22
1 Polar Flocks
rollers exhibit complex dynamics characterized by spontaneous direction reversals.
Different modes of their behavior are shown in Fig. 1.18b. The diagram is not easy to
read. The field intensity H 0 increases along the ordinate, but the frequency ω = 2π f
enters both dimensionless numbers, which also contain the magnetic moment of
the particle μ, its moment of inertia I proportional to its mass and squared radius,
and the rotational drag coefficient α r , proportional to its volume and the viscosity
of the surrounding fluid. Therefore the line H 0 = const at changing frequency, such
as the sequence of dots corresponding to the collective regimes in Fig. 1.18c–f, is
parabolic.
As the frequency of the magnetic field increases, going down the sequence of
dots on the left in Fig. 1.18b, the observed dynamics evolves from a disordered gas
to flocking to coherent vortical motion and back to reentrant flocking (Fig. 1.18c–f).
Interactions of dipolar particles depend on their mutual orientation, and the onset of
large-scale collective behavior is caused by increasing coherence through synchronization of particle orientations by the applied magnetic field. In the gas phase, the
particles move randomly. Their orientations with respect to the field are uncorrelated,
and the angle distribution is almost uniform. With the onset of flocking, all particle
orientation angles converge to two well-separated narrow bands, with spontaneous
reversals between the two directions. The directions become stationary and fully
correlated in the vortex phase. High-frequency flocking is a noise-activated process
when individual particles remain oriented along the field direction.
It should be noted that experiments with both Quincke and magnetic rollers have
been carried out within a fluid medium, but the prevailing interactions are determined
here by the driving field rather than hydrodynamics, so these systems can be still
classified as “dry”. Yet, the observed dynamics, especially in the magnetic system,
is more variegated than anything encountered earlier in this chapter, and gives a
foretaste of the genuine “wet” physics of colloidal systems in Sect. 3.
1 Polar Flocks
rollers exhibit complex dynamics characterized by spontaneous direction reversals.
Different modes of their behavior are shown in Fig. 1.18b. The diagram is not easy to
read. The field intensity H 0 increases along the ordinate, but the frequency ω = 2π f
enters both dimensionless numbers, which also contain the magnetic moment of
the particle μ, its moment of inertia I proportional to its mass and squared radius,
and the rotational drag coefficient α r , proportional to its volume and the viscosity
of the surrounding fluid. Therefore the line H 0 = const at changing frequency, such
as the sequence of dots corresponding to the collective regimes in Fig. 1.18c–f, is
parabolic.
As the frequency of the magnetic field increases, going down the sequence of
dots on the left in Fig. 1.18b, the observed dynamics evolves from a disordered gas
to flocking to coherent vortical motion and back to reentrant flocking (Fig. 1.18c–f).
Interactions of dipolar particles depend on their mutual orientation, and the onset of
large-scale collective behavior is caused by increasing coherence through synchronization of particle orientations by the applied magnetic field. In the gas phase, the
particles move randomly. Their orientations with respect to the field are uncorrelated,
and the angle distribution is almost uniform. With the onset of flocking, all particle
orientation angles converge to two well-separated narrow bands, with spontaneous
reversals between the two directions. The directions become stationary and fully
correlated in the vortex phase. High-frequency flocking is a noise-activated process
when individual particles remain oriented along the field direction.
It should be noted that experiments with both Quincke and magnetic rollers have
been carried out within a fluid medium, but the prevailing interactions are determined
here by the driving field rather than hydrodynamics, so these systems can be still
classified as “dry”. Yet, the observed dynamics, especially in the magnetic system,
is more variegated than anything encountered earlier in this chapter, and gives a
foretaste of the genuine “wet” physics of colloidal systems in Sect. 3.