Coarsening dynamics of ferromagnetic granular networks-experimental results and simulations.

We investigate the phase separation of a shaken mixture of glass and magnetised steel spheres after a sudden quench of the shaker amplitude. After quenching, transient networks of steel spheres emerge in the experiment. For the developing network clusters we estimate the number of spheres in them, and the characteristic path lengths. We find that both quantities follow a log-normal distribution function. Moreover, we study the temporal evolution of the networks. In the sequence of snapshots we observe an initial regime, where the network incubates, followed by a temporal regime where network structures are elongated and broken, and finally a regime where the structures have relaxed to compact clusters of rounded shapes. This phaenomenology resembles the initial, elastic and hydrodynamic regimes observed by H. Tanaka [J. Phys.: Condens. Matter, 2000, 12, R207] during the viscoelastic phase separation for dynamically asymmetric mixtures of polymers. In order to discriminate the three regimes we investigate in the experiment order parameters like the mean number of neighbors and the efficiency of the networks. In order to capture the origin for a viscoelastic phase separation in our granular mixture, we use a simple simulation approach. Not aiming at a quantitative description of the experimental results, we rather use the simulations to define the key interactions in the experimental system. This way, we discover that along with dipolar and steric interactions, there is an effective central attraction between the magnetised spheres that is responsible for the coarsening dynamics. Our simulations show as well three regimes in the evolution of characteristic order parameters.

Retarding the growth of the Rosensweig instability unveils a new scaling regime.

Using a highly viscous magnetic fluid, the dynamics in the aftermath of the Rosensweig instability can be slowed down by more than 2000 times. In this way we expand the regime where the growth rate is predicted to scale linearly with the bifurcation parameter by six orders of magnitude, while this regime is tiny for standard ferrofluids and cannot be resolved experimentally there. We measure the growth of the pattern by means of a two-dimensional imaging technique, and find that the slopes of the growth and decay rates are not the same-a qualitative discrepancy with respect to the theoretical predictions. We solve this discrepancy by taking into account a viscosity which is assumed to be different for the growth and decay. This may be a consequence of the measured shear thinning of the ferrofluid.