Secondary flow due to slow rotation of two spheres

Secondary flow in an unbounded viscous medium, due to steady rotation of two equal spheres about their line of centres, is studied at low rotatory Reynolds number based on the sphere radius. The spheres rotate with the same angular velocity and the distance between their centres is sufficiently large compared with either radius. Expressions for the stream function and hydrodynamical forces acting on the spheres are obtained. It is found that the spheres attract each other. The flow structure is discussed qualitatively and the presence of eddies is noted. © 1987 Oxford University Press.