Slow Motion of a Small Sphere in a Cylindrical Domain
Hidenori Hasimoto · Journal of the Physical Society of Japan · 1976
A general study is made on the slow motion of a viscous incompressible fluid bounded by cylindrical boundaries. The solution of the Stokes equations of motion is reduced essentially to a simple boundary value problem for three harmonic functions. The correction factor to the force on a small sphere moving in a plane perpendicular to the axis of a circular tube is determined to the first order effect of the boundary. A striking result is that in the vicinity of the axis the force is less than that due to the axial motion.