Model of dynamic self-assembly in ferromagnetic suspensions at liquid interfaces

Pace and patterns of magnetic swimmers in a billiard pool

We experimentally investigate magnetic surface swimmers on water. These objects self-assemble from ferromagnetic microparticles and a nonmagnetic disk. They are floating on the liquid surface due to interface tension and move under the influence of a harmonically oscillating homogeneous magnetic field oriented vertically, which is distinguished by its amplitude and frequency. The speed of the surface swimmers strongly depends on these parameters. The functional dependencies between speed and amplitude and between speed and frequency are investigated by independently varying both control parameters. In the first case, the data obtained are in good agreement with the predicted scaling while there are some deviations in the latter case. Moreover, due to the interplay between the surface bound swimmers and the ascending liquid meniscus at the edge of the experimental vessel, different dynamics can be realized. We observe periodic and quasiperiodic trajectories in a circular vessel and aperiodic trajectories in a vessel shaped like a Bunimovich stadium.

Stability and dynamics of magnetocapillary interactions

Recent experiments have shown that floating ferromagnetic beads, under the influence of an oscillating background magnetic field, can move along a liquid-air interface in a sustained periodic locomotion [Lumay et al., Soft Matter, 2013, 9, 2420]. Dynamic activity arises from a periodically induced dipole-dipole repulsion between the beads acting in concert with capillary attraction. We investigate analytically and numerically the stability and dynamics of this magnetocapillary swimming, and explore other related topics including the steady and periodic equilibrium configurations of two and three beads, and bead collisions. The swimming speed and system stability depend on a dimensionless measure of the relative repulsive and attractive forces which we term the magnetocapillary number. An oscillatory magnetic field may stabilize an otherwise unstable collinear configuration, and striking behaviors are observed in fast transitions to and from locomotory states, offering insight into the behavior and self-assembly of interface-bound micro-particles.

Self-assembly of nanorod motors into geometrically regular multimers and their propulsion by ultrasound

Segmented gold-ruthenium nanorods (300 ± 30 nm in diameter and 2.0 ± 0.2 μm in length) with thin Ni segments at one end assemble into few-particle, geometrically regular dimers, trimers, and higher multimers while levitated in water by ∼4 MHz ultrasound at the midpoint of a cylindrical acoustic cell. The assembly of the nanorods into multimers is controlled by interactions between the ferromagnetic Ni segments. These assemblies are propelled autonomously in fluids by excitation with ∼4 MHz ultrasound and exhibit several distinct modes of motion. Multimer assembly and disassembly are dynamic in the ultrasonic field. The relative numbers of monomers, dimers, trimers, and higher multimers are dependent upon the number density of particles in the fluid and their speed, which is in turn determined by the ultrasonic power applied. The magnetic binding energy of the multimers estimated from their speed-dependent equilibria is in agreement with the calculated strength of the magnetic dipole interactions. These autonomously propelled multimers can also be steered with an external magnetic field and remain intact after removal from the acoustic chamber for SEM imaging.

Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential

We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net repulsive to net attractive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which afterwards travel along the modulated landscape at a constant mean speed. We measure the strength of the attractive force between the moving particles and propose an analytically tractable model that explains the observations and is in quantitative agreement with experiment.