Asymmetric three-dimensional Stokes flows about two fused equal spheres
Asymmetric three-dimensional Stokes flows about two fused equal spheres
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围绕两个融合的等球体的非对称三维斯托克斯流
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
M. Zabarankin
中科院分区：
文献类型：
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作者：
M. Zabarankin
本文在圆环坐标系下，得到了两个等尺寸的刚性球在三维Stokes流中作非对称平移和旋转运动的精确解。首先将问题归结为一类亚纯函数的三围线方程，然后通过一阶Mehler-Fock变换将后者归结为第二类Fredholm积分方程.对于特定的函数类，相应的三轮廓和Fredholm方程的等价性已经建立在解析函数的Riemann边值问题的框架内。作为所获得的解决方案的一个例子，压力已计算在身体的表面上的两个问题，和阻力和扭矩，所经历的身体在不对称的平移和旋转，已被计算为身体的几何参数的函数。
Exact solutions to three-dimensional Stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates. The problems have been reduced to three-contour equations for meromorphic functions from a certain class, and then the latter have been reduced to Fredholm integral equations of the second kind by the Mehler–Fock transform of order 1. For the specified class of functions, the equivalence of the corresponding three-contour and Fredholm equations has been established in the framework of Riemann boundary-value problems for analytic functions. As an illustration for the obtained solutions, the pressure has been calculated at the surface of the body for both problems, and resisting force and torque, experienced by the body in asymmetric translation and rotation, have been computed as functions of a geometrical parameter of the body.