Force and torque formulae for a sphere moving in an axisymmetric stokes flow with finite boundaries: asymmetric stokeslets near a hole in a plane wall

A sphere is allowed to move with three degrees of freedom in an axisymmetric flow field and general formulae, correct to the third power of the sphere's radius, are developed for the Stokes resistance experienced by the sphere. These are shown to depend on the behaviour within the sphere of the reflected velocity fields which arise from the presence of fixed boundaries at finite distances from stokeslets placed at the sphere's center. Application is made to the stagnation flow at a plane. Poiseuille flow and flow past a sphere and some comparisons made with exact formulae. Solutions are given for asymmetrically placed stokeslets near a hole in a plane wall or a disk.