Selforganization of magnetic colloids in ferrofluid layers with oscillating magnetic fields:

Nonmagnetic microspheres in a ferrofluid layer acquire a magnetic moment opposite to the amount of ferrofluid they displace when placed in an external magnetic field, and these "magnetic holes" interact then as dipoles. With a constant normal field and a quickly oscillating in-plane one, particles can be led to equilibrium configurations which can correspond to contact, to a finite separation between them, or to a neverending repulsion. This separation can be tuned at will via the geometry of the applied field (as the ratio of normal over inplane magnitudes, or the possible eccentricity of the inplane field to create anisotropic interactions), which practically enables to manipulate large objects placed in ferrofluid layers. Such systems exhibit many phases, extensively studied experimentally at the I.F.E., Kjeller, Norway - a few of typical selforganized states  are displayed below.

The effective interactions of these microspheres in these compound fields are analytically derived  - the susceptibility contrast at the system boundary is essentially responsible for the nontrivial character of those interactions.  Such interactions should be relevant for any colloidal suspension of electrically or magnetically polarizable particles, constrained in layers with important permittivity/permeability contrast along the boundaries.

This enables to classify the possible states of populations of particles (see above figures)- i.e. to derive the phase diagram of the system as a function of the field parameters (at least 10 phases in eccentric inplane fields). This leads also to undertsand and simulate transient phenomena,  as the aggregation dynamics of clusters of large particles, and to understand the fluctuations of chains of small particles under the effect of brownian motion in the carrier ferrofluid. 


These systems present rich enough interaction potentials to have numerous potential applications: controlled manipulation of micrometric objects in ferrofluids via the imposed fields, with potential application to biomedicine, or design of fluids with magnetically or electrically controlled viscosity. On a more fundamental point of view, they may serve as analog model for a broad range of systems in bio- and geo-physics: for example, in regimes where particles organize in long chains, they can be used to model the dynamics of single long proteins under the effect of brownian motion in the embedding fluid, and the aggregation dynamics of populations of those. In other isotropic regimes where they organize in triangular crystals with tunable-at-will equilibrium distances, they can also be used as analog models for hydrofracture of cohesive granular media under the effect of volumic fluid sources: when the separation distance is suddenly decreased, those crystals fragment due to the pressure built-up induced by the expulsion of the embedding fluid, analog of situations where a fluid is homogeneously produced in the intersticial volume of a solid cohesive matrix.

  To read more on the basic theory and experiments, see: Toussaint, R., J. Akselvoll, G. Helgesen, A.T. Skjeltorp and E.G. Flekk°y: Interaction model for magnetic holes in a ferrofluid layer, submitted to Physical Review E. click for a preprint.

About the nonlinear dynamics of particle chains in slow frequency rotating fields, see also the web page on

Particles dynamics and braids.