No lateral migration of a single sphere in a uniform tube in Stokes flow

Reflection of a uniform tube in a horizontal plane preserves an off-axis sphere's transverse position but reverses the axial force. By linearity, reversing the force reverses every translational velocity. By reflection symmetry, it preserves the transverse velocity. Thus the transverse velocity is zero. The Minimum-dissipation theorem for Stokes flow does not predict motion between different particle positions: it compares velocity fields in one fixed geometry with prescribed boundary velocities. Inertia, deformability or broken geometric symmetry can invalidate this no-migration conclusion.