Stability and dynamics of magnetocapillary interactions

TL;DR

This paper analyzes the stability and dynamics of magnetocapillary interactions in floating ferromagnetic beads, revealing how oscillating magnetic fields influence their configurations and locomotion at liquid interfaces.

Contribution

It provides analytical and numerical insights into the stability, equilibrium states, and transitions of magnetocapillary systems, introducing the magnetocapillary number as a key parameter.

Findings

Magnetic fields can stabilize otherwise unstable bead configurations.

The magnetocapillary number governs system stability and swimming speed.

Transitions between locomotory states exhibit striking behaviors.

Abstract

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.