Aggregation of magnetic holes in a rotating magnetic field

We have experimentally investigated field induced aggregation of nonmagnetic particles confined in a magnetic fluid layer when rotating magnetic fields were applied. After application of a magnetic field rotating in the plane of the fluid layer, the single particles start to form two-dimensional (2D) clusters, like doublets, triangels, and more complex structures. These clusters aggregated again and again to form bigger clusters. During this nonequilibrium process, a broad range of cluster sizes was formed, and the scaling exponents, $z$ and $z'$, of the number of clusters $N(t)\sim t^{z'}$and average cluster size $S(t)\sim t^{z}$ were calculated. The process could be characterized as diffusion limited cluster-cluster aggregation. We have found that all sizes of clusters that occured during an experiment, fall on a single curve as the dynamic scaling theory predicts. Hovewer, the characteristic scaling exponents $z',\: z$ and crossover exponents $\Delta$ were not universal. A particle tracking method was used to find the dependence of the diffusion coefficients $D_{s}$ on cluster size $s$. The cluster motions show features of \textit{\emph{Brownian}} motion. The average diffusion coefficients $<D_{s}>$ depend on the cluster sizes $s$ as a power law $<D_{s}>\propto s^{\gamma}$ where values of $\gamma$ as different as $\gamma=-0.62\pm0.19$ and $\gamma=-2.08\pm0. were found in two of the experiments.