Three dimensional slow viscous flow due to the motion of a sphere moving perpendicularly to the axis of a circular cylinder

Abstract

Slow viscous flow due to the arbitrary translational motion of a small sphere in an infinitely long circular cylindrical fluid container is considered theoretically on the basis of the Stokes approximation. An analytical expression for the drag is obtained within the first order effect of the presence of a cylindrical wall. Numerical computation shows that the drag for radial and azimuthal motions monotonically increase as the distance of the sphere from the cylinder axis increases while that for the axial one is known to have minimum at some intermediate point.