUS MOTION OF A SPHERE PARALLEL TO A PLANE WALL .I. MOTION THROUGH A QUIESCENT FLUID
SLOW VISCOUS MOTION OF A SPHERE PARALLEL TO A PLANE WALL .I. MOTION THROUGH A QUIESCENT FLUID
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DOI：
10.1016/0009-2509(67)80047-2
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发表时间：
1967-01-01
影响因子：
4.7
通讯作者：
BRENNER, H
中科院分区：
文献类型：
--
作者：
GOLDMAN, AJ;COX, RG;BRENNER, H
本文导出了平行于半无限大静止粘性流体平面壁的球体在差距宽度趋于零的极限下的平移和旋转运动的Stokes方程的渐近解。在数值意义上，这些解与奥尼尔[1]和Deanand奥尼尔[2]的精确双极坐标解在修正后者的数值计算后渐近一致。结果被应用到一个球的运动“滚动”下的倾斜平面的重力的影响下。它表明，球体不能在物理接触的墙壁，它的'滑动'，因为它滚下的墙壁。该理论与Carty[3]的实验数据不一致的原因初步归因于空化。
Asymptotic solutions of the Stokes equations are derived for both the translational and rotational motions of a sphere parallel to a plane wall bounding a semi-infinite, quiescent, viscous fluid in the limit where the gap width tends to zero. In a numerical sense these solutions are shown to agree asymptotically with the ‘exact’ bipolar co-ordinate solutions of O'Neill[1] and Deanand O'Neill[2] after correcting the numerical computations of the latter. The results are applied to the motion of a sphere ‘rolling’ down an inclined plane under the influence of gravity. It is demonstrated that the sphere cannot be in physical contact with the wall, and that it ‘slips’ as it rolls down the wall. Failure of the theory to agree with the experimental data of Carty[3] is tentatively attributed to cavitation.