Steady solutions to the problem of a ball dynamics in a Stokes–Poiseuille flow

The existence is proved of steady solutions to the problem of motion of a rigid ball in a cylindrical pipe filled with a viscous incompressible fluid. The cross section of the pipe has an arbitrary form and the fluid flow is governed by the Stokes equations. At infinity, the velocity profile tends to that of the Poiseuille flow. It is established that a steady solution exists for an arbitrary position of the ball in the pipe. The ball performs a rectilinear motion along the generators of the pipe, and the linear and angular velocities depend on the position of the ball center in the cross section of the cylinder. © 2015, Pleiades Publishing, Ltd.