We analyze the dynamics of paramagnetic particles on a paramagnetic substrate under a rotational magnetic field. When the paramagnetic particles are subjected to a rotational magnetic field, the rotational plane of which is perpendicular to the substrate surface, the particles form chain clusters caused by the dipole-dipole interaction between the particles and these clusters display a tumbling motion under certain conditions. In this case, the angular momentum of the clusters is converted to a translational one through the force of friction acting between the particles and substrate and, as a result, the clusters move along the surface of the substrate. We analyze the conditions under which the tumbling motion occurs and the dependence of the translational velocity of a cluster on the control parameters by the Stokesian dynamics method. Based on the dynamics of magnetic particles, we propose a method of manipulating nano- and microparticles using a rotational magnetic field. We demonstrate the manipulation of magnetic and nonmagnetic particles, a carbon nanotube, and a biological cell.
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