Slow Viscous Flow Due to the Motion of a Sphere on the Axis of a Circular Cone

Slow viscous flow due to an arbitrary translation of a sphere on the axis of a right circular cone is investigated on the basis of the Stokes approximation. Method of reflections is used to obtain the drag on the sphere and the flow field up to the first-order effect of the boundary. It is found that when the sphere translates axially there appears an infinite sequence of eddies near the vertex if the semi-vertical angle of the cone is less than about 81° and that a similar flow pattern appears if the semi-vertical angle is less than 74.5° when the sphere moves in a direction perpendicular to the cone axis.