= 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.
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