Stress moments of nearly touching spheres in low Reynolds number flow
Stress moments of nearly touching spheres in low Reynolds number flow
复制标题
低雷诺数流动中近接触球体的应力矩
DOI：
10.1007/bf00945124
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
D. J. Jeffrey
中科院分区：
文献类型：
--
作者：
R. Corless;D. J. Jeffrey
如果两个球体几乎接触，并且它们周围的流动由Stokes方程控制，则表面应力的积分矩是差距宽度的奇异函数。以前用于计算零阶矩（力）和反对称一阶矩（力偶）的奇异项的方法在这里被推广到计算垂直于中心线运动的对称一阶矩（应力波）的奇异项。它表明，互易定理需要新发现的奇异性和以前发现的意想不到的关系。它还表明，奇异项可以用来提高收敛速度的级数表达式的应力。然后，级数表达式对球体的所有分离都有效。
If two spheres are nearly touching, and the flow around them is governed by the Stokes equations, the integral moments of the surface stress are singular functions of the gap width. The method used previously to calculate the singular terms in the zeroth moment (the force) and the antisymmetric first moment (the couple) is extended here to calculate the singular terms in the symmetric first moment (the stresslet) for motions perpendicular to the line of centres. It is shown that the reciprocal theorem requires unexpected relations between the newly found singularities and ones found previously. It is also shown that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets. The series expressions then become valid for all separations of the spheres.