  The suspended ferromagnetic particles subjected to the gradient and uniform
magnetic fields experience both the translational force generated by the field
gradient and the rotational torque generated by the fields strengths. Although
the uniform field does not contribute to the force, it nevertheless influences
the translational motion of these particles. This occurs because the
translational force depends on the direction of the particle magnetization,
which in turn depends on the fields strengths. To study this influence, a
minimal set of equations describing the coupled translational and rotational
motions of nanosized ferromagnetic particles is introduced and solved in the
low Reynolds number approximation. Trajectory analysis reveals that, depending
on the initial positions of nanoparticles, there exist four regimes of their
directed transport. The intervals of initial positions that correspond to
different dynamical regimes are determined, their dependence on the uniform
magnetic field is established, and strong impact of this field on the directed
transport is demonstrated. The ability and efficiency of the uniform magnetic
field to control the separation of suspended ferromagnetic nanoparticles is
also discussed.
