Self-Assembly of Spinning Magnetic Particles
Figure 1: This shows a schematic view of the experiments, corresponding to the numerical simulations. The particles spin rapidly at the same rate as the large bar magnet, but then precess about the central axis more slowly based on their separation distance.
Here we make a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a plane in a viscous fluid. The particles experience simultaneously a magnetic torque that drives their individual spinning motion, a magnetic attraction toward the center of the domain and flow-induced interactions. A hydrodynamic repulsion balances the centripetal attraction of the magnetized particles and leads to the formation of an aggregate of several particles that rotates with a precession velocity related to the inter-particle distance. This dynamic self-assembly is stable (but not stationary) and the morphology depends on the number of particles. The repulsion force between the particles is shown to be the result of the secondary flow generated by each particle at low but non-zero Reynolds number. Comparisons are made with analogous experiments of spinning disks at a liquid-air interface, where it is found that the variation in the characteristic scales of the aggregate with the rotation rate of individual particles are consistent with the numerical results.
The work is motivated by the experiments reported by Grzybowski et al [Nature 405, 1033-1036, 2000] in which the self-assembling system is composed of millimeter-sized disks floating just beneath a liquid-air interface. These disks are doped with magnetite resulting in magnetized particles with a permanent dipole moment coplanar with the disk. A large permanent bar magnet rotates at a constant angular frequency above the interface in a plane parallel to the interface. The disks spin about their centers at the same rotation rate as the rotating bar magnet in response to the magnetic torque on the disks. The particles experience also a gradient of the mean magnetic field resulting in a centripetal force toward the axis of rotation of the bar magnet. As the disks are rotating in a viscous fluid, they force the formation of a vortex like flow around their surfaces. Complex hydrodynamic interactions between the spinning disks then take place and drive the formation of supraparticle aggregates.
Figure 2: This snapshot and video sequence shows the structure formed by 7 spherical particles initially seeded randomly in a common plane. The arrows show the flow field in the common plane. The rotation Reynolds number is 2. (Eric Climent) |
Figure 3: This video sequence shows 18 particles initially seeded at random forming a stable self-assembled structure. (Eric Climent) |
For further details see: E. Climent, K. Yeo, M.R. Maxey and G.E. Karniadakis, 2006. Dynamic self-assembly of spinning particles. J. Fluids Engin., to appear.