Structure Formation in Electromagnetically Driven Granular Media

We report structure formation in submonolayers of magnetic microparticles subjected to periodic electrostatic and magnetic excitations. Depending on the excitation parameters, we observe the formation of a rich variety of structures: clusters, rings, chains, and networks. The dynamics and shapes of the structures are strongly dependent on the amplitude and frequency of the external magnetic field. We find that for pure ac magnetic driving the low-frequency magnetic excitation favors compact clusters, whereas high frequency driving favors chains and netlike structures. An abrupt phase transition from chains to a network phase was observed for a high density of particles.

Figure 1

Schematic view of the experimental setup.

Figure 2

Phase diagram for $90\mu \mathrm{m}$ nickel particles in the air-filled cell. Magnetic and electric fields are scaled by the saturation field $H_{\mathrm{sat}}$ and the first critical field $E_1(H=0)$, respectively.

Figure 3

Rescaled cluster area vs time at 0 Oe (a) and 10 Oe (b) magnetic fields. Solid lines represent simple functional dependence (1) for different characteristic growth times $\tau$.

Figure 4

Top panels: Structures formed in an external ac magnetic field: rings, compact clusters, and chains of dipoles. Bottom panels: Patterns formed by nickel spheres (5.3% of the surface monolayer coverage) under magnetic driving at 20 Hz (clustered phase), 50 Hz (netlike structure), and 100 Hz (chains phase).

Figure 5

Saturated chain length vs frequency of applied 15 Oe ac magnetic field for different amounts of nickel $90\mu \mathrm{m}$ particles in the cell. Solid lines are the fits to the expression $y=A+B/(x-f_0)$. Inset: Saturated chain length vs applied ac (100 Hz) electric voltage amplitude for a magnetically driven ($H_{\max }=15\mathrm{Oe}$; $f=25\mathrm{Hz}$) system ($\varphi \simeq 0.10$).