2.3 Vibrated Granular Layers
29
2.3 Vibrated Granular Layers
Experiments with rod-like particles, definitely dry ones, have been carried out in
a vertically vibrated granular layer. This is a venerated device in which the first
non-equilibrium patterns were observed by Faraday (1831). The activity of inanimate matter is facilitated in this setting by external forcing. There is no directed
motion here, but when grains have an elongated shape with nematic symmetry, they
spontaneously align while forming patterns in the plane of the vibrating layer.
However, unlike thin layers of passive nematic liquids, the alignment of elongated
particles in a single dense layer is three- rather than two-dimensional. Blair et al
(2003) observed, alongside a variety of patterns (Fig. 2.7a), spontaneously formed
moving ordered domains of slightly inclined nearly vertical rods on the background
of immobile horizontal rods. The ordered domains coarsened with time to form large
vortices slowly rotating in the direction of the tilt (Fig. 2.7b). Since no motion was
observed in a horizontally vibrated layer, the experimentalists tentatively attributed
this remarkable breaking of chiral symmetry to the interactions of inclined rods with
the bottom of the vertically vibrated container.
The model by Aranson and Tsimring (2003) fitting these observations included
the momentum conservation equation with dissipation caused by friction rather than
viscosity, and the particle density conservation equation with the velocity directed
along the local tilt of the rods. If they had stopped at these two equations, it would
have been a model similar to that of Toner and Tu. However, they were not satisfied
with the simplistic assumption identifying the alignment with velocity, but closed
the description by adding the equation for the evolution of the tilt. The form of this
Fig. 2.7 (a) Examples of patterns in a vibrated layer of granular rods. (b) Snapshots of the
development of a vortex from an initial random state, showing the formation and coarsening of
domains of vertical rods (Blair et al, 2003)
29
2.3 Vibrated Granular Layers
Experiments with rod-like particles, definitely dry ones, have been carried out in
a vertically vibrated granular layer. This is a venerated device in which the first
non-equilibrium patterns were observed by Faraday (1831). The activity of inanimate matter is facilitated in this setting by external forcing. There is no directed
motion here, but when grains have an elongated shape with nematic symmetry, they
spontaneously align while forming patterns in the plane of the vibrating layer.
However, unlike thin layers of passive nematic liquids, the alignment of elongated
particles in a single dense layer is three- rather than two-dimensional. Blair et al
(2003) observed, alongside a variety of patterns (Fig. 2.7a), spontaneously formed
moving ordered domains of slightly inclined nearly vertical rods on the background
of immobile horizontal rods. The ordered domains coarsened with time to form large
vortices slowly rotating in the direction of the tilt (Fig. 2.7b). Since no motion was
observed in a horizontally vibrated layer, the experimentalists tentatively attributed
this remarkable breaking of chiral symmetry to the interactions of inclined rods with
the bottom of the vertically vibrated container.
The model by Aranson and Tsimring (2003) fitting these observations included
the momentum conservation equation with dissipation caused by friction rather than
viscosity, and the particle density conservation equation with the velocity directed
along the local tilt of the rods. If they had stopped at these two equations, it would
have been a model similar to that of Toner and Tu. However, they were not satisfied
with the simplistic assumption identifying the alignment with velocity, but closed
the description by adding the equation for the evolution of the tilt. The form of this
Fig. 2.7 (a) Examples of patterns in a vibrated layer of granular rods. (b) Snapshots of the
development of a vortex from an initial random state, showing the formation and coarsening of
domains of vertical rods (Blair et al, 2003)