Figure 1

(Color online) Tumbling motion of magnetic particles along a magnetic substrate induced by a rotational magnetic field. A cluster composed of magnetic particles on a magnetic substrate rotates following the rotation of the magnetic field. When the frictional force acting between the particle and the substrate is sufficiently large, the cluster moves along the substrate surface.Reuse & Permissions

Figure 2

(Color online) Dynamics of a cluster composed of two paramagnetic particles obtained by the Stokesian dynamics method. The coefficient of dynamic friction, ${\eta }_s$, is 0.5. (a)–(c) show the trajectories of each particle: (a) $k_s=1.0\times {10}^{-2}$, $\mathrm{Ma}=1.0\times {10}^{-3}$; (b) $k_s=1.0\times {10}^{-2}$, $\mathrm{Ma}=1.7\times {10}^{-2}$; (c) $k_s=6.0\times {10}^{-4}$, $\mathrm{Ma}=1.0\times {10}^{-3}$. The magnetic field rotates in a counterclockwise direction and the clusters are moved from right to left. The snapshots in each figure from the right correspond to the 0th, 1.25th, and 2.5th cycles of the rotational magnetic field. (d) shows the isolines of the translational displacement $L$ of the cluster during one cycle of the magnetic field, which is normalized by that in the most efficient case $\left(2d\right)$, as a function of $k_s$ and Ma. $L=◼0.2$; ● 0.4; ▲ 0.6; ◆ 0.8. The solid lines are guides for the eye.Reuse & Permissions

Figure 3

(Color online) Experimental system. (a) Manipulation test cell. A magnetic film is sandwiched between two glass plates. Solution, in which magnetic particles are dispersed, is introduced into the test cell and particles are manipulated along the peripheral surface of the magnetic film. (b) Whole system. The test cell is placed on a horizontal plate surrounded by two pairs of coils. A rotational magnetic field is generated by the two pairs of coils, two function generators, and two amplifiers. The dynamics of the particles are recorded on both the hard disk of a computer and videotape.Reuse & Permissions

Figure 4

(Color online) Tumbling motions of microparticles in rotational magnetic fields. The intensity of the magnetic field, which is rotated in a counterclockwise direction, is $12.7\mathrm{kA}∕\mathrm{m}$. (a) Movement of a chain cluster composed of two paramagnetic particles. The diameter and magnetic susceptibility of each particle are $2.8\mu \mathrm{m}$ and $2.2\times {10}^{-7}\mathrm{H}∕\mathrm{m}$. The magnetic susceptibility of the substrate is $2.2\times {10}^{-8}\mathrm{H}∕\mathrm{m}$. The frequency of the field is $1\mathrm{Hz}$. The trajectories of the two particles are drawn and the snapshots from the right correspond to the 0th, 1.8th, and 4.0th cycles of the rotational magnetic field. The scale bar represents $10\mu \mathrm{m}$. (b) Movement of a chain cluster composed of five paramagnetic particles. The frequency of the field is $1\mathrm{Hz}$. The trajectories of the particles at the tip of the cluster are drawn and the snapshots from the right correspond to the 0th, 1.8th, and 4.0th cycles of the rotational magnetic field. The scale bar represents $10\mu \mathrm{m}$. (c) Movement of nonmagnetic polystyrene particles along a nonmagnetic polystyrene substrate. The diameter of each particle is $6.0\mu \mathrm{m}$. The particles are dispersed in a magnetic fluid. The susceptibility of the fluid is $1.2\times {10}^{-7}\mathrm{H}∕\mathrm{m}$. The frequency of the field is $0.1\mathrm{Hz}$. The trajectories of the two particles are drawn and the snapshots from the right correspond to the 0th, 2.3th, and 4.0th cycles of the rotational magnetic field. The scale bar represents $10\mu \mathrm{m}$.Reuse & Permissions

Figure 5

(Color online) Manipulations of a carbon nanotube and a red blood cell. The intensity of the rotational magnetic field is $12.7\mathrm{kA}∕\mathrm{m}$. (a) Movement of an iron-containing multiwalled carbon nanotube (Fe@CNT) along a magnetic substrate, the magnetic susceptibility of which is $2.6\times {10}^{-5}\mathrm{H}∕\mathrm{m}$. The frequency of the field is $0.5\mathrm{Hz}$. The trajectory of the tip of the Fe@CNT is drawn and the snapshots from the right correspond to the 0th, 1.1th, and 2.0th cycles of the rotational magnetic field. The scale bar represents $5\mu \mathrm{m}$. (b) Movement of a sheep’s red blood cell to which two magnetic particles are attached. The diameter and magnetic dipole moment of each particle in the field are $2.0\mu \mathrm{m}$ and $1.3\times {10}^{-19}\mathrm{Wb}\mathrm{m}$. The magnetic susceptibility of the film is $1.0\times {10}^{-4}\mathrm{H}∕\mathrm{m}$. The frequency of the field is $0.5\mathrm{Hz}$. The trajectories of the two magnetic particles are drawn and the snapshots from the right correspond to the 0th, 1.0th, and 2.1th cycles of the rotational magnetic field. The scale bar represents $5\mu \mathrm{m}$.Reuse & Permissions