论文标题
球形几何形状中的点扭矩和源引起的stokes流动
Stokes flow due to point torques and sources in a spherical geometry
论文作者
论文摘要
近五十年来，用少数流体动力图像奇点编写的Stokes方程解决方案已成为理论和数值计算中的有用工具。在本文中，我们通过在存在具有无滑动或无应力（无剪切）边界条件的固定球体的情况下得出一般点扭矩和点源来扩展已知解的目录。对于轴对称点扭矩和无滑动球，图像系统简化为单个图像点扭矩，让人联想到静电剂中的等电位球体外部电荷的溶液。通过对称性，由于刚性球形壳内部的轴对称点扭矩，这也给出了溶液的简单表示。在所有其余情况下，可以通过物理直观点和线奇点的集合来描述解决方案。我们的结果将有助于理论建模微晶状体的推进以及该几何形状中远场流体动力相互作用的有效数值实现。
Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of known solutions by deriving the flow expressions due to a general point torque and point source in the presence of a stationary sphere with either a no-slip or a stress-free (no shear) boundary condition. For an axisymmetric point torque and a no-slip sphere the image system simplifies to a single image point torque, reminiscent of the solution for a point charge outside an equipotential sphere in electrostatics. By symmetry, this also gives a simple representation of the solution due to an axisymmetric point torque inside a rigid spherical shell. In all remaining cases, the solution can be described by a collection of physically intuitive point and line singularities. Our results will be useful for the theoretical modelling of the propulsion of microswimmers and efficient numerical implementation of far-field hydrodynamic interactions in this geometry.
