Magnetic micro-droplet in rotating field: numerical simulation and comparison with experiment

Abstract

Magnetic droplets obtained by induced phase separation in a magnetic colloid show a large variety of shapes when exposed to an external field. However, the description of shapes is often limited. Here we formulate an algorithm based on three dimensional boundary-integral equations for strongly magnetic droplets in a high-frequency rotating magnetic field, allowing us to find their figures of equilibrium in three dimensions. The algorithm is justified by a series of comparisons with known analytical results. We compare the calculated equilibrium shapes with experimental observations and find a good agreement. The main features of these observations are the oblate-prolate transition, the flattening of prolate shapes with the increase of magnetic field strength and the formation of star-fish like equilibrium shapes. We show both numerically and in experiments that the magnetic droplet behaviour may be described with a tri-axial ellipsoid approximation. Directions for further research are mentioned, including the dipolar interaction contribution to the surface tension of the magnetic droplets, account for the large viscosity contrast between the magnetic droplet and the surrounding fluid.

Spontaneous order in ensembles of rotating magnetic droplets

“…In this applied rotating field, there is a critical volume ≈ 6 (3.5 ) 3 for the droplets. If the volume of a particular droplet is larger than the droplet flattens out into an oblate shape [8,9] that sucks in and merges with smaller droplets in its immediate vicinity. However, if the droplet volume is below this critical value, they elongate and rotate with the same frequency as the field without coalescing.…”

“…Here 2D rotating crystals of a new kind -ensembles of rotating needle-like magnetic droplets (micron-sized and re-sulting from a phase separation [8]) -are observed and described. The observation parameters are chosen in the region, where according to the sequence of bifurcations of such magnetic droplets, the system is above the transition oblateprolate [8,9]. For densely packed needle-like droplets in a rotating field, the axis ratios resulting from an interplay between the droplet breakup and coalescence have been examined by [10].…”

Swarming of micron-sized hematite cubes in a rotating magnetic field – Experiments

“…Using 100× objective with oil immersion and 0.70× camera mount provides a 130 × 95 m 2 field of view. System in Paris is very similar and is described in [10]. In comparison, it uses 40× objective, but allows to make recordings with a synchronized magnetic field up to 60 Oe and a frame rate up to 60 fps.…”

Perspective: Strong microwave photon-magnon coupling in multiresonant dielectric antennas

“…A rigorous analysis of multiresonant magnetofluidic systems requires complex numerical methods 126 . However, in a first approximation, the sound-driven oscillations of air bubbles in a magnetic fluid can be analysed by considering a simple Rayleigh-Plesset equation 122 .…”