Slow Viscous Flow Due to the Motion of a Sphere on the Axis of a Circular Cone
Abstract
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 firstorder 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 semivertical angle of the cone is less than about 81° and that a similar flow pattern appears if the semivertical angle is less than 74.5° when the sphere moves in a direction perpendicular to the cone axis.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 November 1979
 DOI:
 10.1143/JPSJ.47.1670
 Bibcode:
 1979JPSJ...47.1670K
 Keywords:

 Circular Cones;
 Spheres;
 Translational Motion;
 Viscous Flow;
 Vortices;
 Conical Flow;
 Drag;
 Mellin Transforms;
 Fluid Mechanics and Heat Transfer