Fig. 1. (a) illustrates the simplest version of the experimental arrangement used in dynamic self-assembly of rotating magnetic disks. Magnetic force F_m attracts the disks towards the axis of rotation of the magnet, and the vortices these disks create in a surrounding liquid give rise to repulsive, pairwise hydrodynamic forces F_h between them. The graph below the scheme has the profile of the average radial component of the magnetic induction—proportional to the energy of the magnetic field—in the plane of the interface. The photograph in (b) shows an aggregate formed by 37 rotating disks 1.57 mm in diameter. Once organized, this dissipative structure slowly precesses around its center, and is stable for days.

Fig. 2. Complex behaviors in two- and three-dimensional systems of magnetic spinners. (a) shows stable aggregates formed by one large disk (OD 2.07 mm), and N=4 to N=11 smaller disks (OD 1.27 mm); some of the assemblies that form have no elements of symmetry. (b) Pictures in the upper row illustrate the progress of dimerization “reaction” of 10 R plates. The final structures of dimerization reactions of 16 and 17 R plates are shown in the lower row. (c) shows the fusion of two macroscopic “artificial atoms” into an “artificial molecule”. The smaller “atom” is composed of one disk 2.08 mm in diameter, and seven disks 1.27 mm in diameter; the larger atom has one 2.42-mm disk and ten 1.27-mm disks. The “atoms” are initially prepared in two separate energy minima created by field concentrators above the plane of the interface, and are “reacted” by moving the concentrators towards each other. (d) illustrates the effect of the angular velocity ω on the morphology of the 3D dynamic patterns. At low ω (300–500 rpm), the patterns are “staggered” structures. As the rotational speed increases, the interactions between the disks on different interfaces become attractive: the original patterns disappear, and pairs of disks (one from each interface) form. At ω1000 rpm, all disks are oriented in pairs connected by columnar vortices (“eclipsed” structure). (e) illustrates the process of pattern replication using vortex–vortex interactions. In these experiments, magnetically doped squares (2 mm×2 mm×1 mm) were spinning on the PFD/EG-H₂O interface at ω700 rpm, and were used as templates to organize nonmagnetic PDMS rectangles (2 mm×1 mm×1 mm) on the EG-H₂O/air interface into a pattern of squares. The EG layer was 2.5 mm thick. Replication was most efficient when the squares had two of their faces made hydrophobic, so that they were slightly tilted with respect to the PFD/EG interface (schematic graph on the right). The replicated squares remained stable, even when the magnetic field was switched off.

Fig. 3. Examples of fluidic applications based on assemblies of rotating particles. (a) A hydrodynamic membrane composed of 13 1 mm magnetic disks and sorting polymeric microspheres floating at the interface according to their size. (b) (i) shows 19 electromagnets (200 coils each, 0.5 A per electromagnet) used in the carrousel system. Seven gears organize above these electromagnets to manipulate nonmagnetic containers floating at the interface. The carousel first incorporates an empty container (ii), turns it around (iii) until the filling point (iv), completes the revolution (v), expels the filled container (vi), and finally returns to its initial state. The motions of the carrousel are caused by synchronous activation of the electromagnets: When the carousel opens or closes, three electromagnets are simultaneously turned on; when the carousel rotates, six electromagnets are activated at a time. (c) Microfluidic mixer. The upper two pictures illustrate aggregation of magnetic particles from initially uniform dispersion in the fluid into needle-like aggregates above the concentrators. Each needle rotates with angular velocity ω equal to that of the external rotating magnet. Several needles form over large concentrators; smaller concentrators (<50 μm) have exactly one, conical needle above each concentrator (middle picture). An optical micrograph of an array of micromixers in an oval-shaped chamber achieves an almost complete mixing of laminarly in-flowing fluids.

Table 1. Interactions and effects that can be used to synthesize new types of complex systems