STOKES-FLOW OF A ROTATING SPHERE AROUND THE AXIS OF A CIRCULAR ORIFICE OR A CIRCULAR DISK

This paper presents an infinite series solution to the creeping flow e quations for the axisymmetric motion of a sphere of arbitrary size rot ating in a quiescent fluid around the axis of a circular orifice or a circular disk whose diameters are either larger or smaller than that o f the sphere. Numerical tests of the convergence are passed and the co mparison with the exact solution and other computational results shows an agreement to five significant figures for the torque coefficients in both cases. The torque coefficients are obtained for the sphere loc ated up to a position tangent to the wall plane containing either the orifice or the disk. It is concluded that the torque coefficients of t he sphere and the disk are monotonically increasing with the decrease of the distance from the disk or the orifice plane in both cases.